¶ Spherical Triangle Sequence
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Index Entry
Spherical Triangle Sequence:
"Now instead of drawing a circle on the Earth I’m just simply going to draw a triangle. Now I divide the whole surface of the Earth into two areas, a very large southern and a very small northern and they both are triangles so they’re both bound by a closed line with three edges and three angles. And you say, ‘Oh Mister, you’re wrong, because I see 60 degree corners to that triangle, and this must be 300 degrees’outside the corner "and this must be 300 and this must be 300 and the sum of the angles of triangles are always 180 degrees.’ You say can that really be so. And I say yes it is so and let me demonstrate that to you.
“Take, for instance, what we call a great circle. A great circle is a line formed on a sphere by a plane going through the center of the sphere. The equator is such a great circle. The meridians of longitude are just such great circles and they go through the center. 80 degrees north latitude is a lesser circle: it does not go through the center of the sphere. Now great circles are the shortest distances between points on the surface of a sphere. If you would like to demonstrate that we’ll simply go up to 85 degrees north latitude-- it’s really a very small little circle here-- and take the radius”
