 注目の話題
 ニートだけど結婚したいです…
 旦那の借金
 不倫相手だと思われた
Science,English,and math Ⅱ
燻し銀三（ 55 ♂ Oe38xe ）
19/02/13 18:26(更新日時)
【Science,English,and math Ⅱ】
I'm going to start a new thread from now on. It seems that the description on the book of which title,『トリセツ.カラダ』will be over befere long,so after that I'll express on the math,I hope so.
I've wanted to be a splendid English speaker someday,so I've expressed some of English thread,but I'm afraid I find it hard that my hope comes true,but I won't give up,for it seems that I love English.
There are lots of things which I don't know in the world,so I've wanted to express the unknown world for me as much as I can.
新しいレスの受付は終了しました
 レス絞り込み
 スレ主のみ
【Putting the internal organ away in the body】
《The system of the circulatory organ》
The heart is set at the back of the breastbone. Then main artery starts from the heart. It advances toward the head and it draws a hairpin curve and goes down through the side of the backbone. It branches into the two directions of right and left at the height of the waist and goes to the both of the feet.
The artery which goes to the both arms diverges right and left above the hairpin curve. The artery which goes to the right arm branches into other artery which goes to the head on the way.Renal artery 腎動脈 of left and right starts at the height of the waist. Veins accompany the artreies.
Putting the system of the circulatory organ in the body is over.
《The system of the respiratory organ 呼吸器》
Lungs of which shape is a fan are set at the left and right on the breast. Both of the lungs are connected with tubes called the trachea 気管 at the center of the breast,and the tubes are collected to on …
【Putting the internal organ away in the body】
《The system of the respirarory organ》
The tubes called trachea 気管 are collected to on the back of the heart and become one. The trachea which is next to the gullet 食道 leads to the mouth. Putting the system of the respiratory organ away is over.
《The system of the digestive organs》
Part one,the solid organs. The pancreas 膵臓 and duodenum 十二指腸 are outside the peritoneum 腹膜. The pancreas is in the center of the body. It clings to the back. It looks like a thin pennant. The liver is on the right of the pit on the stomach みぞおち. The liver is at the back of the rib. Its shape is a big inverted triangle.
Part two,the digestive organs. The gullet is through the diaphragm 横隔膜 and is connected with the stomach. The stomach is connected with the duodenum. The duodenum runs around the upper part of the pancreas. Its route looks like the Ushaped type コの字形.
The end of the duodenum is connected with the long small intestine. The large and small …
【Putting the internal organs away in the body】
《The system of the digestive organs》
Part two,the digestive organs. The large and small intestines start at the lower left of the body and are connected with the appendix. The large intestine runs around the outer frame in the stomach. Its route looks like a question mark. The large intestine runs through the rectum 直腸 and reaches the anus.
Part three,the connection between the solid organs and the digestive organs. The bile duct 胆管 starts from the liver and the pancreatic duct begins from the pancreas. The bile duct and the pancreatic one is connected and we call it the common bile duct. It's connected with the duodenum. Putting the digestive organs away is over.
《The system of the urinary organs》
Although when the body is built up,the urinary organs and sexual organs grow together,so we tend to confuse with them,they are different mechanism in regard to each function. The pancreas is outside the peritoneum 腹膜,and it's at the…
【Putting the internal organs away in the body】
《The system of the urinary organs》
The pancreas is at the height of the waist and it's on the both side of right and left of the back. Its size is a fist. The right one is a little lower position because of the kidney. The pancreas is connected with the main artery direct. Its blood vessel is thick.The ureter 尿管 starts from the dent of which size is a broad bean and it's connected with bladder. Putting the urinary system away is over.
《The system of the sex organs》
An ovary and a testis 精巣 is a size of the egg of a quail. The ovary is inside of the body and the testis is outside of the body. When being unborn baby,both of the ovary and testis is inside of the body,but after his birth the testis is outside of the body.
The ovary is connected with the womb through an oviduct 卵管 and the ovum is released in the womb. The sperm is released through a spermaduct and the prostate 前立腺. Its goal is the womb. Both of the ovary and testis…
【Putting away the internal organs away in the body】
《The system of sex organs》
Both the ovary and testis produce hormone as the organs of internal secretion. Putting away the sex organs is over.
《The system of the internal secretion》
All the organs of the internal secretion are the size from an azuki bean to an egg of a quail. It's just that they are connected with the blood vessels,so we have only to recognize each place.
The pituitary gland 脳下垂体 is in the center of the brain stem. Its size is as big as big a soybean.
The thyroid gland 甲状腺 is the organ which clings under the Adam's apple. Its shape looks like a nymphalidae butterfly タテハ蝶
The adrenal gland 副腎 looks like a broad bean in regard to its size and shape. It clings to upper part of the kidney.
I hope you can grasp the whole image of the body. I'm going to express the way of indicating of the illustration of the internal organs in the body from now on.
At first we draw a horizontal line on the body. Its upper part…
【The way of indicating the illustration of the intenanal organs in the body】
Its upper part is the breast and lower part is the body. Its border is the diaphragm 横隔膜. There are ovals both on the right and left of the breast. There are lungs. The left one is a little smaller than the right one.
The right lung is divided into three parts and the left one is done into two parts. There is the heart between the lungs. The left part of the heart is a little bigger than the right part. The heart and the lungs are put in perfectly.
The gullet 食道 runs through from the upper part to the lower part at the back of the heart. It's connected with the stomach.
The heart is divided into the four parts. The duodenum 十二指腸 starts from the stomach. Its shape looks like コ,which is one of Japanese phonetic syllabary カタカナ. The pancreas is put in the dent of the コ.
The small intestine starts from the duodenum and its resembles like a hairpin curve. It stops at the right lower part of the stomach.
【The way of indicating the illustration of the internal organs in the body】
Oh! I've made a mistake! The small intestine stops not at the lower right part of the stomach but at the right abdominal region. The large intestine starts there. We call the place the cecum 盲腸,and the appendix is suspended there.
To be exact the cecum is different from the appendix with regard to the structure of the body. The large intestine has each name in each different place. The place where the small intestine changes into the large intestine. We call it the cecum,and there is the appendix at the tip of the cecum. The appendix is suspended from the cecum as if it were a tail.
We say commonly suffering from the appendicitis 盲腸炎,it's an inflammation 炎症 in the appendix. It doesn't happen in the cecum exactly.
The large intestine runs through along the innner frame of the whole body. It looks like a big ? mark. It starts from the right abdominal region,and runs through right upper,left lower,left …
【The way of indicating the illustration of the internal organs in the body】
Oh! I've made a mistake! The small intestine stops not at the lower right part of the stomach but at the right abdominal region. The large intestine starts there. We call the place the cecum 盲腸,and the appendix is suspended there.
To be exact the cecum is different from the appendix with regard to the structure of the body. The large intestine has each name in each different place. The place where the small intestine changes into the large intestine. We call it the cecum,and there is the appendix at the tip of the cecum. The appendix is suspended from the cecum as if it were a tail.
We say commonly suffering from the appendicitis 盲腸炎,it's an inflammation 炎症 in the appendix. It doesn't happen in the cecum exactly.
The large intestine runs through along the innner frame of the whole body. It looks like a big ? mark. It starts from the right abdominal region,and runs through right upper,left lower,left …
【The way of indicating the illustration of the internal organs in the body】
The ? mark of the large intestine starts from the right abdominal region,and runs through the upper right,upper left,left abdominal region,and reaches the center of the lower part of the body. We call the goal the rectum 直腸.
There is the liver of which shape is a triangle at the right upper part of the body. There is a bag called the gallbladder 胆嚢 under the liver. The liver is in front of the large intestine.
The biliary 胆管 starts from the gallbladder. The pancreatic duct runs through the center of the pancreas. The biliary and the pancreatic duct are connected and we call it the common bile duct 総胆,and the common bile duct leads to the duodenum and there is an opening there.
There are kidneys of which shape are oval next to the small intestine. They are both on the right and left side of the small intestine. There is the bladder 膀胱 at the center of the body. It's connected with both of the kidneys…
【The way of indicating the illustaration of the internal organs in the body】
The bladder is connected with the kidneys of the both sides on the right and left side by the ureter. Sticking the spleen 脾臓 of which shape is oval at the end of the pancreas. In the next,I'm going to start the way of putting away the system of the blood vessels away in the body.
The main artery of which mark is ? starts from the heart to the waist. There are 8 of the artreys branching off from the main artery. Each of them runs through the right hand,left place on the jaw,left hand,right foot,left foot,both kidney of right and left side,and abdominal cavity. 腹腔.The artrey which runs through the right hand and the head,so it forks into two.
The way of the illustration of the internal organs in the body is over,so everyone can illustrate. If trying to do,it'll be actually simple. If repeating to illustrate it,everyone will be surprised,for it will know throughly on the body unconsciously.
【Putting together the functions in the body】
《The nervous system》
What to receive,or what to feel is sent or received with the electrical signal in the nervous system,the center of its role is the central nerves,from the cerebrum 大脳. The net of peripheral nerve 末梢神経 spreads over the whole body from the cerebrum. Its basic unit is connection of nerve cells. We also call the nerve cell neuron.
《The system of blood vessel》
The system of blood vessel delivers necessary materials over the whole body,and collects unnecessary ones. Its center of the role is the heart in the breast. The net of the blood vessel spreads over the whole body from the heart through the order of the artrey,the capillary tube 毛細血管,and the vein.
《The respiratory system 呼吸器系統》
An alveolus 肺胞 is a basic unit in the lung. The oxygen is absorbed in the alveolus. The waste of the carbon dioxide is discharged from the alveolus into the blood at the same time. Its center of the role is the breast and the lung.
【Putting together the functions in the body】
《The system of the digestive organs》
The neutrient is taken in from the mouth as food and and absorbed in the capillary vessels of the mucous membrane 粘膜 of the small intestine through the digestive organs. The nutrient is sent into the liver and stored there. After that it's
delivered all the internal organs with circulation of the blood.
The center of the role is the digestive organs in the abdomen. Water is absorbed in the mucous membrane of the large intestine and sent into the lymph vessel,or the blood vessel.
《The system of the urinary organs》
The waste in the blood is filtered through the glomerule 糸球体. The glomerule is a kind of the capillary vessel,and a part of a basic unit of the kidney called nephron. The waste is abandoned from the bladder as urine.
