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The story posits a world that exists only in two dimensions, and our narrator, a humble square, guides us through some of the implications of that. He is visited by a three-dimensional sphere, which he cannot comprehend until he sees the third dimension for himself. The role of women is explained, along with a class system, both of which are a satire of Victorian society at the time.
It poses several interesting thoughts, including the idea that higher dimensional beings have god-like powers over lesser dimensions. In the book, the three-dimensional Sphere has the ability to stand inches away from a Flatlander and observe them without being perceived, can remove 2-D objects from locked containers and " teleport" them via the third dimension apparently without traversing the space in between, and is capable of seeing and touching the inside and outside of everything in the 2-D universe; at one point, the Sphere gently pokes the narrator's intestines as proof of his powers. The book implies that higher dimensions than our own exist, and that a 4-D being could have the same powers over our world as the Sphere had over Flatland.
Numerous companions to Flatland have been written by various authors, including:
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