Flatland

Complex and unclassifiable, Flatland combines social satire and religious allegory in a story set in an alternate universe of geometric forms.

Flatland (1884) is an influential mathematical fantasy that simultaneously provides an introduction to non-Euclidean geometry and a satire on the Victorian class structure, issues of science and faith, and the role of women. A classic of early science fiction, the novel takes place in a world of two dimensions where all the characters are geometric shapes. The narrator, A Square, is a naïve, respectable citizen who is faced with proof of the existence of three dimensions when he is visited by a sphere and is forced to see the limitations of his world.

The introduction to this Broadview Edition provides context for the book’s references to Victorian culture and religion, mathematical history, and the history of philosophy. The appendices contain contemporary reviews; extracts from the work of fellow mathematical fantasy writer/mathematician Charles Hinton; Hermann von Helmboltz’s “The Axioms of Geometry” (1870); and autobiographical passages from Abbott’s The Kernel and the Husk (1886).