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Geometry and Topology at the University of Illinois at Urbana-Champaign: Home

Geometry and Topology

Books on geometry and topology can be found in the Mathemathics Library Stacks on the main level shelved under call number ranges of 514 for topology and 516 for geometry.

What Is Geometry and Topology?

"Geometry (from the Ancient Greekγεωμετρίαgeo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space."  From "Geometry." Wikipedia, The Free Encyclopedia.  Web.  22 June 2015.

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects like the pointlinecircletriangle, and polygon), solid geometry (dealing with objects like the linesphere, and polyhedron), and spherical geometry (dealing with objects like the spherical triangle and spherical polygon). Geometry was part of the quadrivium taught in medieval universities.  Weisstein, Eric W. "Geometry." From MathWorld--A Wolfram Web Resource.

"topology, branch of mathematics, sometimes referred to as 'rubber sheet geometry,' in which two objects are considered equivalent if they can be continuously deformed into one another through such motions in space as bending, twisting, stretching, and shrinking while disallowing tearing apart or gluing together parts. The main topics of interest in topology are the properties that remain unchanged by such continuous deformations. Topology, while similar to geometry, differs from geometry in that geometrically equivalent objects often share numerically measured quantities, such as lengths or angles, while topologically equivalent objects resemble each other in a more qualitative sense.

The area of topology dealing with abstract objects is referred to as general, or point-set, topology. General topology overlaps with another important area of topology called algebraic topology. These areas of specialization form the two major subdisciplines of topology that developed during its relatively modern history." From "topology." Encyclopaedia Britannica. Encyclopaedia Britannica Online Academic Edition. Encyclopædia Britannica Inc., 2015. Web. 12 Feb. 2015.

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