3D Supershapes and Spherical Geometry
Explore 3D Supershapes and spherical geometry in Processing and p5.js. Learn to create spheres, generate 3D Supershapes, and transpose them to web browsers using WebGL.
Floating Bodies and Duality in Spaces of Constant Curvature
Explores p-affine surface area and floating bodies in curved spaces, extending Meyer & Werner's Euclidean results to spherical and hyperbolic geometries. Examines limiting behavior as curvature approaches zero.
Spherical and Elliptic Geometries - Universal Hyperbolic Geometry
Explore spherical and elliptic geometries, from ancient Greek astronomy to modern concepts. Learn about longitude, latitude, measurement techniques, and key theorems in non-Euclidean spaces.
Spherical and Elliptic Geometries - An Introduction
Explore spherical geometry fundamentals: great circles, antipodal points, triangles, and circles. Learn key concepts and visualize ideas with physical models, connecting to 3D space and Euclidean geometry.
Donald Coxeter and Geometry
Explore Donald Coxeter's contributions to geometry, including non-Euclidean geometries, higher dimensions, and connections to art and music in this engaging mathematical journey.
Why All Maps Are Wrong - Theorema Egregium
Explore Theorema Egregium's geometric proof, revealing why no world map can preserve both area and angles. Understand curvature, spherical areas, and the Gauss map in this mathematical journey.
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.
The Geometry of Surfaces - Algebraic Topology Lecture 20
Explore the connection between 2D surfaces and classical geometries, focusing on isometries and introducing hyperbolic geometry through circle inversions in the Beltrami Poincare disk model.
Rational Curvature of Polytopes and the Euler Number - Algebraic Topology Lecture 16
Explore the relationship between polyhedron curvature and Euler number using rational formulation. Learn about Harriot's theorem and analyze various polyhedra, including tetrahedron, cube, and dodecahedron.
The Rotation Problem and Hamilton's Discovery of Quaternions - Part 2 - Famous Math Problems 13b
Explore 3D rotations, their composition, and algebraic representation. Learn about Euler's theorem, vector operations, and the foundations for understanding quaternions in graphics and rocket science.
Existence and Stability of Corotational Wave Maps into Perturbed Spheres
Explore corotational wave maps from Minkowski space to perturbed spheres, examining existence and stability of self-similar solutions in energy-supercritical scenarios.
Rigidity of Convex Surfaces in Space-Forms
Explore rigidity properties of convex surfaces in space-forms, focusing on mathematical concepts and geometric analysis techniques.
The Matsuno-Gill Model on the Sphere - Extended Analysis and Applications
Explore the extended Matsuno-Gill model on a sphere, analyzing its parameters and solutions across different damping and rotation rates. Gain insights into planetary-scale fluid dynamics.
Casimir Dissipation Stabilized Stochastic Rotating Shallow Water Equations on the Sphere
Explore stochastic rotating shallow water equations on the sphere, focusing on Casimir dissipation stabilization techniques and their applications in geophysical fluid dynamics.
Cartesian, Spherical, and Lobachewskian Geometries - Wave Equation - Lecture 3
Explore Cartesian, spherical, and Lobachewskian geometries, and delve into the wave equation's fundamental role in dynamical theories of physics.