2,536
pages

A chiliagon is a polygon with 1000 sides, it has a Schläfli symbol {1000}, one internal angle of a chiliagon is 179.64 degrees.

It is virtually indistinguishable from a circle to an observer, and it's perimeter differs from the circumference of the circle by 4 parts per million.

16th century philosopher René Descartes used 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 as if they were present", as when he imagines a triangle.

The imagination constructs a "confused reperesentation" which is no different from which one constructs a myriagon, a 10000 sided polygon.

However, he does clearly understand what a chiliagon is, just as he understands what a triangle is, and he's able to distinguish it from a myriagon.

Therefore, intellection is not dependent on imagination.

It is also reperesented by other philosophers, such as Immanuel Kant, saying it is "impossible for the eye to determine the angles of a chiliagon to be equal to 1996 right angles, or make any conjecture that approaches this proportion".

Gottfried Leibniz comments the use of a chiliagon by John Locke, noting that one can have the idea of the polygon without having an image of it, and thus distinguishing ideas from images.

Henri Poincaré used the chiliagon as evidence that "intuition is not necessarily founded on the evidence of the senses" because "we cannot reperesent to ourselves a chiliagon, and yet we reason by intuition on polygons in general, which include the chiliagon in that case".

René Discartés inspired philospher Roderick Chisholm and others with similar examples to make similar points.

Chisholm's speckled hen is perhaps, the most famous example of points, showing that one does not need to determine the exact number of speckles to imagine the image successfully.