Spherical Trigonometry

Jim Simons, 15/4/2025

A collection of activities as used in my session at the 2025 conference of the UK mathematical associations


  • 1. Spherical Geometry
  • 2. Proof of Key Equation for Right Angled Spherical Triangles
  • 3. Navigation Using Right Angled Spherical Triangles
  • 4. Proof of Plane Sine Rule
  • 5. Proof of Spherical Sine Rule
  • 6. Proof of Spherical Cosine Rule
  • 7. Navigation Using Spherical Sine and Cosine Rules
  • 8. Plane Menelaus Theorem
  • 9. An Ancient Proof of Menelaus' Theorem
  • 10. A Modern Proof of Menelaus's Theorem
  • 11. A Modern Proof of Menelaus's Theorem
  • 12. Lifting Menelaus from the Plane to the Sphere
  • 13. Menelaus's Spherical Theorem
  • 14. Using Menelaus for Astronomy

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Spherical Geometry

– Jim Simons

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