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Gallery of Pseudospheres

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Author:Robert McLachlan
Description: A short version of an article by Robert McLachlan, "A gallery of constant-negative-curvature surfaces," (Mathematical Intelligencer, Fall 1994, 31-37) about "pseudospherical" surfaces, equally "saddle-shaped" at each point, extensively studied in the nineteenth century and now having a minor revival because of connections with integrable systems. The product of their two curvatures at each point is -1 everywhere, so in a sense they are the opposite (or hyperbolic counterpart) of an ordinary sphere. They can be covered by coordinates known as "Tchebyshev nets."

Levels: College, Research
Languages: English
Resource Types: Graphics, Articles
Math Topics: Hyperbolic Geometry

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