¶ Tetrahedron Inside-Outing of Tetrahedron (1)
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"Now it is also possible for me to push in on the face of the tetrahedron and so it gets smaller. I am pushing the face towards its opposite face and it gets smaller. When it is getting smaller, what do I mean? I mean its edges are getting shorter, the areas of its surfaces are decreasing, but they decrease at a very much higher rate than that at which the lines become shorter. The lines are shortening at the rate of the first power and the areas are shortening at the rate of the second power. The volume is getting smaller at the third power rate-- a very much higher velocity, so you have three rates of change in the phenomenon called size. Symmetry is still there. There is nothing to do with symmetry and nothing to do with the fact that it has four vertexes, nothing to do with its six edges, nothing to do with its 60-degree angles, 60-degreeness, fourness of vertex, fourness of face, sixness of edge and symmetry are all constants and they are in no way altered by the change in size. Size is simply three different things: linear, areal and volumetric rates of change.
"Let me then move this face of the tetrahedron. I am pushing the face towards the opposite vertex. Now it has no size at all. The product of the first power, second power and third
