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Mathematics
Geometry
Non-Euclidean Geometry

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Explore hyperbolic, spherical, and projective geometries that revolutionized mathematics and physics beyond Euclid's axioms. Learn through visual demonstrations and mathematical proofs on YouTube, from introductory concepts to advanced applications in computer graphics and relativistic physics.

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Insights into Mathematics
Non-Euclidean Geometry - Math History - NJ Wildberger
1 review

Explore the complex history and modern interpretations of non-Euclidean geometry, challenging traditional narratives and proposing new perspectives on this fundamental mathematical concept.
- YouTube
- 51 minutes
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Institute for Advanced Study
Raytracing and Raymarching Simulations of Non-Euclidean Geometries - Henry Segerman

Explore advanced raytracing and raymarching techniques for simulating non-Euclidean geometries, covering fractal objects, isometries, and complex mathematical concepts.
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Conference GSI
Generalized Galilean Geometries

Explore Generalized Galilean Geometries, expanding mathematical understanding beyond traditional frameworks. Gain insights into advanced geometric concepts and their applications.
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History of Non-Euclidean Geometry
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IIT Kanpur; NPTEL
An Introduction to Hyperbolic Geometry

Explore hyperbolic geometry and its applications in group theory, covering models, isometries, Fuchsian groups, and hyperbolic surfaces, with insights into geometric group theory.
- Swayam
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The Royal Institution
How Geometry Created Modern Physics

Explore the evolution of geometry from Euclid to Einstein, uncovering how post-Euclidean concepts revolutionized our understanding of spacetime and laid the foundation for modern physics.
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Insights into Mathematics
Universal Hyperbolic Geometry - A Projective and Algebraic Approach

Explore hyperbolic geometry through a projective, algebraic approach using rational trigonometry—no calculus required, connecting to relativity and Minkowski geometry.
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Insights into Mathematics
The Circle and Cartesian Coordinates in Universal Hyperbolic Geometry - Lecture 5

Explore Cartesian coordinates and the unit circle, covering key theorems on lines, points, and circles. Learn about determinants, parametrization, and the intersection of lines and circles in geometry.
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The Royal Institution
The Story of Mathematical Proof - From Ancient Greece to Modern Logic

Explore the evolution of mathematical proof across number theory, geometry, topology, and logic, delving into the fascinating gap between natural and real numbers.
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Insights into Mathematics
A Brief History of Geometry III - The 19th Century - Sociology and Pure Mathematics

Explore the golden age of geometry in the 19th century, covering inversive, projective, non-Euclidean, and complex geometries. Understand key developments and their impact on modern mathematics.
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Perpendicularity, Polarity and Duality on a Sphere - Universal Hyperbolic Geometry

Explore perpendicularity, polarity, and duality on a sphere, including polar triangles and point-plane duality. Gain insights into elliptic geometry and the relationships between geometric elements.
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Insights into Mathematics
Hyperbolic Geometry Is Projective Relativistic Geometry - Full Lecture

Explore hyperbolic geometry as projective relativistic geometry, covering key concepts, models, and theorems. Gain insights into quadrance, spread, trigonometry, and unique results like the Jumping Jack theorem.
- YouTube
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Insights into Mathematics
Menelaus, Ceva and the Laws of Proportion - Universal Hyperbolic Geometry

Explore classical theorems of Menelaus and Ceva in universal hyperbolic geometry, along with new results on triangle proportions and alternate spreads. Learn about ratios, distances, and quadrances in triangular geometry.
- YouTube
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Insights into Mathematics
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.
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Insights into Mathematics
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.
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