¶ Spherical Triangle Sequence (2B)
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Index Entry
This is now a spherical triangle in which the angles are 120 degrees each. . . Now this other spherical triangle has angles of 180 degrees each: what we call a circle turns out to be a spherical triangle. Remember there is a hemisphere up there and one down here; and quite clearly that is the equator. . . . Here we have the spherical triangle of 120 degree angles in the northern hemisphere of the sphere-- which you don’t tend to see, simply because you tend to look at the smaller one. There is a tendency of man to look at the smaller one. In fact, I will draw a triangle on the board and one of the problems when i put two triangles together and got four, you remember, was because they turned out to be complementary triangles. I draw a triangle on the board here and you are used to the Greek way of just looking at the area bound by the three sides. In fact, the Greeks defined a triangle as an area bound by three lines turning upon themselves, a closed line of three increments. It happens, however, that I have divided the surface of the blackboard into an area on this side of the line and an area on the other side of the line and every time I put in a line it actually divides something. We have a tendency to be extremely biased and only to look at an area on one side of the line.
