Menelaus, Ceva and the Laws of Proportion - Universal Hyperbolic Geometry

Explore classical theorems and new results in universal hyperbolic geometry in this 42-minute video lecture. Delve into Menelaus' and Ceva's theorems, which relate to triangles and ratios of distances or quadrances. Discover the Triangle proportions theorem and the Alternate spreads theorem. Learn about the dual versions of Menelaus' and Ceva's theorems. Follow along as the instructor proves Ceva's theorem and presents its dual form. Gain insights into the connections between trigonometry and these geometric principles throughout the lecture.

Introduction remarks on trigonometry
Ceva's theorem
Menelaus' theorem
Menelaus' dual theorem
Triangle proportions theorem
Alternate spreads theorem
Proving Ceva's theorem
Ceva's dual theorem