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The Geometry of the Sphere

http://math.rice.edu/~pcmi/sphere/

Provider: John Polking, Rice University


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The Geometry of the Sphere is posted on the by its author John C. Polking at Rice University and was initially the text portion of an Advanced Mathematics Course for high school teachers.This website discusses the “incidence relations between great circles, the notion of angle on the sphere, and the areas of certain fundamental regions on the sphere, culminating with the area of spherical triangles.” The author builds upon this information to prove and discuss the consequences of Girard’s Theorem and uses those results to prove Euler’s Theorem.