《The system of sex organs》
Sperm is produced in the testis 精巣 in the body of a male,and the ovum 卵子 is produced in the ovary 卵巣 in the body of a female. The female has the…
【Putting together the functions in the body】
《The system of sex organs》
The women have the womb where a fertilized egg is brought up to be an unborn baby.
《The system of internal secretion》
It's the internal organs which secrete the hormone in the blood. When secreting the hormone,there are the internal organs as target,and the secreting the hormone acts on there alone,it's so to speak,a special order.
《Homeostasis 恒常性》
There is the border between the body and its outside. Taking in necessary things inside the body from the outside and releases unnecessary things outside the body. It's the basic rule. It means that the body wants always to keep a fixed stable situation. For example,the blood pressure is 120,the cardiac rate 80,and the temperature 36.
We call the function which tries to keep the fixed stable situation the maintenance of the homeostasis. If saying it in other words,the body is the system which maintains the homeostasis. The mechanism of the body looks like…
【Homeostasis】
The body looks complicated seemingly,but it's simple actually. Both of the necessary and unnecessary things go in and out through the capillary vessels,of which aim is keeping the stable and fixed situation of the body.
【Medical outline】
《Living and dying》
Living is opposite of dying. Living means breathing,its heart beats,and being able to think something. Being dead is opposite of them. When being dead,no one breathes,its heart stops,and it's unconscious.
Being dead means that both its breath and the beat of the heart stops,and dilatation of the pupil 瞳孔散大. They are the three symptoms of the death. The dilatation of the pupil means losing light reflex 対光反射.
Light makes the diameter of the pupil change. The brighter the light is,the larger the diameter of the pupil becomes. The amount of the light which reaches to the pupil is controlled with the reflex. As a result the retina can adapt itself to various the strength of light. It means that the brain stops …
【Medical outline】
《Living and dying》
In short,the dilation of the pupil means stopping the activity in the brain. Thus both of stopping breathing,and beating the heart,and the dilation of the pupil which is the brain death used to be the three symptom in regard to the death long ago.
However with the development of the medical science,the one could have been dead in the old days isn't dead easily. Even if it stops breathing,an respirator 人工呼吸器 can support its life. In consequence,some people have appeared. They think of the loss of conscious as important element concerned the death. When the one was falls into the situation of the brain death,it means that the one is dead really. It's the conception of the brain death.
There is a reason for the rule of the brain death,for the internal organs of the one who was the brain death is transplanted to others,but there have been other various opinions on the brain death,so the discussion on the brain death has been done both in …
【Medical outline】
《We don't have to be afraid of being dead》
There have been such the other various opinions on the brain death that the discussion on the brain death has gone on both in the academic meeting and the National Assembly.
Everyone is always dead once. No one is immortal. The author of the book said in the book like the next. "I'm sure the duty of the one who is alive is going on living until being dead." He continued like the next.
Even if being able to live a long life,the ones who read this book can't live for 100 years from now on. On the other hand,4,6 billion years have past since the earth was born. We the human beings have appeared on the earth and long years have passed but it's below a billion years.
If comparing it with the human life span which is at most about a century,it's just for an instant,however even if it's for an instant,how elaborate the body of we the human beings are made! Each of our bodies is a precision instrument. If trying to create the…
【Medical outline】
《We don't have to be afraid of being dead》
If trying to create the same things as our bodies,even if its budget is ¥10 billion,it won't be enough,so we're the one who are worth ¥ 10 billion,however even if we take care of ourselves and we do our best,we'll always be dead a hundred years later. Therefore we should live until being dead. It's one of choices.
The author continues. "If coming across the situation in which you are forced to feel like dying,I want you to remember my remarks once. 『We don't have to make a haste so much,for we'll always be dead 100 years later.』There is one more thing. 『If having to face something dangerous,we don't have to do our best,it's just that we have only to run away from it.wwwww.』
《Death and medical science》
The death of myself has nothing to do with me at all,for I myself can never think of it after my death. In short the death is the conception for others who are still alive. The way of dealing with the dead shows an …
【Medical outline】
《Death and medical death》
The way of dealing with the dead shows a basic attitude for the way of handling the others who are still alive. If being dead,its consciousness disappears. Then no one can feel happy,sad,painful,nor hard. In short our death itself doesn't matter at all for us.
We don't have to think of the thing after our death. It's the thing which others do. In fact our death is the business for the others who are still alive. Then do we have to think nothing about the our death? No,for everyone is always dead,so everyone has to think over the universal thing. Then what should we do?
Its answer is that we should think over what to do after others' deaths. It links to the thing which we want others to do after our death.
《If others are dead》
The author said in the book. "I find it important to research the cause of death of the others. Researching the cause of the others means thinking of them as something great. If being aware of the cause of …
【Medical outline】
《If others are dead,what should we do?》
For example,if being aware of cause of the death of a near relative like a grandfather,its relatives will be relieved. If unable to being aware of the reason why he was dead,its relatives' remain being worried about his death. As a result it's important for others who are still alive to research the cause of the death.
《An anatomy》
Researching the cause of the death used to be a good chance for studying from a medical point of view. It had been said that the anatomy was a basis for the medical science from the time of Hippocrates. The general idea hadn't changed until the end of the 21th century.
A phrase that a corpse is an active master for studying the medical science has been said in China too,so as to the anatomy, it's no doubt that learning from the corpse was natural from the standpoint of the medical science in the world.
When doing the anatomy,the corpse is mutilated,its internal organs are taken away from the…
【Medical outline】
《An anatomy》
When doing the anatomy,the corpse is mutilated,its internal organs are taken away from the corpse,and the corpse is damaged extremely. It's a hard work. The anatomy is researching the cause of the death by damaging the corpse. Roughly speaking,there are two reasons for the anatomy.
The anatomy is done so as to be verified that the person wasn't dead unfairly. Then the anatomy is done for the society. The anatomy is done in order to research the cause of the death and to make good use of it for the medical development.
However there are lots of people who hate to being damaged the corpse of the family members,so the anatomy has hardly been done recently in Japan. Considering the situation,if the Japanese society is criticized that it has made light of the medical base,none of us the Japanese can talk back to it.
《Autopsy imaging appears》
To be exact,the phrase that just after being dead researching the cause of the dead is rather fovorable than …
【Medical outline】
《Autopsy imaging appears》
To be exact,the phrase that just after being dead,researching the cause of the death is more favorable rather than the anatomy,for after being death,the corpse always doesn't have to be done the anatomy because of the autopsy imaging.
The anatomy began to decline from the latter part in the 21th century,and the medical science was on the verge of a crisis little by little,but a new technology appeared then,and situation that after being dead,the way of researching the cause of the death has made a rapid progress as general idea because of the autopsy imaging.
The autopsy imaging is the way of diagnosis of the corpse with its image. When being dead,checking up the outward appearance of the corpse was done,and the anatomy was done in the 20th century,but the situation has changed dramatically from the 21th century.
If using the autopsy imaging,without being damaged the corpse,the cause of the death can be researched,so the new technology…
【Medical outline】
《Autopsy imaging appears》
The new technology called the autopsy imaging seems to have changed the society and medical science so much. Instead of the anatomy,without being damaged the corpse,the autopsy imaging can research the cause of the death. The family members' feeling doesn't hurt so much,if comparing it with the anatomy.
However the autopsy imaging isn't always almighty,so it sometimes seems to fail to clarify unclear part of the death,so then the anatomy is forced to be done,but the family members seem to be easy to accept the situation then. By the way an abbreviation of the autopsy imaging is Ai.
《The Ai cooperates with the anatomy and both of them functions smoothly》
The Ai isn't always an examination which expels the anatomy. It's the examination which makes up for the fault of the anatomy,but the Ai is the examination which is done at first easily,so just after being dead when researching the corpse is done,instead of the anatomy,the Ai will be …
【Medical outline】
《The anatomy corporates with the Ai and both of them functions smoothly》
The Ai is the easy examination and is done at first,so just after death,when researching the cause of the death,instead of the anatomy,the Ai will be made use of more and more in the future. On the other hand,the anatomy will display its efficiency as assistant for the Ai from now on.
《The people who object to the Ai》
It is regrettable when something new starts,some people who object to it appear. For example,the people who object to the Ai are government officials. They seem to insist on like the next.
The Ai is such a device for new examination that it costs a lot of money.
By the way,my electric dictionary is suddenly out of order. Its button doesn't function any more,so I'm forced to stop describing. I'm sorry for it.
【Medical outline】
《The people who object to the Ai》
The government officials continue like the next. "Japan is filled with such the debt that we can't spend any money on the device at all" if changing their viewpoint,it seems that they make little of our near relatives' death. They've thought little of us,haven't they?
《Other people who object to the Ai》
There are other people who object to the Ai. They are the one who have been engaged in the autopsy,for example,specialists in the forensic medicine 法医学,or pathologists 病理医学者
The Ai doesn't make anyone understand the cause of the death entirely,so we have to dissect 解剖 the corpse for ourselves. They have insisted on like that,but they are in the wrong.
While there are more than a million of people who are dead in Japan every year,there are no more than 50 thousand people who are dissected. Without being dissected,the cause of death of the great number of people have been set up every year. Therefore,researching the cause of…
【Medical outline】
《Other people who object to the Ai》
Therefore researching the cause of the death with the Ai is vital at least.
The people who are engaged in the autopsy are afraid that their job will decrease,if the Ai is introduced,so they've spread bad things on the Ai,and they've tried to do the Ai for themselves,but what they have done is beside the point.
There are difference between the autopsy and the Ai on the technical skill. They are different as if they were succer and swimming. The insistence of the people who are engaged in the autopsy is as if a swimmer insisted on being a regular player in soccer in what is called J league. They are calling at the wrong house. 御門違い
《There are another people who object to the Ai》
There are another people who object to the Ai. They are the doctors who do diagnosis with the Ai. They hate to do the new job,so they use various excuses and try to avoid the new job,for example,they are busy,they can win little money with the Ai…
【Medical outline】
《There are another people who object to the Ai》
They are busy,they earn little money with the Ai,they can't get help from another,they can't understand how to do it,the Ai isn't their job,etc…they are their excuse to neglect their job. They think they have only to do their job as usual. They are frequently in high position in a learned society.
