¶ Module
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Index Entry
Module: A Module:
"Take a one-quarter tetrahedron and make a line which is a perpendicular bisector from any given vertex to the opposite edge. Those three perpendicular bisectors cut the one-quarter tetrahedron into six pieces of pie. This quarter-tetrahedron divided into six symmetrical components; each one of them must be one-sixth of a quarter–and this is one-twentyfourth of a tetrahedron. This is a very interesting piece of geometry because we find that it can be unfolded–you can make it out of paper if you like. These are the angles you actually have in your paper: 30 degrees; 35 degrees and 16 minutes; and 19 degrees and 28 minutes. Those do not add up to 90°. This is not a 90° angle. This is an asymmetrical triangle with three different size edges. It is not 90° and not 60°. It has these folded edges and you can fold it up, but as it lays out it becomes a whole triangle, even though it is not 90° angles.
"If you take a regular tetrahedron and take its three slanting faces and open them up as if they were hinged on the base, you will have for the base an equilateral triangle. In other words, the regular equilateral triangle: bisect its edges and fold up the three corners and you have a tetrahedron. A tetrahedron
¶ Citations
- Oregon Lecture #6, p.219, 10 Jul’62
