¶ Spherical Triangle Sequence
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Index Entry
Spherical Triangle Sequence:
"travel on the equator. I’m going to go one-quarter way around the Earth. Then I’m going to take another meridian and ride up to the north pole again. And because I went a quarter way around the Earth, and then I left the equator at 90 degrees, looking down on top of what I’ve done, I went like this, and therefore the angle at the north pole must also be 90 degrees. So here’s a spherical triangle of 90°, 90°, and 90°, adding up to 270° in its corners. These are the triangles we really do deal with in our Universe.
“If we were to bisect the edges of that triangle with great circles, interconnecting them, the angles would be about 73° at each corner. If I bisect them again and interconnect them with much smaller triangles, the corners are around 63°. Then if I get a smaller one here that 60 degrees and some minutes, or maybe 60 degrees and some seconds-- but they never get down to exactly 60° in each corner. That is, it will always be a little more than 180 degrees. So the smaller the triangle, the more you approach the 180-degreeness which you never arrive at. But the amount the triangles at the corners add up to more than 180 degrees we call the spherical excess, which you must always calculate when you’re doing”
¶ Citations
- SIMS Address, U.Mass., Amherst, Talk 13, p.19, 22 Jul’71