Without understanding the Ai,some people object to the Ai so much that the Ai has hardly spread in the world. There are lots of obstinate people who are in high position. It's the defect in Japanese society,but residents strongly want the Ai to be introduced into the society,so I want the people in high position to listen humbly to the voice of the residents.
The author of the book said like that.
Roughly speaking,I've finished describing the book of トリセツ.カラダ カラダ地図を描こう. There are a few pages left at the end of the book,but I'm going to omit them. Next time I'm going to express the book on math. I hope I can carry it out.
【Mechanism of number】
《The concept which starts from counting something》
We can imagine easily the concept that math starts from counting something from the historic point of view. When counting apples,oranges,or other things,the concept of the numbers like 1,2,3,is abstracted from the different kinds of things. It's what is called the birth of a natural number.
We've used the numbers without difficulty at present but we the human being would have needed a long history until we got the concept,for there is a big difference between counting something and grasping the number abstractly.
Needless to say the abstract has never been done by the specific person alone. It has been recognized by lots of people through the long history gradually.
When counting apples or oranges,arithmetic operations like addition and subtraction were introduced in the society naturally. How much they can count is aside,small ones in the natural number seemed to be recognized naturally.
【Mechanism of number】
《The concept which starts from counting something》
The concept which starts from the natural number leads to the discovery of zero and introduction of minus number,and integral numbers are 整数 completed. Dividing something into some parts expands to rational numbers. The rational number means the a fractional number of which both denominator 分母 and numerator 分母 are composed with the integral number.
Irrational number which is an answer of a square root 平方根 is added to the rational number,and real number is
completed,but the announcement of the irrational number has been restrained for a while,for some mathematician like Pythagoras found hard that other people accepted the concept of the irrational number.It seemed that they were conscious that the irrational number was something unnatural as its name is indicated.
Imaginary numbers 虚数 are added to the real numbers,and the expansion of the number comes to an end for the time being,but its process …
The expansion of the numerical concept seems to come to an end for the time being,but its distance has never been easy. The numerical concept which we the human being have gained through the long history is the valuable thing which was brought by wisdom of the human being.
【Discovery of zero】
《Being conscious clearly that there is nothing and displaying it. It's significant》
Zero in math means that there is nothing. There is nothing but is there something significant for the existence? Some people may have thought like a simple question,for we've been used to the 『0』so much everyday that we are hardly aware of its benefit unless being asked.
It is said that India is the birthplace of the symbol of zero,0. When looking up a star which is blinking in the night sky,it looks like a dot or a small circle,so the Indian described the star with ・or 0. They called the zero シューニャ in their language. The シューニャalso means the god who created the world in India.
The concept of the シューニャ…
【Discovery of zero】
《Being conscious clearly that there is nothing and displaying it. It's siginificant》
It seems that the conception of zero which means nothing had learned to be described with either of the sign of ・or 0,coupled with the religious reason in India.
There are two significance of existence with regard to the zero. The one is it indicates the situation of nothing. The other is it's useful when dictating its digit for some number like 230.
When describing some number,the decimal classification system or the binary classification system are used. Then the sign of 0 is indispensable.
Some people used to put space where there should be the zero long long ago,but we find it hard to recognize how many number of the zero there are. At first,if the number of the first digit is zero,we aren't sure whether or not there is the space there.
The digits are described with Chinese characters like 一、十、百、千、万、億 in both Japan and China. There are each name for each digit in…
【Discovery of zero】
《Being aware clearly that there is nothing and displaying it. It's important》
There are each name for each digit in each country,but the way of displaying numbers has a limit. The concept of a number like the binary system or decimal system overcomes the limit and then the zero is indispensable.
For example,there is a number 31415906535897932304626. Instead of the Arabic numericals,if trying to display it with Chinese character it's 三百十四垓千五百九十京六千五百三十五兆八千九百七十九億三千二百三十万…
I should display the number in English,but I won't,for I find it complicated,so I'm forced to recognize the zero is indispensable.
When looking around us,we find the place is filled with the zero. For instance,"A start from zero" "Water is frozen at 5 degree centigrade" or "An outoftown telephone call 市外局番 zero"
【The part of minus number】
《If making use of the numbers dynamically,a minus number appears inevitably》
The number is used when counting something,it takes a step,we've learned to…
【The part of zero】
《If taking advantage of each number dynamically,a minus number appears inevitably》
The number is used when counting something,and it takes a step forward,we've found calculates are useful.
There are three apples,and there are five apples. If adding two of them there are eight apples,so addition is introduced into us naturally,so subtraction is also same…I want to say so,but it's not so easy.
There are 5 apples. Then we can take 3 apples,but when there are 3 apples we can't take 5 apples. A minus number appears after being worried about the situation.
There are 3 apples. It means that the number of the apples are three,but is there the minus number of the apple? It doesn't exist at all,but we make use of the minus number. Why? In short,it's like the next.
The minus numbers correspond to phenomena in natural science or the situations of our activities everyday as the human being,and when displaying it the minus number is useful. In other words,there are lots of…
【The part of a minus number】
《If making use of a number dynamically,a minus number appears inevitably》
In other words,there are lots of phenomena naturally which correspond to the minus number. The author indicates some examples for it.
For example,let's suppose that I had income of $ 300,and if spending $ 500, I'm $ 200 in the red. Then a theory that the part of the red is minus stands up.
Or there is a basic point. Let's suppose that its eastward was plus. Then if walking 7kilometers eastward and walking 10 kilometers westward,it means 7  10 = 3. It means I'm at the point of 3 kilometer the westward and I'm at the point of 3 kilometers the eastward. It's the way of thinking as vector.
Descartes displayed some numbers on a number line 数直線. The numbers displayed on the number line would have extended to a real number later. The number line on which an equation of 35 is displayed is in the book.
The real number means that a rational number like a fractional number or…
【The part of a minus number】
《If making use of a number dynamically,a minus number appears inevitably》
The real number means rational number like a fractional number or irrational number.
When solving an equation,if its answer was minus,it didn't used to be permitted as answer from the historic point of view. We used to think the minus number was irrational one. Its days of obscurity lasted long.
Geometric idea of the number line by Descartes removed the blot on its name. To tell the truth,the geometric idea saved the crisis of existence of an imaginary number 虚数.
【Expansion to an irrational number】
《The concept of the number extends from calculations like addition,subtraction,multiplication,and division to rational number》
There are 6 apples. If three people wants to take the apples equally,two apples have to be distributed to each of the three,but if there's one apple,then the apple has to be divided into three equally. Without the remainder,no one can figure within the range…
【Expansion to an irrational number】
《The concept of the number extends from the four basic operation of arithmetic to rational number》
Without any remainder no one can figure within the range of integral numbers,so if wanting to divide the one into three equally,we need to think up a new number,so we are forced to describe the number was onethird. In short a fractional number appears.
The fractional number of which both of denominator 分母 and numerator 分子 are integral number is rational number. When natural number is extended to integral number,we've learned to do addition and subtraction at will,at the same time,when the integral number is extended to the rational number,we've learned to do multiplication and division at will.
In this way the system of rational number in which we can do the four basic operation of arithmetic is completed,so we can add,subtract,multiple and divide at will.
There are two simple question as to the four basic operation of arithmetic on the…
【Expansion to a rational number】
《The concept of number extends from the four basic operation of arithmetic to a rational number》
There are two simple questions to which almost all of us used to occur with regard to the four basic operation of arithmetic on rational number. The author said."I'm going to answer them."
The one is addition of fractional numbers. For example,when a half is added to onethird,its answer is twofifths,isn't it? Without reducing the fractions to a common denominator 通分,we add one fractional number to the other as they are,its answer becomes like that,but needless to say it's in the wrong.
There are illustrations for the answer in the book. They are two rectangles. They are the same size,but the one is divided into two and the other is done into three,
And there are three other illustrations. Each of them are divided into six. One of them is black on the part of its onethird,and the other is black on the part of its half,and the last one is black on the…
【Expansion to a rational number】
《The concept of a number extends from the four basic operation of arithmetic to a rational number》
The last rectangle is black on the part of fivesixths.
The first two rectangles means the fractional numbers which aren't reduced to common denominators. The former is a half and the latter is one third.
The second three rectangles are the fractional number which are reduced to common denominators. The first is onethird,the second one is half,and the last one is fivesixths.
As for the fractional number,we can't add any of them if their denominators are different. In short reducing of fractions to a common denominator means that different sizes of the rectangles change into the same size,so we can count them easily.When each size is different,neither we can add nor subtract exactly.
When multiplying each two of minus number,its answer is plus. Why? It's other simple question.
ー2 × 3 ＝ ー６ It means that minus 2 is added three times,so it's …
【Expansion to a rational number】
《The concept of a number from the basic operation of arithmetic to a rational number》
ー2 × 3 ＝ ー 6,it means that minus 2 is added three times so it's easy to understand for even me,but ー 2 × ー 3 ＝ 6…why? I'm going to think why it is.
Intuition tells me that minus is opposite of plus. One minus number multiply by other minus number means that opposition of the opposition,so it returns as it is,so it's plus. To tell the truth I can't understand it any more,but the book expresses like the next.
The distributive law stands up to the plus number. Considering that the distributive law stands up to the whole rational number,minus number multiple by multiple minus number becomes a plus number is indicated. By the way what is the distritbutive law?
It's the equation that a（b+c）＝ab + ac. Then there are next two equations,the one is a×0＝0,and and let's suppose the a was ー2,and other equation is 0 = 3ー3. It means that ー2 × 0 ＝3 ー3… I find it tedious…
【The fact that there is an irrational number】
《Even if we can recognize the rational number,we find impossible to acknowledge an irrational number》
I don't feel like expressing the distributive law and calculation of multiplication of minus numbers no longer. I'm not interested in it at all. If you are please research it for yourself.
By the way as to the numbers which we use everyday life,as long as there are rational numbers,it looks enough,but the people in the ancient were conscious that it's insufficient. It's in relation to the Pythagorean theorem. It's relation of each of three side,x,y,and z in a rightangle triangle.
The theorems doesn't remain as geometric significance but has a tremendous impact on the concept of numbers. What is the Pythagorean theorem?
