Reading assignment spherical geometry - Part 1

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Carefully read the sections 1, 2, 3 and 4 and answer the following questions:

  • Q1. What are geodesics? Why are they important?
  • Q2. What are antipodal points?
  • Q3. What do we know about the sum of the angles if a triangle on the sphere?
  • Q4. What is the defect of a triangle? What would the defect of a quadrilateral be? Why?
  • Q5. How many regular tessellation of the sphere do we have? How does that compare to Euclidean geometry?
  • Q6. What are Platonic Solids and how are they related to spherical geometry?