# Chiliagon

Regular chiliagon

A whole regular chiliagon is not visually discernible from a circle. The lower section is a portion of a regular chiliagon, 200 times larger than the smaller one, with the vertices highlighted.
Edges and vertices 1000
Schläfli symbol {1000}
Coxeter–Dynkin diagram
Symmetry group Dihedral (D1000)
Internal angle
(degrees)
179.64°
Properties convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a chiliagon (pronounced /ˈkɪli.əˌgɑn/) is a polygon with 1000 sides.

## Properties

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

$A = 250a^2 \cot \frac{\pi}{1000} \simeq 79577.2\,a^2$

This result differs from the area of its circumscribed circle by less than 0.0004%.

Because $1000=2^3 \times 5^3$, it is not a product of distinct Fermat primes and a power of two, thus the regular chiliagon it is not a constructible polygon.

## Philosophical construction

René Descartes uses the chiliagon as an example in his Sixth meditation to demonstrate the difference between pure intellection and imagination. He says that, when one thinks of a chiliagon, he "does not imagine the thousand sides or see them as if they were present" before him -- as he does when one imagines a triangle, for example. The imagination constructs a "confused representation," which is no different from that which it constructs of a myriagon. However, he does clearly understand what a chiliagon is, just as he understands what a triangle is, and he is able to distinguish it from a myriagon. Therefore, the intellect is not dependent on imagination, Descartes claims, as it is able to entertain clear and distinct ideas when imagination is unable to.[1]

## References

1. ^ Meditation VI by Descartes (English translation).

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### Look at other dictionaries:

• Chiliagon — Chil i*a*gon, n. [Gr. ?; chi lioi a thousand + ? angle.] A plane figure of a thousand angles and sides. Barlow. [1913 Webster] …   The Collaborative International Dictionary of English

• chiliagon — noun /ˈkɪlɪæɡən/ (rare) A polygon with a thousand vertices and a thousand edges. , 1995: If Kants claim is just that it is impossible to have a sensory experience of the absence of space, then by contrast it is not impossible to have a sensory… …   Wiktionary

• chiliagon — (Gk., chilioi, 1,000 + gonia, angle) A closed plane figure with 1,000 internal angles (thus almost indistinguishable from a circle). Chiliasm is the doctrine that Christ will come again and reign for 1,000 years, a form of millenarianism …   Philosophy dictionary

• chiliagon — chilˈiagon noun A plane figure with 1000 angles • • • Main Entry: ↑chiliad …   Useful english dictionary

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• List of mathematical shapes — Following is a list of some mathematically well defined shapes. See also list of polygons, polyhedra and polytopes and list of geometric shapes.0D with no surface*point1D with 0D surface*interval *line2D with 1D surface*Bézier curve: ( As + Bt )… …   Wikipedia

• Star polygon — Set of regular star polygons {5/2} {7/2} …   Wikipedia

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