There is an isosceles triangle 二等辺三角形 which is right angle. Then two sides which aren't oblique sides 斜辺 and each length is 1. Pythagorean theorem says addition of each second power of the two sides is equal to …
【The fact that ther is an irrational number】
《Even if we can recognize a rational number,we find impossible to acknowledge an irrational number?》
Pythagoras' theorem says that addition of second power of two sides is equal to the second power of the oblique. Then the length of the oblique side isn't an rational number. The Pythagoras school has discovered it.
However the demonstration in those days depended on their intuition,so it's not logical,so it's the weakness,but they acknowledged that there is a number which isn't rational number. It's significant.
However the Pythagoras school seemed to be confused the unexpected fact so much,for the fact of the irrational number is opposed to their philosophy that every length should be described with the rational numbers,so they tried to prevent it from leaking out,but it leaked out,lots of other people have learned to know in the society.
A number which is the second power of 2 is equal to the diagonal line of a regular square of …
【The fact that there is an irrational number】
《Even if we can recognize a rational number,we find it impossible to find an irrational number》
A number of which is the second power of 2 is equal to the diagonal line of a regular square of which side 1 exists. We can't deny its its existence. It's not any rational number,so when describing it we need a mark something new,so √ has appeared. It is said that Descartes is the first one who start to use the mark of √．
We call the number which isn't rational number but we have to use the mark of √ a irrational number. We call the one which the rational number and irrational are united real numbers. When lined up the real numbers it becomes a line,and each point of the line is deemed a real number. In other words,the real number is the line itself. It is said that we can explain even the time with the real number.
To my sorrow even if the time is explained with the real number,I find it impossible it understand it!
I've said there is a…
【A mysterious imaginary number】
《Does an imaginary number exist really?》
When being squared,is there a number which becomes minus? The people used to be worried about it long long a year ago,for when real number squares it becomes plus number or 0. As a result,no one could find the number like the imaginary one then.
We introduce a new number,it's the imaginary number,when being squared it becomes — 1. It's expressed with a sign like √—. It's in the solution of the formula in a quadratic equation 二次方程式の解の公式 when coming across the imaginary number for the first time. I'm sure I'll never come across the number until I'm dead.
Judging from its name,we seem to suffer from labor pain until we recognize the number. If the number is expanded to the imaginary number,we can solve both of the equation of quadratic,cubic,and biquadratic,but it has been unclear that the solution of the imaginary number has what kinds of meaning.
Speaking of the imaginary number,it develops into philosophical
【 An imaginary number】
《Does the imaginary number exist really?》
Speaking of the imaginary number,it will get to something philosophical "Is there the imaginary number?" or “What is the imaginary number?" It is a German great mathematician Gauss who brought the dispute on the existence an end.
While real numbers are expressed on the points of a straight line,the imaginary number is expressed on the point of a coordinate 座標. Gauss thought like that. He regarded a plane as a group of dots which are the imaginary numbers. We call it a complex plane 複素平面.
The imaginary number has now been fully accepted by given the geometric feeling of the plane,though I've never accepted it at all. Too hard to understand it at all. The more I read the book,the less I can understand!
The imaginary number is indispensable not only as mathematical theory but the one in quantum mechanics 量子力学. Moreover if using the imaginary number in the electric theory,it seem that we can express its theory clearly.
【Simple but mysterious…】
《A prime number 素数 looks like an atom of number,for we can't resolve it the form of the product 積 any more》
The prime number is the base of natural numbers. It's one of natural numbers which is bigger than 1. If the number trying to be divided by any other number,except for 1 and the number itself,there is always a remainder.
Gauss who is a Germa great genius on math said like the next. When learning the integral numbers,its central lesson is studying the prime numbers,for however bigger number than 1,all the numbers are resolved into the products of the prime numbers.
If taking no account of its order,the way of resolving the number is only one. While all the materials are composed of atoms,all the numbers are made up with the prime numbers. While the proper of the materials has a peculiarity of the atoms and their combinations,the natural numbers has the peculiarity of the prime numbers and their combinations.
By the way how can we judge whether or not…
【Simple but mysterious…】
《The prime number looks like an atom in numbers,for we can't resolve it in the form of the product any more.》
By the way how can we judge whether or not it is the prime number? When being some natural number,if trying deviding with each other smaller number except for the number itself one after another,we can recognize whether or not it's the prime number.
We'll be aware instantly that we have only to try with some numbers below its square root,but if being tremendous number,it'll be hard even if we use computer,so when verifying it actually,we have to make full use of the computer plus mathematic study. We have to try saving energy.
On the other hand the prime number is frequently used for a cryptogram 暗号文 by taking advantage of its difficulty. If the prime number is so important,how many are there the prime numbers? Simple question may occur to us like that.
Unexpectedly someone answered the question in ancient time. It's Euclid who is famous in …
【Simple but mysterious…】
《The prime number looks like an atom in mumbles,for we can't resolve it in the form of a product any more》
Euclid is famous for in the field of geometry. Its answer is so simple. The prime numbers exist limitlessly. I'm wondering how we can find the prime number. It's the way to find the prime number from 1 to 100.
At first we take away 1. Then except for 2,we take away the multiples of the 2. Except for the 2, 3 is the smallest prime number,so except for the 3,we remove the multiple of the 3. Then except for the 3, 5 is the smallest prime number,so except for the 5,we take away the multiples of the 5…we have only to continue more and more like this.
Euclid used reductio 背理法 and demonstrates that ther are the prime number limitlessly. When demonstrating at first we deny a conclusion. Then we continue an inference 推論. Then there is a contradiction in the inference. It means that denying the conclusion is in the wrong,so the conclusion is right.
【Simple but mysterious】
《A prime numbers look like an atom,for we can't resolve it in the form of product any more.》
I'm sure I need to express the content of the reductio on that there are prime numbers limitlessly,but to my sorrow I can't understand it very much,so if you are interested in it,please research for it for yourself.
【There is each meaning in each number】
Each number used to have each meaning in Ancient Greece. For example,1 means a creation,and 2 symbolizes a female,and 3 is a male. 5 which is addition of 2 and 3 means a marriage,and 6 which is special one.
Except for the 6 itself,the divisors of the 6 is 1,2,and 3. When adding three divisors,it becomes 6. The Ancient Greek found this mysterious nature,and named the 6 a perfect number. It's also an origin of Genesis 創世記 that the God creates everything in 6 days. It means that the creation of the God must be perfect.
There is a natural number,N. Except for the N itself,if adding its all divisors and it becomes N…
【There is each meaning in each number】
There is a natural number,N. Except for the N,when adding its all divisors and it becomes the N,we call it a perfect number. There are other perfect numbers. The next one is 28,which is relatively easier to find. The next one is harder than we expect. Far from it,we need lots of perseverance to search it. It's 496,and the fourth is 8128. The Ancient Greek found these four numbers.
The fifth perfect number is found in the Middle Age. It's 33,550;336. There was no computer in the Middle Age,but how patient one who found the fifth perfect number,I'm wondering.
We can find 31 perfect numbers because of the computer,it seems to be less than we expect,it means that perfect ones are less,I'm wondering.
While the perfect number is the nature of the number itself,there are two kinds of numbers which are related each other. The one is the numbers of friendship and the other is the one of engagements.
There are two natural numbers,A and B. Except for…
【There is each meaning in each number】
There are two natural numbers,A and B. Except for the A itself,the addition of of the divisor is equal to the B,and except for the B itself,the addition of its divisor is equal to the A. Then we call the two the number of friendship.
Except for 1 and the A itself,the addition of its divisor is equal to the B and except for 1 and the B itself,the addition of its divisor is equal to the A. Then we call the the two the number of engagement.
If trying to discover the numbers for ourselves,I'm afraid I need to have lots of patience. The smallest numbers of friendship are 220 and 284 and the smallest numbers of engagement are 48 and 75.
By the way the numbers of engagement which we have known are combinations of odd number and even number alone. The numbers of engagement of which combination is odd numbers alone or even numbers alone has never been discovered yet,so we may call them the numbers of engagement,the author said like that.
【What is a function?】
《Vending machines for a soft drink or a ticket for a train are also the function》
Speaking of the function,primary function or quardratic function occur to us at once. If thinking over it a little more ,we may hit on trigonometric function三角関数,exponential one指数関数,or logarithmic one 対数関数.
We may recognize the concrete function,but when being asked,"What is the function itself?" Lots of people may find it hard to answer exactly,so at first let's start from answering the question.
As for two things when the one is fixed,the other is done. We call the relation the function. It's a grave definition with regard to the function.
For example let's suppose there was a factory. 10 cars are produced an hour there. Then the factory makes 20 cars by two hours,30 cars by 3 hours… When its time is fixed the number of cars which is produced is done. Its relation is the function. If showing the relation with a formula it's y＝10x. Needless to say the x means the time and …
【What is a function?】
《A vending machine for a soft drink or a ticket for a train are also the function》
Needless to say the x is the time and the y is the number of the car which is produced. There seems to be lots of functions around us.
There are some members in a group. If each age corresponds to each member,it's also the function. At first each name of us is the function. It's the function which each people corresponds to each name. Then we can't have two kinds of name at the same time. It's limited to either the name in a family register of a pen name.
There is a vending machine in a station. If inserting some money into the vending machine and pushing buttons for our destination,we can get its ticket. In short the correspondence from the button to the ticket for the destination is the function. Other vending machines for the soft drink or liquor are the same.
There are some research workers in a university. Each number is assigned each of them,for when using a name,there…
【What is a function?】
《Vending machines for a soft drink or for a ticket in a station are also the function》
Each number is assigned to each research worker,for when using a name,if being the same name it doesn't go well,but as to the numbers for the research worker,different numbers are assigned to them,so any mistake won't happen. The function which different one corresponds to other different one is the function of 1 to 1.However two buttons sometimes one kind of soft drink,so in general all the functions aren't 1 to 1.
Our everyday life seems to be filled with the functions like this. In other words,even if it seems to be complicated,if showing it with the function,it's put in order and we may find it easy to recognize.
