Instructor:Spherical Geometry Exercises Solutions

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  1. Yes, every point on the sphere has exactly one antipodal points.
  2. Although tessellations of the plane suggest infinity because they can be continued forever, Escher felt the necessity of an edge harmed the effect. Escher says that as you turn the ball, the neverending series of motifs suggests infinity. On the other hand, there are only finitely many motifs on the ball. Which is more compelling?