When drawn on a sphere, the interior angles of a triangle sum to greater than pi! This is because the shortest distance between the vertices of the triangle are the geodesics of the sphere, or in other words, the great circles that have the center of the sphere as their origin and pass through two of the triangles vertices. They are called geodesics because they are the lines of least curvature, or the curves that most closely represent a straight line on a curved surface. This is a result from elliptic geometry, a non-euclidean geometry.
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