【If using a graph,we can see right away】
《A straight line for the primary function,a parabola 放物線 for the quadratic one,and hyperbola 双曲線 for an inverse proportion 反比例》
In general,it seems to be easy to understand the function with a graph,for the graph…
【if using a graph,we'll see it at once】
《A straight line for the primary function,parabola for the quadratic function,and hyperbola for an inverse proportion》
General speaking,it seems to be easy to understand the function with a graph ,for the graph appeals us more visually than a formula. I'm going to adopt some basic functions and think over each of graph.
There are plenty of functions,and the one which belongs to the easiest one to understand is the primary function. Its formula is y ＝ax ＋ b. If showing it with the graph it becomes a straight line. When the b is 0,it's y ＝ax. The formula shows us a relation that the a is in proportion to the b. It's a straight line which goes through the origin on the graph.
The proportion has been adopted for calculations in various reactions on chemistry,besides the proportion is necessary in varied scene everyday life.
For example,a spring balance バネばかり has nature that weight is in proportion to stretch of the spring. When its density …
【If using a graph,we'll see it immediately】
《A straight line for the primary function,a parabola for the quadratic function,and a hyperbola for the inverse proportion》
When the density is fixed,the cubic volume and the weight is in proportion,and if the electric resistance is the same,the electric current is proportion to the voltage.
There is the quadratic function close to us. If dropping a little stone from the rooftop of a building,its falling distance is the quadratic function of the time. If taking no account of the air resistance,it's shown with the next formula.
y=4.9t squared. It means the whole of 4.9 isn't squared but the t alone is squared.
If wanting to know the depth of a well or the height of a bridge,we have only to drop the little stone from the bridge or the well. Then we need to see how much it takes for the stone to reach the surface of the water and make use of the formula.
If showing the quadratic function with a graph,it becomes the parabola. In general…
【If using a graph,we'll see it at once】
《A straight line for the primary function,parabola for the quadratic function,and hyperbola for the inverse proportion.》
In general,a locus 軌跡 of throwing something is the graph of the quadratic function,so we call the graph the locus.
The volume of a sphere is the function of its radius,so its formula is V = fourthirds multiple πr. Then the r alone is cubed to the third power.
By the way whenever I show a fractional number or an involution 累乗,I find it complicated,for I've wanted to express everything in English,but I don't think it's easy to show. I wish I could show it more easily.
As for the inverse proportion,we can find lots of its examples. When moving from one point to other in car,its speed is inverse proportion to its time. When electric resistance is fixed,the electric current is also inverse proportion to the voltage.
The inverse proportion is showed with the formula,y=a xth,and we call the curve on the graph the hyperbola.
【The innermost secret of the solution for an equation】
《The solution of a question starts from setting up an equation as it is.》
A function only looks like an equation,though they are related deeply. The equation is a formula of two functions which is tied with =. Solving the equation means finding the value which meets the equation.
Speaking of math in Ancient Greece or in Ancient Egypt,it almost means geometry. On the other hand it is said that Diophantine is an early settler 草分け with regard to algebra in Alexandria from the 3rd to the 4th century.
It is said there are some sentences on his tombstone like the next.
"I grew up as a boy for one sixth of my lifetime and grew up as a youth for one twelfth of my lifetime. I was unmarried for one seventh of my lifetime. After 5 years my marriage,my son was born,and my son was dead 5 years ago. Then my son's age was as half as mine. When being dead how old was I?"
If wanting to solve the question like that,we fix the value which…
【The innermost secret of the solution for an equation】
《The solution of a question starts from setting up the equation as it is.》
If wanting to solve a question like that,without thinking anything,it's just we have only to adapt the sentence in the question to the equation as it is. Without thinking of various answers,nor having wicked thought,we have only to make the equation as the sentence in the question showed. It's a key to solving the problem.
If being able to make the equation,it's just that we have only to solve it. We frequently have to change the equation into other one so as to solve it. Then we add,subtract,multiple,or divide the same number on the both side of the equation,without using 0.
The way of thinking is very simple and easy. As to the transformation into plus or minus we call it transposition of a term,but without thinking of transposition,we do the same thing both on the side of the equation. It is easy for us to understand. There is no room for …
【The innermost secret of solution for an equation】
《The solution of a question is starting from setting up its equation》
There is no room for misunderstanding then.
An equality is thought to be a situation which two things are evenly balanced on a pair of scales. When putting same weight both on sides of the scale or removing the same weight from the pair of scale,it is evenly balanced. The equality is also the same theory.
Actually a mathematician who is famous for the education for math has devised a teaching material,called algebra balance. If using it,we can measure a weight of minus,according to the book,数学のしくみ,written by 川久保勝夫.
As you know,I have little knowledge on math,so I can't imagine how the weight of minus and the algebra balance at all.
The author set up an equation,being based on the sentence on the tombstone of the mathematician.
He lived to be the age of X. Onesixth of his life he led as boy. One twelfth of his life he led as youth. Oneseventh of his life he…
【The innermost secret of solution for an equation】
《The solutio of the problem starts from setting up the equation》
Diophantus lived for onetwelfths of his life as a youth. He lived a single life for oneseventh of his life. His son was born after 5 years he got married. His son was dead and he was also dead after 4 years. When his son was dead the son's age was
equal to half of his father's lifetime. How old is Diophantus?
Its equation is the next.
Onesixths・X ＋ onetwelfths ・X + onetwelfths・X＋5＋half・X+4 = X
Seventyfiveeightyfourths・X ＋9＝X
9＝nineeightyfourths・X
X = 84
I hate to say,but I can't understand why the answer is 84 clearly. When reducing the fractions to a common denominators I can understand. After that I can't grasp why it is. In short I hate math,but I'm going to go on expressing on math…maybe.
【If adopting the method of calculation based on fuguring the number of cranes and tortoises from the totals of their legs,simultaneous equation is more useful】
【If adopting the method of calculation based on figuring the number of cranes and tortoises from the totals of their legs,simultaneous equations are easier連立方程式】
《Even if it's very complicated,we can solve it at once with the the simultaneous equations》
I've expressed on the equation last time,then unknown quantity was one,but when the question is complicated,the unknown quantity isn't always single. If the unknown quantity is two kinds the method of calculation based on figuring the number of cranes and tortoises from the totals of their legs,what is called 鶴亀算.
By the way when trying to express it in English,it's long a little,so I make it a rule to call it the method of calculations.
When there are two kinds of unknown quantity,we call it an equation with two unknowns 二元方程式. Then without being two equations we can't solve the question. I'm going to use the equation with two unknowns with the method of calculations.
There are cranes and tortoises. Their total number is 8.
【If adopting a method of calculation on figuring the number of cranes and tortoises from the total of their legs,a simultaneous equation is easier】
《Even if it's complicated,we can solve it with the simultaneous equation》
When adding their legs its total numbers are 22. Then how many are the cranes? And how many are the tortoises?
Without using any algebra,we used to solve the question like the next long ago.
The crane has two legs and the tortoise four legs. If the all the tortoises pull their two legs,the total numbers of the legs of the crane and the tortoises are 16. 2×8＝16,but the original numbers of the legs used to be 22. The difference is 6. All the tortoises pulled their two legs. 6÷2＝3,so the tortoises are 3,as a result,the cranes are 5.
The way of solving the question is making the tortoise pull its two legs,but we don't have to do it with the algebra. The crane is X,and the tortoise is Y,so the number of the leg of the crane is 2X,and the tortoise is 4Y.
After that…
【If adopting a method of calculation based on figuring the number of cranes and tortoises from the totals of their legs,a simultaneous equation is easier.】
《Even if it's complicated,we can solve it right away with the simultaneous equation》
After that without thinking anything,it's just that all we have to show an equation with the question and solve it.
X + Y = 8. The total number of the crane and the tortoise are 8.
2X + 4Y = 22. The total number of their legs are 22.
I'm going to solve the equations. At first multiple 2 by both sides of the former equation. 2X + 2Y = 16. Then subtract the the second equation from the third equation on both sides,so 2Y = 6,Y = 3.
When substituting the answer to the first equation,X + 3 = 8,so X = 5. The tortoises are 3 and the cranes are 5.
If using a matrix 行列,we can solve the simultaneous equation at once. I'm going to express it its chapter later,but the problem is whether or not we can reach there…
【The solution of the formula is helpful】
【The solution of the formula is very helpful】
《We can distinguish the property of the solution in a discriminant of a quadratic equation二次方程式》
An equation with two unknown and a quadratic one resemble when saying in Japanese.
While the equation with two unknown means that there are two unknown numbers such as x and y in the equation,there is one unknown number in the quadratic one,but the quadratic one includes the square of x.
General form of the quadratic equation is ax（only part of the x is squared）+ bx + c =0. As for the quadratic equation,we can solve it with factorization 因数分解 as long as it's a special case,however in general we can't always solve it with the factorization,so someone contrived the solution of the formula.
The solution of the formula is familiar with the math in high school. If using it,our mathematical ability improves so much,maybe…even if the a,b,and c are what kinds of number we don't have to mind them.
As to the solution of the formula,√ appears,and…
【The solution of formula is very helpful】
《We can distinguish the property of the solution in a discriminant of a quadratic equation.》
I've tried to express on the solution of the formula,but I hate to say it's too hard to understand. In short,when it's value is minus,it means that the solution of the equation isn't a real number.
The number with which we usually deal is the real number,so then there is nothing with regard to the solution,but even if its is minus of,it seems to be all right in a wide sense in mathematic.
As you know,I'm not good at math at all,but when there is a thing which we can't understand,we need one more thing in order to understand the situation. I'm wondering if it's a complex number. Its square root is minus.
If it's irrational and strained,the phrase of the complex number must have disappeared,I'm sure. The book of 数学のしくみ uses a graph and expresses on the complex number though…
【The secret of solution with regard to a cubic equation】
《As for the solution,it's the most interesting episode in the history of math》
It seems that the solution of liner equation and quadratic one has been familiar with us from long ago,and the intellectual curiosity of the human being has moved forward to the solution of the cubic and biquadratic solution naturally.
There is an episode of the solution and announcement of the solutio which is very interesting. It happened in Italy in the 16 century.
The one who dealt with the solution was スキピオ デル デル フェロ in Bologna universiy. He discovered a special solution on the cubic equation,and he told it for his disciple,but he didn't make public his discovery.
On the other hand,ニコロ フォンタナ discovred an ordinary solution. He was born into a very poor peasant,but he studied math with educationally,and getting over lots of difficulty and he won the solution of the cubic equation.
