Projection of a Torus

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|ImageDesc=The four-dimensional object is defined parametrically by
|ImageDesc=The four-dimensional object is defined parametrically by
|AuthorName=Thomas F. Banchoff
|AuthorName=Thomas F. Banchoff
 +
|AuthorDesc=Thomas F. Banchoff is a geometer, and a professor at Brown University since 1967.
 +
|SiteName=The Mathematics of In- and Outside the Torus
 +
|SiteURL=http://www.math.brown.edu/~banchoff/art/PAC-9603/tour/torus/torus-math.html
|Field=Algebra
|Field=Algebra
|InProgress=Yes
|InProgress=Yes
}}
}}

Revision as of 15:29, 4 June 2009

Image:inprogress.png
Projection of a Torus
A four-dimensional torus projected into three-dimensional space.

Contents

Basic Description

It is impossible to visualize a complete four-dimensional object, since we have only ever lived in three-dimensional space. However, there are ways to capture parts of the four-dimensional object in three-dimensional space. A useful analogy is a world map. We can capture the essence of the three-dimensional globe on a two-dimensional map, but only by using a projection, which distorts the three-dimensional object in some way to fit on a two-dimensional surface.

A similar process is carried out to create this page's main image. A four-dimensional object, described further below, is projected into three-dimensions using two different projections.

A More Mathematical Explanation

The four-dimensional object is defined parametrically by

The four-dimensional object is defined parametrically by




Teaching Materials

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About the Creator of this Image

Thomas F. Banchoff is a geometer, and a professor at Brown University since 1967.








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