# Projection of a Torus

(Difference between revisions)
 Revision as of 15:13, 4 June 2009 (edit)← Previous diff Revision as of 15:14, 4 June 2009 (edit) (undo)Next diff → Line 6: Line 6: 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

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