Question

Let's consider polygons. In flat space, their sides are straight line segments. On a sphere the sides are segments of great circles, which are the closest you can get to

straight lines on a sphere. (Hartle doesn't mention that, so watch out!) Great circles go around the center of a sphere. For example, the equator is a great circle, but other lines of constant latitude are not. O Are lines of constant longitude great circles? (b) In flat space, the interior angles of a triangle must sum to 7 (radians). On a sphere you can have more. For example, you can have triangles with three right angles so the sum is 37/2. Sketch such a triangle. (c) In flat space, there is no such thing as a digon (a polygon with two sides). On a sphere, there is. Sketch one.

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