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A while ago I read about a really old science fiction novel/novella (could have been more than a century old) where there weren't exactly people, but geometric figures in a 2-D world.

I think the protagonist (and maybe narrator) was a square and he visits the one dimension world. Later, his world is visited by a 3D geometric figure which takes him to the three dimensional world. The point was there are more dimensions than those the 2D-world figures knew.

That's all I can remember right now. Does anyone know the title of this novel?

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I presume that this would be "Flatland: A Romance of Many Dimensions" (written 1884 under the pseudonym "A.Square", real name Edwin Abbott Abbott).

Plot summary from wikipedia:

The story describes a two-dimensional world occupied by geometric figures, whereof women are simple line-segments, while men are polygons with various numbers of sides. The narrator is a square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions. The Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points", and attempts to convince the realm's monarch of a second dimension; but is unable to do so. He is himself visited by a three-dimensional sphere, which he cannot comprehend until he sees Spaceland (a tridimensional world) for himself. This Sphere visits Flatland at the turn of each millennium to introduce a new apostle to the idea of a third dimension in the hopes of eventually educating the population of Flatland. From the safety of Spaceland, they are able to observe the leaders of Flatland secretly acknowledging the existence of the sphere and prescribing the silencing of anyone found preaching the truth of Spaceland and the third dimension. After this proclamation is made, many witnesses are massacred or imprisoned (according to caste).

After the Square's mind is opened to new dimensions, he tries to convince the Sphere of the theoretical possibility of the existence of a fourth (and fifth, and sixth ...) spatial dimension; but the Sphere returns his student to Flatland in disgrace.

You can download the whole book for free here at Project Gutenberg.

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    They even made a film of it: youtube.com/watch?v=eyuNrm4VK2w – BadSkillz Feb 10 '15 at 11:02
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    If you liked Flatland you might enjoy Flatterland: Like Flatland, Only More So like I did. – 22nd Century Fza Feb 10 '15 at 11:10
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    Parodied in the Futurama episode "2-D Blacktop". – David Conrad Feb 10 '15 at 16:51
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    @22ndCenturyFza: The sequel "Sphereland" is also entertaining, as is Kee Dewdney's book "The Planiverse", which gives a more realistic look at a two-dimensional world. – Eric Lippert Feb 10 '15 at 17:31
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    The pseudonym "A. Square" was a deliberate pun on "Abbott Abbott"; one must presume he felt that adding "E." would not improve the joke. – MJD Feb 11 '15 at 20:23

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