Flatterland is a 2001 book by mathematician and science popularizer Ian Stewart about non-Euclidean geometry. It was written as a sequel to Flatland, an 1884 novel that discussed different dimensions.
Almost 100 years after A. (which we find out stands for Albert) Square's adventures in Spaceland that were related in Flatland, his great-great-granddaughter, Victoria Line (Vikki), finds a copy of his book in her basement. This prompts her to invite a sphere from Spaceland to visit her, but instead she is visited by the "Space Hopper" (a character looking somewhat like the "Space Hopper" children's toy with a gigantic grin, horns and a spherical body). The Space Hopper, more than being able to move between Flatland and Spaceland, can travel to any space in the Mathiverse, a set of all imaginable worlds. After showing Vikki higher dimensions, he begins showing her more modern theories, such as fractional dimensions and dimensions with isolated points. Topology and hyperbolic geometry are also discussed, as well as the Projective "Plain" (complete with intersecting "lions") and the quantum level. Hopper and Victoria also visit the Domain of the Hawk King to discuss time travel and the Theory of Relativity.
Ian Stewart often includes puns and topical references in his popular writing, and "Flatterland" is no exception.
- The heroine's name, Victoria Line, and her mother, Jubilee Line, are both lines on the London Underground.
- Her great-great grandfather's name is the fictional Albert Square in London, from the BBC soap opera EastEnders. Her father, Grosvenor Square, is the square situated in the Mayfair district of London.
- Hawk King is a simple pun on the surname of the famous astrophysicist Stephen Hawking, whose research includes the Theory of Relativity and Hawking radiation.
- Vikki, while traveling in the Topological Dimension, also meets a one-sided cow named Moobius (derived, of course, from the Möbius strip) who sells her milk in Klein bottles (the strip and the bottle both being one-sided topological figures).
- The Doughmouse, the Harsh Mare and the Mud Hutter are the counter-parts in Topologica (the rubber-sheet continent) of Carrol's Doormouse, March Hare, and Mad Hatter, respectively. The Doughmouse works with a dough tea set, dough being flexible.
- ISBN 0-333-78312-3 Original hardback from Macmillan
- ISBN 0-7382-0442-0 Hardback edition by Perseus
- ISBN 0-7382-0675-X Paperback edition by Perseus
- ISBN 0-330-39377-4 Mass-market edition by Pan