From Math Images

Tesseract
Field: Geometry
Image Created By: Robert Neil Boyd
Website: rialian.com

Tesseract

This is an image of the generalization of the cube to the fourth dimension.

Basic Description

The tesseract is the four dimensional hypercube. it is analogous to the cube in the same way that the cube is to the square; and the square to the line; and the line to the point. Tesseracts are also known as tetracubes or hypercubes. Although hypercubes also refer to objects analogous to the three dimensional cube in even higher dimensions than four.

To begin understanding the tesseract it is helpful to start with a point and build up from there.

We will first start with a zero-dimensional object, a point, and then build up to our four-dimensional object, a tesseract. Think of how a line is formed from a point by moving the point out in one direction. The line is therefore a one-dimensional object.

Take this one dimensional object and move it out perpendicularly to form a square. We have now formed a two-dimensional figure, a square.

We can again move the square out in the direction perpendicularly to itself. We have now built a cube, which is a three-dimensional figure.

Based on everything we have built up so far, starting with the zero-dimensional point, we can now generalize to understand how to build the tesseract from the cube. In each step, we took the original figure and swept it out in a new direction perpendicular to every direction of the original object. We can then imagine a new direction the is perpendicular to every dimension of the cube; that is, this new direction is perpendicular to the length width and height of the cube. If we can imagine sweeping the cube out in this new direction we have now created a tesseract that exists in the fourth dimension.

References

University of Minnesota Geometry Center The Tesseract or Hypercube

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