Rational Trigonometry - An Overview - Universal Hyperbolic Geometry
Introduces rational trigonometry using vectors, replacing distance and angle with quadrance and spread. Covers key concepts, formulas, and laws, offering a purely algebraic approach to trigonometry and geometry.
Rational Curvature, Winding, and Turning in Algebraic Topology - Lecture 11
Explores rational curvature, turn angles, and winding numbers in algebraic topology. Introduces new geometric concepts for describing polygons and planar curves, emphasizing practical applications in mathematics.
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.
Meusnier, Monge and Dupin - Differential Geometry - Lecture 1
Explores the contributions of French geometer Meusnier to differential geometry, focusing on curvature, asymptotic directions, and umbilic points, with applications of Rational Trigonometry.
Examples of Curvatures of Surfaces - Differential Geometry Lecture 30
Explore curvature formulas for surfaces through examples like spheres, ellipsoids, and cubic surfaces. Learn to calculate mean and Gaussian curvatures using linear algebra and characteristic coefficients.
Japanese Temple Problems - Famous Math Problems 14
Explore Japanese temple geometry problems, focusing on a 13-year-old's 1847 challenge. Compare classical and rational trigonometry approaches, revealing surprising algebraic insights and symmetries in triangle geometry.
Colored Spreads and Generalizations in Rational Trigonometry - Lecture 2
Explore colored spreads in planar geometries, visualizing red and green spreads using cross products and determinants. Learn about generalized dot products and Pythagoras' theorem in different geometries.
Coloured Spreads and Generalizations in Rational Trigonometry - Lecture 1
Explore colored spreads theorem, planar dot products, and geometric interpretations of quadrances in blue, red, and green geometries. Gain insights into rational trigonometry and linear algebra concepts.
Half-Slope and the Full Group of Euclidean Isometries - WildTrig: Intro to Rational Trigonometry
Explore half-slopes in planar reflections and rotations, circle sums, and translations to understand Euclidean isometries. Gain insights into rational trigonometry and algebraic approaches to geometry.