''Sphereland: A Fantasy About Curved Spaces and an Expanding Universe'' is a 1965 translation of , a 1957 novel by

Dionys Burger Dionys Burger (10 July 1892, Amsterdam - 19 April 1987) was a Dutch secondary school physics teacher and author of the novel ''Sphereland ''Sphereland: A Fantasy About Curved Spaces and an Expanding Universe'' is a 1965 translation of , a 1957 no ...

, and is a sequel to ''

Flatland ''Flatland: A Romance of Many Dimensions'' is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by "A Square", the book used the fictional two-dime ...

'', a novel by "A Square" (a pen name of

Edwin Abbott Abbott Edwin Abbott Abbott (20 December 1838 – 12 October 1926) was an English schoolmaster, theologian, and Anglican priest, best known as the author of the novella ''Flatland'' (1884). Biography Edwin Abbott Abbott was the eldest son of ...

). 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.

Plot summary

The

Circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...

s (who are appointed as priests/leaders of Flatland due to their many sides, or an appearance thereof) do not take A Square's revelation about a

third dimension Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...

to be accurate, and A 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 A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, an ...

with more than 180 degrees, he is fired from his job and generally considered a crackpot, since such a construction is not possible in

Euclidean geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's approach consists i