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 (D_{1000}) 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
This result differs from the area of its circumscribed circle by less than 0.0004%.
Because , 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
 ^ Meditation VI by Descartes (English translation).
Regular polygons Listed by number of sides 1–10 sides 11–20 sides Others  Triacontagon
 Chiliagon
 Apeirogon
Star polygons Categories: Polygons
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Look at other dictionaries:
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