#### Title

The Kakeya Needle Problem

#### Date

5-28-2015 2:15 PM

#### End Time

28-5-2015 3:00 PM

#### Location

Ackerman (ACK) 141

#### Department

Mathematics

#### Session Chair

Matthew Nabity

#### Session Title

Pi Mu Epsilon Induction and Speaker

#### Faculty Sponsor(s)

Matthew Nabity

#### Presentation Type

Presentation

#### Abstract

In 1917, Japanese mathematician Soichi Kakeya posed the following question. ``In the class of figures in which a segment of length 1 can be turned through 360°, remaining always within the figure, which one has the smallest area?’’ In other words, if a unit needle is dipped in ink and placed in the plane, what is the least area inked out while maneuvering the needle so as to exchange its endpoints? In 1928, Russian mathematician A.S. Besicovitch answered the question with a surprising result. In this talk, we will explore sets in which the needle can be reversed, also known as Kakeya sets, as well as develop the figure needed for Besicovitch’s solution.

#### Recommended Citation

Rosales, Kendall, "The Kakeya Needle Problem" (2015). *Academic Excellence Showcase Schedule*. 261.

http://digitalcommons.wou.edu/aes_event/2015/all/261

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The Kakeya Needle Problem

Ackerman (ACK) 141

In 1917, Japanese mathematician Soichi Kakeya posed the following question. ``In the class of figures in which a segment of length 1 can be turned through 360°, remaining always within the figure, which one has the smallest area?’’ In other words, if a unit needle is dipped in ink and placed in the plane, what is the least area inked out while maneuvering the needle so as to exchange its endpoints? In 1928, Russian mathematician A.S. Besicovitch answered the question with a surprising result. In this talk, we will explore sets in which the needle can be reversed, also known as Kakeya sets, as well as develop the figure needed for Besicovitch’s solution.