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.
Menelaus, Ceva and the Laws of Proportion - Universal Hyperbolic Geometry
Insights into Mathematics via YouTube
Overview
Syllabus
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
Taught by
Insights into Mathematics
Related Courses
-
Orthocenters Exist - Universal Hyperbolic Geometry
-
Theorems Using Perpendicularity - Universal Hyperbolic Geometry
-
Quadrance and Spread - Universal Hyperbolic Geometry
-
Parallels and the Double Triangle - Universal Hyperbolic Geometry
-
The Cross Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger
-
First Steps in Hyperbolic Geometry - Universal Hyperbolic Geometry
