The Triple Quad Formula in Universal Hyperbolic Geometry
Explores the Triple quad formula in hyperbolic geometry, its proof, and related concepts. Compares with Euclidean geometry and discusses algebraic challenges, providing exercises for deeper understanding.
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.
Extending Arithmetic to Infinity - Real Numbers and Limits Math Foundations
Explore extending arithmetic to infinity using rational numbers and projective geometry. Learn about integral points, theorems, and distributive laws in this mathematical journey.
Elementary Projective Geometry - Elementary Mathematics Explained
Explore elementary projective geometry, focusing on line geometry and basic concepts like joins, meets, and quadrangles. Learn through hands-on constructions and discover fascinating correspondences in geometry.
Pappus and Pascal - Elementary Mathematics Explained
Explore Pappus' and Pascal's theorems in projective geometry, learning key concepts and historical context. Gain insights into reading mathematics and appreciating these fundamental results.
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.
Analytic Geometry and the Continuum - Math History - NJ Wildberger
Explores Cartesian geometry's development, merging numbers and geometry, and discusses issues with the continuum, irrational numbers, and decimal expansions, including pi's continued fraction approximations.
Analytic Geometry and the Continuum - Math History - NJ Wildberger
Explore Cartesian geometry's development, merging numbers and geometry. Delve into conics, cubics, Bezout's theorem, and the continuum, discussing ancient Greek influences and challenges with irrational numbers and pi.
First Steps in Hyperbolic Geometry - Universal Hyperbolic Geometry
Explore fundamental concepts of universal hyperbolic geometry, including perpendicularity, quadrance, spread, and key theorems, with a focus on projective study of circles and relativistic geometry.
Apollonius and Polarity - Universal Hyperbolic Geometry
Explore Apollonius' polarity concept in hyperbolic geometry, focusing on the crucial role of circles and their relationship to points and lines in the projective plane.
Universal Hyperbolic Geometry - NJ Wildberger
Discover a revolutionary approach to hyperbolic geometry, simplifying complex concepts using high school algebra and projective geometry, with connections to Einstein's special relativity theory.
Homeomorphism and the Group Structure on a Circle - Algebraic Topology 2 - NJ Wildberger
Explore homeomorphisms, group structures on circles, and projective geometry in this algebraic topology lecture, blending fundamental concepts with novel approaches and historical insights.
Perspectives in Math and Art by Supurna Sinha
Explore the fascinating intersection of mathematics and art during the European Renaissance, focusing on Projective Geometry and its impact on artistic representation and mathematical development.
Hyperbolicity in Presence of a Large Local System
Explore hyperbolicity in complex algebraic varieties with Yohan Brunebarbe. Learn about Green-Griffiths and Lang conjectures, and their validity for varieties with large complex local systems.
Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2, Lecture 2
Explora superficies racionales sobre cuerpos, profundizando en conceptos avanzados de geometría algebraica y teoría de números con expertos internacionales.
The Circle and Projective Homogeneous Coordinates - Universal Hyperbolic Geometry Lecture 7a
Introduction to projective geometry and its relation to universal hyperbolic geometry, exploring concepts like affine spaces, perspective, and one-dimensional projective geometry.
The Circle and Projective Homogeneous Coordinates in Universal Hyperbolic Geometry - Lecture 7b
Explores projective geometry as the foundation of universal hyperbolic geometry, focusing on the circle in projective homogeneous coordinates and its significance in mathematics and physics.
Pappus' Theorem and Cross Ratio in Projective Geometry - Universal Hyperbolic Geometry 3
Explore Pappus' theorem, cross ratio, and key projective geometry concepts. Learn about invariance, transformations, and applications in hyperbolic geometry through theorems and exercises.
A Brief History of Geometry II: The European Epoch - From Cartesian to Differential Geometry
Explore the European evolution of geometry, from Cartesian to differential, highlighting key developments and their impact on mathematics. Gain insights into this fundamental discipline's historical significance.
Sphere Geometry and Complex Analysis - Algebraic Topology Lecture 4
Explore advanced concepts in sphere geometry, including inversive geometry, Riemann sphere, complex analysis, and projective lines, enhancing understanding of algebraic topology.
Teaching Connections Between Algebra and Geometry - Part 2
Exploring connections between algebra and geometry, including Cartesian geometry, conics, projective geometry, triangle geometry, and rational trigonometry for a fresh approach to math education.