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Chiliagon : ウィキペディア英語版
Chiliagon

In geometry, a chiliagon (pronounced ) is a polygon with 1000 sides or 1000-gon. Several philosophers have used it to illustrate issues regarding thought.
== Regular chiliagon==
A ''regular chiliagon'' is represented by Schläfli symbol and can be constructed as a truncated 500-gon, t, or a twice-truncated 250-gon, tt, or a thrice-truncated 125-gon, ttt.
The measure of each internal angle in a regular chiliagon is 179.64°. The area of a regular chiliagon with sides of length ''a'' is given by
:A = 250a^2 \cot \frac \simeq 79577.2\,a^2
This result differs from the area of its circumscribed circle by less than 4 parts per million.
Because 1000 = 23 × 53, the number of sides is neither a product of distinct Fermat primes nor a power of two. Thus the regular chiliagon is not a constructible polygon. Indeed, it is not even constructible with the use of neusis or an angle trisector, as the number of sides is neither a product of distinct Pierpont primes, nor a product of powers of two and three.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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