Insights into Mathematics Courses

Pythagoras' Theorem in Universal Hyperbolic Geometry

Explore the hyperbolic version of Pythagoras' theorem, its importance in geometry, and the concept of quadrance. Learn about planar coordinates, formulas, and proofs in Universal Hyperbolic Geometry.

• YouTube
• 36 minutes
• On-Demand
• Free Video

Quadrance and Spread - Universal Hyperbolic Geometry

Introduces algebraic definitions of quadrance and spread in Universal Hyperbolic Geometry, comparing with Rational Trigonometry and exploring main laws and exercises in this advanced mathematical framework.

• YouTube
• 36 minutes
• On-Demand
• Free Video

The J Function, SL(2) and the Jacobi Identity - Universal Hyperbolic Geometry

Explores connections between hyperbolic geometry, matrix algebra, and Lie theory, demonstrating how the Jacobi identity proves the concurrence of triangle altitudes in projective geometry.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Parallels and the Double Triangle - Universal Hyperbolic Geometry

Explores parallels, double triangles, and perspective centers in Universal Hyperbolic Geometry, offering new insights into Euclid's parallel postulate and its historical implications.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Medians, Midlines, Centroids and Circumcenters - Universal Hyperbolic Geometry

Explore triangle geometry in universal hyperbolic geometry, covering medians, midlines, centroids, and circumcenters. Discover unique properties and connections in this algebraic framework.

• YouTube
• 34 minutes
• On-Demand
• Free Video

Reflections and Projective Linear Algebra - Universal Hyperbolic Geometry

Explore reflections in hyperbolic geometry through projective linear algebra. Learn about null points, reflection matrices, and the sl(2) Lie algebra. Gain insights into fundamental symmetries and their mathematical representations.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Midpoints and Bisectors - Universal Hyperbolic Geometry

Explore midpoints and bisectors in hyperbolic geometry, including reflections, perpendicularity, and geometric constructions. Learn key differences from Euclidean geometry in this advanced mathematical exploration.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Mechanics and the Solar System - Math History - NJ Wildberger

Explore the historical development of planetary motion theories, from Earth-centered models to Newton's laws, highlighting key figures and their contributions to our understanding of the solar system.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Apollonius and Polarity Revisited - Universal Hyperbolic Geometry

Explores Apollonius' polarity in hyperbolic geometry, focusing on null points, quadrangles, and the relationship between poles and polars. Includes explicit formulas and computational examples.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Calculus - Math History - N J Wildberger

Explore the historical development of calculus, from ancient Greek origins to Newton and Leibniz's revolutionary work, covering key concepts and influential figures in mathematics.

• YouTube
• 1 hour
• On-Demand
• Free Video

Theorems Using Perpendicularity - Universal Hyperbolic Geometry

Explore perpendicularity in hyperbolic geometry, including duality, triangles, and the Base center point. Learn a general theorem approach and investigate concepts using Standard Triangle 1.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Orthocenters Exist - Universal Hyperbolic Geometry

Explores orthocenters in universal hyperbolic geometry, introducing key concepts like triangles, altitudes, and Desargues' theorem. Culminates in defining orthic line, orthostar, and ortho-axis in hyperbolic triangle geometry.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Duality and Perpendicularity - Universal Hyperbolic Geometry

Explore perpendicularity in universal hyperbolic geometry, including duality, altitudes, and key theorems. Learn about unique aspects like perpendicular points and their applications in geometric analysis.

• YouTube
• 33 minutes
• On-Demand
• Free Video

Computations with Homogeneous Coordinates - Universal Hyperbolic Geometry

Explore algebraic definitions of points and lines in hyperbolic geometry, learn key theorems, and understand their applications in computational geometry and Cartesian coordinates.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Projective Geometry - Math History - NJ Wildberger

Explore the origins and development of projective geometry, from Pappus to Desargues and Pascal, and its fundamental role in mathematics and 3D space understanding.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video