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The Knife: A Dimension Splicer

Adam Russell Halvorsen
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The fourth dimension is an intriguing space, home of complex figures literally beyond the imagination. Although it is impossible to `see' even the simplest of these objects in their totality, it is necessary to cheat, and either project their entire images onto three-space or take three-dimensional cross sections of the objects, and by viewing an animation of adjacent cross sections, get an idea of what the entire object looks like. One of the greatest barriers in looking at these objects lies in the difficulty of `opening them up` so that their three-dimensional cross sections can be observed. 4DKnife.m is a Mathematica package written to see and study these fascinating objects in a variety of ways taking a very understandable yet powerful new approach.

*Mathematics > Geometry > Solid Geometry

fourth dimension, pure mathematics, geometry, 4D Slicer, the knife, 4DSlicer
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4DKnife.doc (30.1 KB) - Plain-text documentation
4DKnife.m (19.3 KB) - Mathematica package
Examples.m (2.6 KB) - Common examples