Mathematical game had been popular in those day. フォンタナ …
【The secret of solution with regard to a cubic equation】
《As to the solution,it's the most interesting episode in the Mathematical history》
フォンタナ challenged フェロ to the mathematical game. The mathematical game was done on view to general public. They prepared 30 questions each other and they had tried to solve the questions each other.
While フォンタナ solved all フェロ's questions in 2 hours,フェロ couldn't solve フォンタナ's questions at all. フォンタナ tried not to open the solution to the public because of the manners and customs then,but カルダン in Milan was interested in the solution very much.
カルダン talked フォンタナ into showing him the solution. He made a promise not to leak the solution to others and succeeded in getting the solution out of フォンタナ. It caused a heated dispute over two of them.
カルダン broke his promise and showed the solution in his book. Needless to say フォンタナ stamped his foot in frustration and protested to カルダン about breaking the promise,but カルダン pretended ignorance.
フォンタナ was in…
【The secret solution with regard to a cubic equation】
《As to the solution,it's the most interesting episode in mathematical history》
フォンタナ who was in the extreme distress challenged カルダン to do an opened mathematical match,but instead of カルダン,フェラリwho was カルダン's pupil appeared the place where the match was done. フェラリwas young and spirited mathematician. Unfortunately カルダン was defeated then.
In this way,the one who discovered the solution of the cubic equation becomes カルダノ. His name isn't カルダン but カルダノ. I'm sorry for it.
As for the solution of quartic 四次方程式,フェラリhas done.
This is the famous episode in relation to the cubic equation or quartic in mathematical history,but this kind of thing isn't always in the past. Similar incident seems to happen sometimes at present.
【is there a solution of quintile 五次方程式?】
Both of the solution of the cubic equation and quartic was discovered in ITaly in 16th century,so everybody thought the solution of quintile was also done easily,but …
【Is there a solution of quintile? 】
However the most shocking incident in the history of mathematic has happened.
A young Norwegian mathematician アーベル demonstrated that there is no formula of solution in relation to the quintic. Then he was 21 years old.
Being unable to solve absolutely. It doesn't occur to everyone at ease. It seems to be one of the hardest things to do…oh! I've tried to describe the episode but I've lost interest in it. To begin with I hate math. I'm not interested in the quintic at all.
Even if being able to solve or not,it doesn't matter. It's none of my business.
【If turning into a triangle…】
《As to a space of a figure which is surrounded by straight lines, we can find it easily as long as it divides into triangles》
As It is said that Egypt is the gift from the Nile,the Nile river supported the Egyptian culture and flooding of the Nile river which happened almost every year stimulated development technique of surveying. The word of geometry is made up …
【If turning it into triangles …】
《As to a space of figure which is surrounded by straight lines,we can find it easy as long as it's divided into triangles》
The word of the geometry is made up with geo and metry. It means a land and its measurement. It shows the two relations between them plainly.
I'm going to handle a space of a figure which is surrounded by complicated curve at integration 積分,and I'm going to deal with the one which is surrounded by straight lines this time.
In general,as to the figure which is surrounded by straight lines,its shape will never be fixed if each length of sides is given,for a quadrangle 四角形 of the length of all sides is 1 is just a lozenge ひし形,so both its shape and space is varied.
On the other hand,if being fixed each length of the three sides,its shape is also done in relation to a triangle. It's one of the congruent conditions 合同条件 on the triangle,the two triangles of which three sides are the same are congruent. As to the condition,the …
【If turning it into a triangle …】
《As to a space of a figure which is surrounded by straight lines we can find it easy as long as it's divided into triangles.》
This is a point which is remarkably different from other figures with regard to the triangle.
If divided into triangles and fixed each length of sides,its shape is done and as a result it's space is done. In short,when showing a figure,if using a triangle as one of piece,we can show the figure precisely.
In this way a land is divided into triangles and is drawn on a plan of a registry book. The way of thinking is applied to measurement of lands,its triangular surveying. I'm going to express its detail at the trigonometric functions.
There is one more application,it's a diagonal brace すじかい. When building a house it's put between posts diagonally. Without putting the diagonal brace,the house is easily broken. Not only the house but all the constructions like abridge or a tower is constructed,being based on a triangle,for…
【Geometry will revive】
《What's called 五心 in a triangle》
All the constructions are based on triangles,it's not for beauty but for it's adopted so as to keep balance on the construction.
It's been a long time since geometry disappeared from textbooks in high school but lots of people seem to want to it revive,for not only it's beautiful and fascinating as material but the demonstration is important for a proof. Plenty of people have learned to recognize it. Geometry seems to be taught in high school. I'm relieved that I 'm not a student in high school any more.
What is called 五心 is also included in the geometry. The five of them are in a triangle,it's a center,inner center,circumcenter,excenter 傍心,orthocenter 垂心.
Dividing each three angle of a triangle into half and drawing lines from each triangle,and there is a point where the three lines intersect. It's the center of the triangle.
Drawing a perpendicular垂線 line from each side to each angle and there is a point where the three …
【The shape which the God has created】
《They calculate as long as there is π there. The drama of the π.》
I've tried to express what's called 5心,for the author insists that the geometry is beautiful and the 五心 is also included,but I don't think so,in addition without illustrating them,I find it hard to make others understand,so I give it up. I'm going to express other topic.
No figure is more beautiful than a circle. Ancient people seemed to think the circle was a perfect one which the god created.
The circle is also mysterious,for it's always the same shape however it is,so the length of the circumference and its diameter is the same ratio whether the size of the circle is big or small. It's the ratio of the circumference of a circle to its diameter, the π. It is Euler who used the mark of the π for the first time. The mathematician appears in various field of math.
The calculation of the π has long history. Ancient Babylonia people used to adopt an approximate value of the π…
【The shape which the God has created】
《They calculate as long as there is π there. The drama of the π》
Ancient Babylonian people used to adopt 3 as the approximate value of the π. It's said that Ahmed is the oldest mathematic book of the ancient Egypt. The book said that the value of the π is 3.16049…so it's value is very close to the π.
It's Archimedes who tackled the calculation of the π theoretically. He was a Greek mathematician. He adopted a regular polygon 正多角形 which was inscribed 内接 or circumscribed 外接 a circle and calculated the π both from the bigger polygon and the small one.
As to the regular polygon which is inscribed to the circle is made up with 6 regular triangles of which side is 1,so it's circumstance is 1×6 ＝6,and its diameter is 2,so 6÷2＝3.
On the other hand other regular polygon which is circumscribed the circle is made up with 6 right triangles. The two sides which put the right angle between them is 1 and route 3. Its oblique side 斜辺 is 2 and the oblique…
【The shape which the God has created.】
《They calculate as long as there is the π there. The drama of the π.》
Archimedes divided both the triangles which is inscribed and circumscribed into 96. The circumference of inscribed triangles is 3.1408…and the circumscribed ones is 3.1428…,so the π is between them. It's showned as an inequality like the next.
3.1498 ＜ π ＜ 3.1428.
To my surprise,Archimedes calculated the value of the π as an approximate value of about 3.14 then.It's the one which we usually use the approximation at present.
After that mathematicians have learned to calculate the π as if it's were a famous saying of the mountaineer,'We climb because there is the mountain there.' so they continue calculating the π there is the π there.
New ways of calculating the π have been found after differential and integral calculus 微分積分 was born in the 17th century. In addition when being invented a computer,needless to say the calculation of the π has made rapid progress.
As for …
【Spreading all over the same shape】
《When tiling,can we do it what kind of regular polygon?》
As for an efficiency of a computer what number of digit can the computer calculate? It's a kind of barometer for the computer ,so the calculation of the π has gone on at present.
When walking along the streets which are lined with old neat rows of stores and houses in Europe,some people tend to be fascinated with geometric pattern spreading all over the road made of stone,without realizing it,they can't take their eyes off it.
The stylish tile spreading all over the floor in a fashionable hotel or company takes part in creating a good atmosphere. The way of tiling seems to be varied.For example, the one which spread the same pattern all over and two kinds of pattern is done. I'm going to describe the way of tiling the same regular polygon here.
The tile of which shape is a regular square is the most popular. We can see it in a bathroom. The other ones which occurred to us at once are…
【Spreading all over the same shape.】
《When tiling,can we do it with what kinds of regular polygon?》
The other tiles which occur to us at once is a regular hexagon of which shape is a honeycomb,and a regular triangle. It seems that any kinds of shape is suitable for the tiling,but it doesn't,for if adopting a regular pentagon,there are some space between them.
When tiling,without being any space and spreading the same shape all over,it's limited to the regular triangle,the regular square,and the regular hexagon. If trying to do with a regular heptagon ７角形,it seems to be impossible.
If tiling with the regular polygon of the same shape without being any space,the one which becomes 360 degree when displaying is suitable.
By the way,the sum of interior angles of a polygon is found with an equation of (n−2)×180,then the n is the number of angles of the polygon,even if its shape changes its value is fixed,according to the book,though I don't know why. The number of the angle seems…
【Spreading all over the same shape】
《When tiling,can we do it with what kind of regular polygons?》
The number of the angles decides the sum of the internal angles.
An equation of one of angles of a regular polygon is (n−2 )divided by n,and multiply its value by 180.
When collecting regular polygons of the same shape around one point without being any space,what's kind of the regular polygon? It's equation is multiply m by (n−２) divided by n,and multiply its value by is equal 360. The 360 means 360 degree. The m is the number of the regular polygon.
Though its calculation is showed in the book,but to my sorrow,I can't understand it very much. It's sub title is 入門ビジュアルサイエンス,so there are a lot of illustrations in the book. Without showing any illustrations,I find it hard to express what I want to say.
By the way,the m and n is more than 2,for there is no 2角形. If solving the equation,it's value is 3,4.or6,so the tilting of the regular polygon is regular triangle,regular square,and…
【Spreading all over the same shape】
《When tiling,can we do it with what kind of regular polygons?》
The number of the angles decides the sum of the internal angles.
An equation of one of angles of a regular polygon is (n−2 )divided by n,and multiply its value by 180.
When collecting regular polygons of the same shape around one point without being any space,what's kind of the regular polygon? It's equation is multiply m by (n−２) divided by n,and multiply its value by is equal 360. The 360 means 360 degree. The m is the number of the regular polygon.
