3:00 PM - 3:50 PM
[P-66] Kakeya Problem
Keywords:Kakeya Problem(掛谷問題)、Kakeya Set(掛谷集合)、Deltoid curve(デルトイド)
100 years ago, a Japanese mathematician Soichi Kakeya (1886～1947) proposed the following problem. “What is the smallest area required to rotate an 1 cm segment 180°?” This is called the Kakeya problem, and the set (shape) which satisfies the condition is called a Kakeya set.
The answer to the problem was first believed to be Reuleaux triangle by Kakeya, but as the time goes by, many mathematicians made another Kakeya set with smaller area than that of Reuleaux triangle. In the end, Abram Samoilovitch Besicovitch considered a figure with the area being any positive number. Therefore, by Besicovitch, it is proved that we can create a Kakeya set with the area as small as we want.
One of the idea to make the area of the set smaller is to move the segment along lines. The area of lines are 0, so translating the segment along the line allows us to move the segment in a long distance.
Another idea is to cut an equilateral into small pieces and combining again. This allows to rotate the segment 60° with a shape which has much smaller area.
We are going to go through the ideas concretely in our poster, which leads to understand better about creating Besicovitch’s answer to Kakeya’s enigma.
The answer to the problem was first believed to be Reuleaux triangle by Kakeya, but as the time goes by, many mathematicians made another Kakeya set with smaller area than that of Reuleaux triangle. In the end, Abram Samoilovitch Besicovitch considered a figure with the area being any positive number. Therefore, by Besicovitch, it is proved that we can create a Kakeya set with the area as small as we want.
One of the idea to make the area of the set smaller is to move the segment along lines. The area of lines are 0, so translating the segment along the line allows us to move the segment in a long distance.
Another idea is to cut an equilateral into small pieces and combining again. This allows to rotate the segment 60° with a shape which has much smaller area.
We are going to go through the ideas concretely in our poster, which leads to understand better about creating Besicovitch’s answer to Kakeya’s enigma.