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Edwin Abbott's "Flatland, A Romance of Many Dimensions"… is a story of two dimensional creatures dwelling in a planar universe. They can't conceive of a 3rd dimension, it's beyond their experience. The central character of Flatland is A. Square.

A. Square's perception of a sphere passing through his world is first a point, then a growing circle. As the Sphere's equator moves south of the plane, the circle shrinks and then vanishes. So the planar creature perceives the 3D object as a series of two dimensional sections. Here's my attempt to illustrate this notion:…

Abbott goes on to point out the possibility of 4 dimensional spaces (and higher). Euclidean 4 space is self consistent, adding a 4th dimension introduces no contradictions. A good mathematical look at higher dimensional spaces is Coxeter's "Regular Polytopes"… . There are physics theories that speculate our universe may have more than 3 spatial dimensions.

My interest in polychora and higher dimensional polytopes has led me to become a fan of Jonathan Bowers. He has been rendering sections of polytopes with POV-Ray for years. His shortened terms for polytopes have become widely used by those studying these objects.

So I am delighted Bowers (aka Hedron Dude) has started a gallery on Deviant Art. Please check him out:…; Thumbnails don't do his images justice. To appreciate the intricacy and detail of his art, full view is definitely needed.


Hop David
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1sand0s Featured By Owner May 9, 2013  Hobbyist Artisan Crafter
You may want to check out Flaterland, a modernization / unofficial sequel to Flatland, if you've not heard of it. It gives a solid discussion on an infinite number of dimensions, time travel, Klein (think that's right. The fourth dimensional one) bottles, and many other interesting tidbits I cannot recall. It is crammed with basic math ideals while staying at a layman's reading level, i.e. I understood it but super advanced math is over my head. Good stuff.
bear48 Featured By Owner Sep 13, 2012  Professional
I has been years since read that story
Hop41 Featured By Owner Sep 24, 2012
Besides Abbott's Flatland, there is A. K. Dewdney's Planiverse [link]
bear48 Featured By Owner Sep 24, 2012  Professional
that is another good one
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