Science, math and English 12th

【Putting a problem in the breast pocket always】

《Whether or not being able to step forward in the next?》

The answer is the one on the photo. The length on the line is 27.3cm. Its point is the angle crossing between the vertical line and other two lines is 120 degrees. If connecting with the degree of 120, it’s shorter than the diagonal lines.

You may have thought the shortest distance is the one connecting straight lines each other, but to tell the truth, as to the total distance, it’s the shortest. Two of the oblique lines alone are longer than the right answer, but the length….

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【Putting a problem in the breast pocket always】

《Whether or not being able to step forward in the next?》

…but the length connecting four points in total is shorter than the diagonal lines in total. Why?

As the part of the center line is used in two roads going for the diagonal direction mutually, if the line is connected with two points alone, without being the straight line, it’s longer like the photo, but as to the four points, as there is the part which is used mutually, the broken line is shorter than in total.

If looking at the shape of the v both of the up and the down…

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【Putting a problem in the breast pocket always】

《Whether or not being able to step forward in the next?》

…the diagonal lines made up with dotted line is by far bigger than the one made up with the solid line. Even if adding the central part, the one made up with the solid line is shorter than the one made up with the dotted line.

Everyone thinks somehow the diagonal lines is the shortest. Thinking somehow is right to some extent, but it(s sometimes in the wrong. It’s all right as long as using the math for the part which is in the wrong.

The student asked why is it the 120 degrees?

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【Putting a problem in the breast pocket always】

《Can we do a magic tricks?》

It’s the group theory is that the students study in university at first, and the author said he was going to do the magic tricks with the playing cards, making use of the group theory from non on.

There are five cards of 10, J, Q, K, and A here, and preparing for four kinds of cards like heart, spade, diamond, and clover and lining them up in order like the photo.

Collecting each of them and piling up and turning them over and shuffle them from now on, but the meaning of the shuffling the cards in this case is…

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【Putting a problem in the breast pocket always】

《Can we do the magic tricks with the math?》

…but the meaning of shuffling the cards in this case is dividing the cards as you like and overlapping them again like the photo. Wherever dividing cards, of how often doing them, it’s all right, so the order on the cards must have been at random.

I’m afraid I failed to say, the cards of the each number on the heart, diamond, clover, and spade is starting from A, K, Q, J, 10 and ending at 2, and piling up like the photo of the right page, and they are shuffled. After shuffling what happened to the…

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【Putting a problem in the breast pocket always】

《Even if the number is different, it’s equal?》

…it causes to discover a material which has new nature.

As long as being able to understand the cyclic permutation, we can see the secret of the conjuring trick by the playing cards.

Before shuffling the playing cards, they are put in a circular way like the upper part on the photo. How shuffling them, as it’s the cyclic permutation, so the order on the numbers doesn’t change.

After shuffling, it’s the one like the lower part on the photo. If taking the cards one by one from the top in the…

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【We’ve heard the breath from the math】

《How much can we trust the eyewitness report?》

Adding the probability of seeing the B and testifying it’s the B correctly to the one of seeing A and making a mistake it was the B, and dividing the one when seeing the B and saying it was the B correctly with the addition of the two of the probabilities like the photo.

When calculating it, it’s twelve twenty ninths, 41%, in short, the probability that the culprit is B is 41%, so the probability on the A is the culprit is 59%.

When saying the B is the culprit, the culprit becomes A at once with the…

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