Tangent Groupoid in Noncommutative Geometry - Lecture 9
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
A Sheaf-Theoretic Construction of Shape Space
Sheaf-theoretic approach to construct shape space using Persistent Homology Transform. Explores homotopy sheaves, metrics, stability theorems, and approximation of manifolds.
An Arithmetic-Geometric Limit
Explore an intriguing arithmetic-geometric limit problem, delving into mathematical concepts and problem-solving techniques to unravel its solution.
Tangent Groupoid in Noncommutative Geometry - Lecture 10
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Tangent Groupoid in Noncommutative Geometry - Lecture 7
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Tangent Groupoid in Noncommutative Geometry - Lecture 8
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Null Points and Null Lines in Universal Hyperbolic Geometry - Lecture 12
Explore null points and null lines in universal hyperbolic geometry, including rational and projective parametrization, joins and meets theorems, and a triply nil triangle.
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.
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.
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.
Barycentric Coordinates and Subtractive Arithmetic of Vectors - Algebraic Calculus and dCB Curves 9
Explore barycentric coordinates and vector arithmetic in affine geometry, enhancing understanding of de Casteljau Bezier polygons and curves. Gain insights into advanced mathematical concepts and their applications.
Archimedes' Area Formula for Archimedean de Casteljau Bezier Cubics - Lecture 8
Discover a new cubic version of Archimedes' Parabolic Area Formula for special de Casteljau Bezier curves. Explore the Archimedean condition and its fascinating geometric connections.
Bernhard Riemann and the Complex Sphere - Geometric Thinking in Mathematics
Explore Riemann's geometrical thinking on the complex sphere, from abstract discussions on mathematical space to practical applications in complex analysis and higher-dimensional geometry.
Platonic Solids and Their Symmetries - Dynamics on Graphs 10
Explore Platonic solids' symmetries, focusing on rotations and reflections. Discover connections to exceptional structures in mathematics and physics, laying groundwork for understanding 4D regular solids.
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.
Verifying Archimedes' Parabolic Area Formula with Algebraic Calculus - AC and DCB Curves 5
Explore a novel algebraic approach to calculus, focusing on curves and geometry. Learn how to verify Archimedes' parabolic area formula using quadratic de Casteljau Bezier curves and the Fundamental theorem of Algebraic Calculus.
Quadratic Curvature for Algebraic Curves - Differential Geometry Lecture 15
Explores advanced formulas for curvature of algebraic surfaces in 3D space, focusing on the normal paraboloid as key to encoding quadratic metrical information and curvatures in general situations.
Fun with Polyominoes - Elementary Mathematics Explained - Lecture 6
Explore polyominoes: shapes made from connected squares. Learn to count different forms, solve tiling puzzles, and use checkerboard patterns in this engaging mathematical adventure.
Inconvenient Truths About the Square Root of 2 - Real Numbers and Limits
Explores the concept of sqrt(2), its historical significance, and modern approaches, challenging traditional views on irrational numbers and highlighting logical issues in mathematical analysis.
Lines and Parabolas - Quadratic Polynomials and Geometric Relations
Explore advanced parabola concepts: algebraic calculus, subderivatives, tangent lines, Taylor expansions, and geometric relations. Learn to analyze and graph parabolas using completing the square method.