Topology - Research Article from Macmillan Science Library: Mathematics

This encyclopedia article consists of approximately 3 pages of information about Topology.

Topology - Research Article from Macmillan Science Library: Mathematics

This encyclopedia article consists of approximately 3 pages of information about Topology.
This section contains 657 words
(approx. 3 pages at 300 words per page)
Buy the Topology Encyclopedia Article

Topology is sometimes called "rubber-sheet geometry" because if a shape is drawn on a rubber sheet (like a piece of a balloon), then all of the shapes you can make by stretching or twisting—but never tearing—the sheet are considered to be topologically the same.

Topological properties are based on elastic motions rather than rigid motions like rotations or inversions. Mathematicians are interested in the qualities of figures that remain unchanged even when they are stretched and distorted. The qualities that are unchanged by such transformations are said to be topologically invariant because they do not vary, or change, when stretched.

Topology

As an example, the figure shows a triangle, a square, a rough outline of the United States, and a ring. The first three shapes are topologically equivalent; we can stretch and pull the boundary of the square until it becomes a circle or the U.S...


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This section contains 657 words
(approx. 3 pages at 300 words per page)
Buy the Topology Encyclopedia Article
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Topology from Macmillan. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.