Sphereland
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Sphereland is a 1965 novel by Dionys 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.
[edit] Plot
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. Then after some time, society becomes more open to the ideas of Spaceland and, overall, to change and advancement. However, when a prominent surveyor finds a Triangle with more than 180 degrees, he is fired from his job and generally considered a crackpot, since such a construction is not possible in Euclidian geometry. He eventually makes friends with the grandson of A. Square, a Hexagon, because he is a mathematician and scientist. Together, they come upon a theory to explain the unusual 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. However, the established scientific community is not able to comprehend the idea proposed by the two and thus they do not attempt to enlighten Flatland. Furthermore, as the residents of Flatland advance, they begin to travel in space and they see distant worlds like their own and the surveyor tries to find the distance between their world and these distant worlds, using trigonometry and radar. From his calculations, he and the hexagon determine that the universe is expanding and thus they again try to reveal this theory to the outside world but again it is not accepted. Therefore, like his grandfather in the previous novel the hexagon writes a book that is not to be opened until the theory of the expanding universe is discovered and accepted by others. Then they live a low-key existence without any more contact with the sphere.
[edit] Purpose
As with Flatland itself, the Flatlanders' encounter with the third dimension are intended to encourage consideration of how higher dimensions would appear to us. In this case, specifically the concept that the universe is the three-dimensional surface of a four-dimensional hypersphere.
