Projection of a Torus
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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 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. | ||
- | + | |ImageDesc=The four-dimensional object is defined parametrically by | |
|AuthorName=Thomas F. Banchoff | |AuthorName=Thomas F. Banchoff | ||
|Field=Algebra | |Field=Algebra | ||
|InProgress=Yes | |InProgress=Yes | ||
}} | }} |
Revision as of 15:14, 4 June 2009
Projection of a Torus |
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Projection of a Torus
- A four-dimensional torus projected into three-dimensional space.
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
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