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SpherelandSphereland is a 1965 novel by Dionysus Burger, and is a sequel to Flatland, a novel by A. Square (A pen name of Edwin Abbott Abbott). The novel expands upon the social and mathematical foundations on which Flatland is based. It is markedly different from the first novel in that it has a more prosaic ending and treatment of society. The Circles (who are appointed as priests/leaders of flatland due to their many sides, or an appearance thereof) do not take the Square's revelation about a third dimension to be accurate, and the Square is ostracized by his community. However, when a prominent surveyor finds a triangle with more than 180 degrees. Since such a construction is not possible in two dimensional geometry, he is fired from his job and generally considered a crackpot. He eventually makes friends with the square, since they are both outcasts from the community. Together, they come upon a theory to explain the erroneous measurements: They actually live on a very large sphere, and the triangles have more than 180 degrees due to being inscribed on a non-planar surface. With help from the sphere from the first novel, they are able to prove this theory. Eventually, the leaders of Flatland are forced to agree with the finding of the two squares, and monuments are dedicated to two of them for being the first to escape the 2-dimensional thinking of their universe.
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