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Spheres
Author

Rolf Sulanke
Organization: Humboldt-University Berlin
Department: Mathematics
URL: http://www-irm.mathematik.hu-berlin.de/~sulanke
Old MathSource #

0210-092
Revision date

2000-12-12
Description

The packages contain basic functions and modules for working in pseudo-euclidean vector spaces, and in the spaces of spheres, circles, and point pairs (= 0-spheres) in Moebius and Euclidean geometries. The notebooks treat examples and complete this material. Conformal invariants classifying pairs of subspheres, geodesics of the sphere space, the circle space, and the 0-sphere space are considered. Many constructs are valid for any finite dimension and any index of the scalar product. The 3-dimensional case is emphasized. 3D-graphics are animated with the OpenGL-Viewer of MathGL3d.
Subjects

*Mathematics > Geometry > Plane Geometry
*Mathematics > Geometry > Solid Geometry
*Mathematics > Geometry > Surfaces
Keywords

spheres, circles, throws, pseudo-euclidean geometry, Moebius geometry, conformal invariants, stationary angles, orthogonalization, vector objects, matrix objects, spiral surfaces, inversions, tubes, Killing forms, stereographical projections, MathGL3d
Downloads Download Wolfram CDF Player

Download
spheres.txt (13.8 KB) - ASCII text file
Download
OpenGLViewer.m (1.5 KB) - Mathematica package
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eusphere.nb (157.8 KB) - Mathematica notebook
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euvec.m (14.1 KB) - Mathematica package
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init.m (1.5 KB) - Mathematica package, master package
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liealg.m (13.7 KB) - Mathematica package
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mcirc.m (15.4 KB) - Mathematica package
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mcircles.nb (269.8 KB) - Mathematica notebook
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mspher.m (8 KB) - Mathematica package
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mspheres.nb (131.8 KB) - Mathematica notebook
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pairs.nb (171.9 KB) - Mathematica notebook
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pseuklid.nb (82.2 KB) - Mathematica notebook
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pseuvec.m (8.6 KB) - Mathematica package
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sphs4.tgz (197.1 KB) - gzipped tar file of all items
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sphs4.zip (202 KB) - zipped file of all items
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spiralsf.m (2.2 KB) - Mathematica package