What is the name of a 1000 Sided Polygon?
A 1000-gon chiliagon is a polygon with 1,000 sides.Philosophers use chiliagons to show ideas about the nature and workings of thought, meaning, and mental representation.
A regular chiliagon is represented by Schlfli symbol 1,000 and can be either a truncated 500-gon or twice-truncated 250-gon.
A regular chiliagon has an internal angle of 179.64.The area of a regular chiliagon has sides of length.
The number of sides is not a product of Fermat primes or a power of two.The regular chiliagon is not constructible.It is not constructible with the use of neusis or an angle trisector, as the number of sides is neither a product of Pierpont primes or powers of two and three.The quadratrix of Hippias is one of the techniques required for the construction of a chiliagon.A 9 angle can be constructed with compass and straightedge, which can then be quintisected twice using an auxiliary curve to produce the 0.36 internal angle required.
In his sixth meditation, René Descartes uses the chiliagon as an example to show the difference between imagination and pure intellection.When one thinks of a chiliagon, he doesn't imagine the thousand sides or see them as if they were present before him, as he does when one imagines a triangle.The imagination and myriagon are both examples of a "Confused representation."He is able to distinguish a chiliagon from a myriagon because he understands what a triangle is.Descartes claims that the intellect is not dependent on imagination as it is able to entertain clear and distinct ideas.Pierre Gassendi, a contemporary of Descartes, believed that the word "chiliagon" meant a figure with a thousand.[3]
The example of a chiliagon is used by other philosophers.It is impossible for the eye to determine the angles of a chiliagon to be the same as 1996 right angles.John Locke uses the chiliagon as a way to distinguish ideas from images, and as an example, says that one can have an idea of the polygon without an image.[5]
The chiliagon is an example of why intuition is not necessarily founded on the evidence of the senses.[6]
Similar examples have been used to make similar points by other 20th-century philosophers.The "speckled hen", which does not have a determinate number of speckles to be successfully imagined, is perhaps the most famous of these.[7]