¶ Spherical Triangle
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RBF Definitions
"What you and I have been brought up on as a triangle is the most extreme case of the most local aspect of what is inherently a spherical triangle. Even if we imagine it, it is still special case. And when we make it conceptual the brain immediately makes it special case. The brain is designed for special case.
"I say to a child: Draw a triangle. And he says: Where? And I say: Draw a triangle. And he draws it on the ground. The triangle divides the whole Earth into two areas: the complementary very big triangle and the local little triangle. Concave and convex are not the same: ergo, we have inherently four triangles. And the four triangles mean the manifestation of our friend the tetrahedron which is always there for the accountability. There is nothing you can do without the tetrahedron being there.
“A plane triangle is just an extremely limited case of the spherical. If you learn the spherical the plane geometry is included, but not the reverse. It is starting with wholes. Plane trigonometry is an abstract ratio of edges to angles but spherical trigonometry is all ratios of angles to angles, which is much simpler.”
¶ Citations
- RBF at Bell Lab. videotaping, Phila., PA, 23 Jan’75
