A movie to explain mathematics while Japanese mathematicians use magic tricks is on sale

Hidetori positiveAlthough he was originally a French classicalist, he suddenly entered the world of mathematics and became a mathematicianCambridge University Trinity CollegeHe also has a background of a different color that he also served as mathematical chief. In order to learn happily while feeling familiar with mathematics, Mr. Toki branded movies to explain mathematics in an easy-to-understand manner while using magic tricks and toys,NumberphileIt is open to the channel of. In the following movie as an example, commentary using paper and coasters using magic tricks has been made.

Round Peg in a Square Hole - Numberphile - YouTube


It is a very ordinary round coaster that Mr. Toki is showing to the camera.


And a single piece of paper with a square hole in the center is also available. It is clear that the diagonal of the square is smaller than the diameter of the coaster.


Although it seems that the coaster can not pass through this hole anyway, Toki branch folds paper ......


When trying to pass a coaster through a hole ......


For some reason the coasters passed through the hole.


I will open the folded paper again and try to compare the coaster with the hole, but it does not look like it is torn and spreading, the hole remains smaller than the coaster as before.


Why is it possible such a strange thing?


First of all let's just fold this paper and check it. In this case, the diagonal of the square that is in the hole is the gap with the greatest distance.


However, as mentioned earlier, it is clear that it is impossible for a coaster to pass through a hole because the diameter of the coaster is larger than the diagonal.


So fold the paper in three dimensions so that the planes are brought together.


Then, as the flat paper becomes three-dimensional, the angle between the sides opens.



Finally, the two sides became straight.


As the shape of the hole changed, the size changed and the coasters were able to pass through.


If A is the length of one side of the square, the diagonal is (A × √ 2). On the other hand, the length becomes (A × 2) when the square becomes a straight line. The handwriting of this handicraft is in the size of the square hole drilled in the paper.


In order to make the coaster look as if it can not pass through the hole, it is first necessary to cut out the hole so that the length of the square diagonal (A × √ 2) is smaller than the diameter of the coaster.


However, if you fold the paper three-dimensionally and make the square into a straight line, the hole will be the length of two sides of the square. To make it possible to pass through the coaster at this time, the length of two sides (A × 2) must also be larger than the diameter of the coaster. When setting the diameter of the coaster as R, it is a magic trick to make a hole to clear the two conditions "(A × √ 2) R".


Because Tokiwa uploads various other movies in addition to others, the person who is worrisomeTsubasa's movie list uploaded to NumberphileIt is also ant to check.