Though its calculation is showed in the book,but to my sorrow,I can't understand it very much. It's sub title is 入門ビジュアルサイエンス,so there are a lot of illustrations in the book. Without showing any illustrations,I find it hard to express what I want to say.
By the way,the m and n is more than 2,for there is no 2角形. If solving the equation,it's value is 3,4.or6,so the tilting of the regular polygon is regular triangle,regular square,and…
【Spreading all over the same shape.】
《When tiling,can we do it with what kind of regular polygon?》
If solving the equation,it’s value is 3,4,or 6,so tiling of regular polygon is a regular triangle,a regular square,and a regular hexagon. If allowing for transformed hexagons,three are more various tilings.
【The beauty is a sense of balance.】
《We have been fascinated by golden ratio.》
If a circle is a flawless figure which the god has created,a rectangle of golden ratio which we the human has created is also beautiful and fascinating. It’s a size of paperback pocket edition.
If feeling that the rectangle is beautiful,the ratio of both height and length is important,and the golden ratio which we have been fascinated as literary gem for a long time. We call a rectangle of which ratio of height and length is golden one golden rectangle.
Dividing the length with the ratio is golden section,and painting,carving,and architecture have adopted it widely. It is said that Eudoxos who …
【The beauty is a sense of balance.】
《We have been fascinated by golden ratio》
It is said that Eudoxos who thought up the golden ratio. He was in the era of a philosopher,Plato,and Italian genius,Leonardo da Vinci named it golden ratio later.
I’m going to express on the secret of charm of the golden ratio from now on. Unexpectedly it’s related to the solution of a quadratic equation.
There is a rectangle,ABCD here. Then we change it into a regular square and other rectangle. If the first rectangle and second one are similar in shape,two of them are golden rectangles and its ratio of height and length is the golden ratio.
I’m going to find the value of the ratio with calculation actually. Let’s suppose that the height was 1 and the length was X,and I’m going to set up its equation.
The equation shows that the first rectangle and the second one which is separated from the first one look exactly alike,though then we need to make the first one turn 90 degree. Its equation is X:1＝1:…
【The beauty is a sense of balance.】
《We have been fascinated by golden ratio》
The equation is X:1＝1:(X−1). X(X1)=1. X squaredX1=0,so X=half of 1+ route 5,so X ≒ 1.62,according to the solution of the equation,though to my sorrow it doesn’t always mean that l calculate it for myself. It’s just that l made an exact copy of the book. To tell the truth I can’t understand the solution of the equation at all.
Leonardo da Vinci made use of the golden ratio for various areas in his artistic activity like art,industrial art,and architecture. Ancient art and architecture also adopted the golden ratio,but is it so beautiful? I’m wondering if it’s just the rectangle.
【Solve it with a ruler and compasses.】
《Greek three hardest problems,doubling the cube,dividing the angle into three equally,and squaring the circle.》
There are Greek three difficult problems in history. They are problems of drawing figures which we solve with a ruler and compasses.
The first one is doubling the cube. It’s …
【Solvie it with a ruler and compasses】
《Greek three hardest problems. Doubling the cube,diving an angel into three equally,and squaring the circle》
The first one is doubling the cube, if doubling the volume of a cube,what times should we make each side of the cube ? We call it Delian problem. If showing it in an equation,it’s X cubed ＝2A cubed.
In short it means that whether or not we can draw the solution of a cubic equation with a ruler and compasses.
The next one is dividing an angle into three equally. Then we also use the ruler and compasses alone. It also arrives at a conclusion of drawing a figure with the cubic equation.
The last one is squaring the circle. There is a circle. Drawing a square of which space is equal to the circle.
Why do we use the ruler and compasses alone? A straight line is done with the ruler. It’s shown with a linear equation. The circle is done with the compasses. It’s shown with a quadratic equation.
A point of intersection by drawing line is a …
【Using a ruler and compasses and solve it】
《Greek three hardest problems. Doubling the cube. Dividing an angle into three equally,and squaring the circle.》
A point of intersection by drawing lines is a solution of simultaneous equation,so it’s a solution of the linear equation and the quadratic one. In a word,we use ー × ÷ ＋ and find the value from each coefficient from the equations.
By the way,I can manage to understand the straight line means the linear equation,but why does the circle mean the quadratic equation? The point of intersection …
Lots of mathematicians have been worried about the problems for a long long long,no less than 2000 years,but on the other hand the problems have stimulated the development for mathematics which is related to the problems,but they reach the conclusion at last. To my surprise it was done in the 19th century. Unexpectedly it’s impossible.
Doubling the cube and dividing a triangle into three equally reach questions that we solve it by …
【Use a ruler and compasses and solve it】
《Greek three hardest problems. Doubling a cube. Dividing an angle into three equally. Squaring a circle》
Doubling a cube and dividing an angle into three equally reach the conclusion of solving a cubic equation by drawing figures. In general we need the cubic root so as to solve a cubic equation,but when drawing the figures,it’s just that we can find a square root.
The problem of squaring a circle is different from the other two essentially. If trying to demonstrate it’s impossible,it’s by far harder than the others. Its key is the demonstration that pi is a transcendental number. What is the transcended number?
If thinking of an integral number as coefficient,it can’t be any solution of any algebraic equation. We can show a squared root with a figure but we can’t a cubed root.
By the way,when expressing,I am forced to recognize that we have little knowledge on math,but I don’t feel like studying math. It’s too late to do.
【Euclid geometry】
《The best seller next to the Bible. It’s the base of mythology 方法論 on modern science》
It is said that geometry has started from surveying land in Ancient Egypt. It’s developed greatly in the era of Greece. Euclid formulated the perfect system of the geometry. It’s Euclid’s principles,but it’s not only the fruit of study by Euclid alone but by other Ancient Greek mathematician like Thales,Pythagoras,Hippocrates,and Eudoxos. It’s a classic which is said the best seller next to the BIble in Europe.
The best seller starts from definition which is an agreement with words like points,lines,surfaces,angles,or spheres. The definition changes into a selfevident truth 分かり切った真理,and gets to demonstration,for even if they tried to demonstrate,the chain of demonstration will never end,so they should start something which is accepted without any demonstration. Aristotle said like that,and Euclid recognized it very much.
The composition of definition,axiom,公理,theorem,and…
【Euclid’s geometry】
《The best seller next to the Bible. It’s the base of methodology on modern science》
The composition of definition,axiom,theorem,and demonstration done by Euclid has been the base not only for math but methodology of modern science widely as good example of scientific way. For example,Principia which was done by Newton is a theory of dynamics and gravitation. It’s written with the style of Principia.
Great part of Euclid’s principles had been adopted in Europe as textbook as it is until the 19th century. In addition some schools had used it until only nowadays.
The whole Principles are made up with 13 volumes, and the famous Pythagoras theorem is in the last part of the 1st volume,and other parts are conditions of congruent 合同 triangle,drawing figures of a regular polygon. The book deals with five kinds of regular polyhedron 多面体 in the 13rd volume.
The descriptions are so various that they aren’t only geometry but comparison theory,the theory of integral …
【Euclid’s geometry】
《The best seller next to the Bible. It’s the base of methodology on modern science》
The descriptions are so various that they aren’t only geometry but comparison theory,the theory of integral number,取りつくし方 which is base of integration 積分,but needless to say,to my sorrow,I know none of them.
It is said that the principles are immortal work on mathematic history,and it’s had influenced on not only math but thought and culture,however there is a point of issue about which lots of mathematicians have been worried in the Principles. It’s an axiom on parallel lines.
I’m going to express it in the next time at a slow speed,but before it I’m going to show five of Euclid’s axioms.
1 When there are 2 of any points,we can draw a line on the 2 points.
2 There is any segment 線分. We can extend both end of the segment.
3 If there is any point,and we regard it as a center,and we’ll draw a circle of which radius is any 任意
4 All the right angles are equal.
The last one is…
【Euclid’ geometry】
《The bestseller next to the Bible. It’s the base of methodology on modern science》
There are two lines and other one which cross. Roughly speaking the two lines are horizontal ones and the other is vertical one. There are two interior angles at the place where the two horizfontal lines and vertical one cross. Let’s suppose that the sum of the two interior angles were less than 2 right angles.
Then if the two horizontal lines extend from the point where the interior angles are less than 2 right angles,the two horizontal lines cross. To tell the truth I find it natural,but it turned out to be one of the most important question.
《There is other geometry which doesn’t belong to the compendition of Euclid》
It’s started from parallel lines. When looking at the 5 axioms of Euclid in the last response they are easy and natural,except for the last axiom. On the other hand,the fifth one seems to be a little more complicated. The fifth one is so called the axiom of …
【Euclid’s geometry】
《There is other geometry which doesn’t belong to the compendium 体系 of Euclid》
The fifth one is so called the axiom 公理 of parallel lines. If saying the axiom in a modern way,it’s the next one.
There is a straight line.There is other straight single line alone which passes on the one point outside the former line. The two straight lines are parallel. This is why the axiom is called the one of the parallel lines,but as you know,I’m not so intelligent and I’m not sure of it.
If there is a parallel line,there is two points at the both ends of the straight line,so if there is other straight line which is parallel to the former,there are two points at the both ends of the other one,so it means that the other one pass on two points,I’m sure,though I’m afraid I may make a blunder again.
To return to our main topic… The fifth axiom has been paid attention by plenty of mathematicians for a long time. For example they said,“I don’t think the fifth axiom is necessary …”
【Euclid’s geometry】
《There is other geometry which doesn’t belong to the compendium of Euclid》
They said,“I don’t think the 5th axiom is necessary,for we can arrive at the 5th one from other four axioms.” There used to be lots of mathematicians who tried to demonstrate their theory,but none of them succeeded in it. It has been mysterious for no less than two millenniums.
However,it was solved in the 19th century unexpectedly. Even if they tried to deny the 5th axiom,they can construct other compendium of geometry like the one of Euclid which doesn’t contradict. Some genius on mathe discovered it independently. It’s what is called the birth of non Euclidean geometry.
There is illustrations on the difference between the Euclidean geometry and non Euclidean one on the book of which title,数学のしくみ,however to my sorrow,without any illustration,I can’t describe what they tried to say in my poor English,so if you’re interested in it,please look over some books or search and so on.
