# Directory of Higher Dimensional Resources

Higher-dimensional geometry considers the properties of figures with four or more dimensions. An object of zero dimensions is a single point. It needs no coordinates. The first dimension takes up the space of a line, and has only one coordinate (the x coordinate). The second dimension takes up the space of a plane, and has two coordinates, x and y. Examples of two-dimensional shapes are circles and squares. The third dimension is all space that we know of, and it uses three coordinates, x, y, and z. Examples of three-dimensional shapes are cubes, spheres, and cones. The fourth dimension is space with an extra dimension beyond the third, and it uses four coordinates, x, y, z, and w. Examples of four-dimensional shapes are the tesseract and the hypersphere.

## Resources in This Category

• #### Four-Space Visualization of 4D Objects

http://steve.hollasch.net/thesis/
Mathematical and computer programming oriented approach. Discusses wireframe rendering and ray-tracing.

• #### Fourth Dimension: Tetraspace

http://hi.gher.space/
A discussion of rotation, levitation, wheels, and bodies of water. Classification of "rotatopes" (cubes, spheres, and cylinders), and a Java applet to visualize projections and intersections of the shapes. Includes book reviews, a glossary, links, and a forum.

• #### Hyper Dimensia

http://www.hyperdimensia.com/
Tutorial which aims to give readers an understanding of the fourth dimension by having them use a java applet to rotate a cube and a hypercube to see multiple views of the shapes at once.

• #### HyperCube by Harmen

http://harmen.vanderwal.eu/hypercube/
A short introduction to the fourth dimension, plus a hypercube java applet game.

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