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Outline
Spherical Trigonometry
Spherical Geometry
Proof of Key Equation for Right Angled Spherical Triangles
Navigation Using Right Angled Spherical Triangles
Proof of Plane Sine Rule
Proof of Spherical Sine Rule
Proof of Spherical Cosine Rule
Navigation Using Spherical Sine and Cosine Rules
Plane Menelaus Theorem
An Ancient Proof of Menelaus' Theorem
A Modern Proof of Menelaus's Theorem
A Modern Proof of Menelaus's Theorem
Lifting Menelaus from the Plane to the Sphere
Menelaus's Spherical Theorem
Using Menelaus for Astronomy
Spherical Trigonometry
Author:
Jim Simons
Topic:
Geometry
,
Sphere
,
Trigonometry
A collection of activities as used in my session at the 2025 conference of the UK mathematical associations
Spherical Geometry
Proof of Key Equation for Right Angled Spherical Triangles
Navigation Using Right Angled Spherical Triangles
Proof of Plane Sine Rule
Proof of Spherical Sine Rule
Proof of Spherical Cosine Rule
Navigation Using Spherical Sine and Cosine Rules
Plane Menelaus Theorem
An Ancient Proof of Menelaus' Theorem
A Modern Proof of Menelaus's Theorem
A Modern Proof of Menelaus's Theorem
Lifting Menelaus from the Plane to the Sphere
Menelaus's Spherical Theorem
Using Menelaus for Astronomy
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