Projection of a Torus
From Math Images
- A four-dimensional torus projected into three-dimensional space.
Projection of a Torus |
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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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