【Euclid’s geometry】
《There is other geometry which doesn’t belong to the compendium of Euclid》
The non Euclidean geometry has been so different from others’ sense in everyday life that it wasn’t accepted by the society easily,in addition all the mathematicians who were engaged in studying the geometry led unfortunate lives.
Gauss was an influential figure in mathematician’s world,so he seemed to have great influence on other mathematicians,but even he avoided talking with others about the Non Euclidean Geometry in official place.
When some mathematicians were in difficulty because of the Non Euclidean Geometry,Gauss recognized it but he closed his eyes to their difficulty.
Instead of the 5the axiom,some mathematicians who were in difficulty like Lobachevskii and Bolyai adopted other axiom. It’s says like the next. “There is a straight.line. It’s A. There is a point outside the B. There are numberless straight lines which passes on the B and are parallel to the A.”
【Euclidean geometry】
《What I’ve thought》
Some mathematicians say,“There is a straight line. It’s A. There is a point outside the A. It’s B. There is a single straight line alone which passes on the B and is parallel to the A” it seems to be true in Euclidean geometry. I’m wondering if it has no contradiction at all,but I’m not sure of it.On the other hand what other mathematicians said is different,but they say it has also no contradiction at all,the book said so.
I hate to say,but I’m so stupid that I can’t understand any problem at all,but the Euclidean geometry and non Euclidean geometry reminds me of an episode on 矛盾.
A merchant said his pike which is equivalent to 矛was so strong that no shield could defend the pike. He also said his shield was so strong that no pike could break the shield.A person told the merchant to use his pike to his shield,and what happened? The merchant couldn’t answer.
To tell the truth,I can’t understand what is what!
【What is matrix 行列 and vector used for?】
《The matrix and vector are seemingly enumeration 羅列 of numbers,but it has deep meaning》
The problem is whether or not I can understand it…
It is often said that we the Japanese like a parade. When going to foreign countries,a group of the Japanese marched in,and they tried to act together.
There is the parade in math,but we don’t call it parade in math. It’s called matrix. As to the form itself,the people’s parade isn’t different from the matrix in math so much.
As to the matrix in math,the ones which are lined up are numbers,or letters which means some numbers,but if the numbers or letters are just lined up,there doesn’t seem to be mathematic significance very much. Then where is the significance of existence for the matrix?
Answering the question is the aim of this chapter,the author says like that. It looks like just an enumeration of numbers,but they make us feel things are magical. We learn the magical way and make use of it.
【Non Euclidean geometry】
《A straight line which isn’t straight》
A straight line is the one which is connected between the two points by the shortest course. Let’s think of the shortest course which connects the big cities on the earth,Los Angels and Tokyo. It’s not the straight line,but a curve.…
I’ve tried say there are several things which we can make use of the Euclidean geometry but to my sorrow I find it impossible,I have little knowledge on math.
However even if the Euclidean geometry isn’t perfect,it’s a compendium 体系 which doesn’t have contradiction as geometry. It says the conditions of congruent 合同 triangles,the theorem of sine,five centroid of a triangle.
I can understand how great the Euclidean geometry it is somehow…maybe,I’m not sure of it…
It’s just that I was excited a little and I’m embarrassed. Even if whether or not a straight lien is parallel to other,I don’t mind it at all. It seems meaningless,but there are lots of people who have devoted themselves to it…
【What is matrix 行列 and vector is used for?】
《The matrix and the vector are seemingly enumerations of numbers,but they have deep meanings》
The vector ranks with the matrix. While the vector is a special version of the matrix,it reacts with its own way. Both of the vector and matrix used to be a kind tool which we deal with natural scientific phenomena mathematically,but their practicable range has extended more and more,and they become the one which is connected with not only mathematic field but ordinary society.
Both of the matrix and vector has been put to practical use everywhere in the society as a means with which we arrange and analyze various information. They have played an active part in not only natural scientific field like physics,engineering,civil engineering,and architecture,but social science like business administration,statistics,and accounting.
In addition,they play an active role in the fiele which connects with business direct like marketing,production control…
【Addition and subtraction of the vector】
《Rolfe of calculation draw out of the power from the matrix and vector》
If looking at the matrix and vector blankly,it’s just that they are enumeration of numbers. When bringing rules of calucuration there,mutual connection is closer,and their abilities are shown. For example,even if we have an electric appliance of multifunction,without reading its manual,we can’t use it at will.
However,it doesn’t always mean that we have to steel ourselves against it. It’s not so difficult,so we don’t have to be worried about it. It’s not as hard as so much,it’s just that I want you not to spare some kind of effort a little,the author said like that.
By the way,the vector is shown with an arrow. Its direction is the one of the vector. Its length is the size of the vector.
I’m going to start from addition of the vector. When there are two kinds of vector,A,B,its addition means that the parallelogram 平行四辺形 of each side is A and B.and its diagonal line is…
【Addition and subtrsction on the vector】
《The rule of the calculation draws out of the power from the matrix and vector》
As for the last of my response on the subtitle,it’s not Rolfe but the rule. I made a mistake. Though it’s my own sentence,I was forced to be worried about it. I’m sorry for it.
When there are two kinds of vector,A,B,its addition means that a paralellgram of each side is A,and B,and its diagonal line is the vector,the sum of the addition of A and B on the vector. It’s a rule on the vector.
While there is the A of vector,there is other A which is minus. They are on the same line and its length is also same but its direction is opposite. It’s also the rule on the vector.
Being based on the rules,AB defines as A＋（ーB）,it’s an addition. If showing it with a component,I’m wondering if it’s an arrow,it’s easier. As to the addition and subtraction of the vector,when being shown with the component,we can think of them as the addition and subtraction of the component.
【Addition and subtraction on the vector】
《The rule of calculation draws out of the power from the vector and matrix》
The way of thinking of adding and subtracting of the component means a definition of addition and subtraction of the matrix as it is.
However there is one thing of which we should be careful. If each size of the vector and matrix isn’t the same,both of the addition and subtraction doesn’t stand up a bit.
【The way of multiplication on the matrix】
《The multiplication makes the vector and matrix move dyanamic》
If going on proceeding with the topic on the product 積 on the matrix,there is a few necessary words which I have to indicate.
Speaking of the 行列 in Japanese usually,it’s a single meaning which is the combination of the 行 and 列 ,but there is each meaning in two of the words in math. The 行 is a row which is a horizontal line. When there are a group of several lines,we call each row 1st row,second row…from the upper part.
As to a vertical the group of the …
【The way of multiplication on the matrix】
《The multiplication makes the vector and matrix move dynamically》
As to the vertical line of the group of the several lines,we call each of them a column. We call each of them first column,second column …from the left. As you may be aware of it,its the origin of the word,行列.
When the number of the row is M,and the number of the column is N,we call the matrix the one of which row is M and of which column is N. If it’s more simplified,it’s the matrix of M×N.
When each number of row and column is same,and each component of both the row and column is the same,we call it a square matrix.
Oh! I’m afraid I’ve failed to say an essential and basic thing. Each of the row and column in the matrix is made up with some numbers which is lined at random,and we call each number the component or element. When saying,the component of the 3rd row,2nd column,or the element of（3rd,2nd）,it means the element of the place where the 3rd intersects the 2nd.
【The theory of vector makes us fly in the sky】
《A plane flies in the sky by the composition of lots of power from the vector》
A plane which is heavier than the air can fly in the sky. A pitcher throws a curve or screwball in a game of baseball. When serving a tennis player puts a spin on a ball and smashes the ball into its opponent’s court. All of these are the same theory.
The principle which is common to all of them is the theorem of Bernoulli,which have had a great influence on almost all of the sports in which the players handle the ball or which is basic principle in aeronautical engineering 航空力学.
However it doesn’t seem to be so difficult,maybe,I hope so.
The theorem is when there is flow of air and fluid,the more it’s speedy the less its pressure. It’s a very simple theorem,though the author said like that, the more it’s speedy the bigger the pressure which it receives,I’m wondering.
If using the theorem and the way of thinking on the composition of vector we can …
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ぁしぃたぃゎーるど ２
ぁさぁ～☀️ ぉはょぅ～～😁✋ ぁっいけど しょくょくは ぁりますょ 😋 ぁっちゃんは ぁりますか～😋💓
55レス 429HIT 
寂しいな😢
涙もでない…
154レス 2304HIT 
おもう
おはよう。
43レス 689HIT 
みっちゃん雑記⑦
みなさん(ボンクラパゲ爺~🐷は除く) おはようごんざます(´∀｀)✋ みっちゃん🍀 いよいよ吾が輩も 今日からスマホデビューをします 因みに らくらくスマホではありませんので 悪しからず しぇばっ(｀_´ゞ
364レス 6548HIT 
ハコニワだけ
髪の手入れしてないのか栄養不足なのか 髪の毛傷んでる なんだかとても老けて見える
85レス 2138HIT



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カラオケ?8レス 63HIT

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たまに呟く⑦
東子さん、お返事ありがとね😄 私も割と指示出されないと動けない から、毎回支持出されたり 注意や、お叱りが凄く有り難いよ😅 お義姉さんもそうだと思うけど、 細かいところは分からないから、 東子さんの思いや情報が 上手く伝わるといいね👍
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思った事をレス！
終わりだ。
444レス 2211HIT 
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おっさん報道特集戦争孤児
TBSの報道特集の番組は、観ていて勉強になりますよ。 シリアの現在の様子や、日本の戦前戦後の様子などを詳しく放送しているので勉強になります。 戦争への備えは日本もいろいろとやっていますので、問題はないと思います。 おっさんは反日ではなく、安倍ちゃん支持のタカ派です。 おっさんの親戚は、男の三兄弟がいたけど、三兄弟とも戦死。 天皇が終戦の日に『深い反省の念に向かって』と、戦争の過ちをのべられていました。 一度、TBSの報道特集をご覧になってください。 絶句するようなことを報道しておりますので勉強になりますから。
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友達になってください
はい、波乱万丈です！ 毎日が死神どの闘いですよ。 こんな私でも、話し相手になりますか？ 成功も失敗の経験も、豊富ですよ。 きっと貴女にも、役立つでしょうね。 (苦笑)
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今日の出来事
不健康だな。 こんなの良くない。
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