# Definition:Kakeya's Constant

## Definition

Kakeya's constant is defined as the area of the smallest simple convex domain in which one can put a line segment of length $1$ which will coincide with itself when rotated $180 \degrees$:

$K = \dfrac {\paren {5 - 2 \sqrt 2} \pi} {24} \approx 0 \cdotp 28425 \, 82246 \ldots$

## Also known as

Kakeya's constant is also known as the Bloom-Schoenberg number, for Melvin Bloom and Isaac Jacob Schoenberg.

## Source of Name

This entry was named for Soichi Kakeya.