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Author:Ivars Peterson (MathTrek)
Description: When topologists started to explore the world of geometric forms in higher dimensions, they found that neither the intuition nor the vocabulary of ordinary geometry was sufficient to describe and classify the new forms they discovered. They introduced "manifold" as a general term for a certain common type of higher-dimensional geometric object. In everyday parlance, a manifold is a pipe or chamber bristling with subsidiary tubes. Its mathematical manifestation encompasses surfaces that locally appear flat, or Euclidean, but on a larger scale may bend and twist into exotic and intricate forms. A circle, although it curves through two dimensions, is an example of a one-dimensional manifold, or one-manifold...

Levels: Middle School (6-8), High School (9-12), College
Languages: English
Resource Types: Articles
Math Topics: Higher-Dimensional Geometry, Topology

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