Spherical Trigonometry

Jim Simons, Apr 15, 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

1.

Spherical Geometry

– Jim Simons

2.

–

3.

–

4.

–

5.

–

6.

–

7.

–

8.

–

9.

–

10.

–

11.

–

12.

–

13.

–

14.

–

Information