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