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An open surface with X-, Y-, and Z-contours shown.

In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R³ — for example, the surface of a ball. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.

• See also: Wikipedia, Wiktionary

• Related: Volume form, Poincaré metric, Area element, Roman surface, Boy's surface, Tetrahemihexahedron

The Classification of Surfaces and the Jordan Curv... The Classification of Surfaces and the Jordan Curve Theorem www.maths.ed.ac.uk/~aar/jordan/ - Web

Math Surfaces Gallery, with 60 ~surfaces and Java ... Math Surfaces Gallery, with 60 ~surfaces and Java Applet for live rotation viewing xahlee.org/surface/gallery.html - Web

Math Surfaces Animation, with JavaScript (Canvas H... Math Surfaces Animation, with JavaScript (Canvas HTML) for tens surfaces rotation viewing wokos.nethium.pl/surfaces_en.net - Web

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The Classification of Surfaces The Classification of Surfaces www.math.ohio-state.edu/~fiedorow/math655/classification.html - Web

History and Art of Surfaces and their Mathematical... History and Art of Surfaces and their Mathematical Models maxwelldemon.com/2009/03/21/surfaces-1-the-ooze-of-the-past/ - Web

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