# Definition:Kakeya's Constant

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## 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 $180 \degrees$:

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

This sequence is A093823 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Also known as

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

## Also see

## Source of Name

This entry was named for Soichi Kakeya.

## Sources

- 1983: François Le Lionnais and Jean Brette:
*Les Nombres Remarquables*... (previous) ... (next): $0,28425 82246 \ldots$

- Wisewell, Laura and Weisstein, Eric W. "Kakeya Needle Problem." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/KakeyaNeedleProblem.html