Designing with Complex Geometry - Class 2
Explore advanced geometric design techniques, including curve types, point manipulation, mathematical expressions, and 3D transformations to create complex floral patterns.
Polynumbers and De Casteljau Bezier Curves - Algebraic Calculus and DCB Curves - N J Wildberger
Explore polynumbers and de Casteljau Bezier curves in algebraic calculus. Learn new formulas for planar integration and use GeoGebra to visualize these remarkable curves, with applications in design and animation.
Relativistic Dot Products and Complex Numbers - Wild Linear Algebra B
Explore relativistic dot products, complex numbers, and chromogeometry in planar geometry. Discover the symmetry between Euclidean and relativistic geometries using 2x2 matrices, unit circles, and isometries.
Energy, Momentum and Linear Algebra - Wild Linear Algebra B
Explore conservation of momentum and energy in mechanics using linear algebra, featuring a geometric interpretation of elastic collisions and a butterfly collision diagram for particle interactions.
The Relativistic Dot Product - Wild Linear Algebra B
Explore the relativistic dot product in Einstein's Special Relativity, comparing it to the Euclidean dot product and examining its applications in geometry and physics.
Circles and Spheres via Dot Products II - Wild Linear Algebra A
Explore 3D Euclidean dot products, quadrance, linear functionals, and spheres. Learn about projections, Pythagoras' theorem, and perpendicularity in three-dimensional space.
Dot Products, Pythagoras' Theorem, and Generalizations - Wild Linear Algebra A - NJ Wildberger
Algebraic approach to metrical geometry using dot products and quadrance. Introduces symmetric bilinear forms for understanding relativistic geometry, with applications to linear algebra and physics.
Geometry with Linear Algebra - Wild Linear Algebra A - NJ Wildberger
Explore the connection between linear algebra and geometry, focusing on Pythagoras' theorem and perpendicularity. Learn how linear algebra provides a solid framework for understanding Euclidean and other geometries.
Curvature for the General Paraboloid - Differential Geometry - NJ Wildberger
Novel approach to surface curvature using projective geometry and linear algebra. Explores paraboloid curvature through characteristic polynomials, offering insights for higher-dimensional generalizations.
Paraboloids and Associated Quadratic Forms - Differential Geometry
Explore paraboloids and quadratic forms in differential geometry, covering diagonalization, eigenvalues, and Dupin's indicatrix. Learn key concepts for understanding surface curvature.
Trigonometry in Elliptic Geometry II - Universal Hyperbolic Geometry - NJ Wildberger
Explore elliptic trigonometry laws, including Spread, Cross, and Dual cross, using linear algebra. Learn proofs for Thales', Pythagoras', and Triple Quad formulas in elliptic geometry.
Metrical Structure and Curvature of a Parabola - Differential Geometry
Explore metrical structures and curvature in differential geometry, focusing on parabolas. Learn about symmetric bilinear forms, relativistic geometries, and their applications in physics.
The Geometry of the Dihedrons and Quaternions - Famous Math Problems
Explore the geometry of Dihedrons and Quaternions, comparing their properties and connections to relativity, linear algebra, and complex numbers. Gain insights into fundamental mathematical structures.
How to Construct the True Complex Numbers I - Famous Math Problems
Exploring the construction of true complex numbers using field theory and linear algebra, challenging traditional approaches and introducing novel concepts for a modern understanding.
The Boole Mobius Transform - MathFoundations - N J Wildberger
Explore the Boole-Mobius transform, connecting Boolean functions and polynomials through linear algebra. Learn about binary representations and their relation to set theory in this mathematical deep dive.
Affine and Projective Geometry, and the Problem of Lines
Explore affine and projective geometry, focusing on points, vector spaces, and lines in 2D. Learn to solve geometric problems using projective coordinates and understand curve representation.
Geometry With a General Dot Product - WildTrig: Intro to Rational Trigonometry - N J Wildberger
Exploring advanced geometry using rational trigonometry and general dot products. Extends metrical geometry beyond chromogeometry, introducing new concepts of quadrance, perpendicularity, and spread.
Seminar - Some Fundamental Formulas from Metrical Algebraic Geometry
Explore fundamental formulas in metrical algebraic geometry, connecting classical theorems to modern discoveries. Gain insights into affine and projective variants applicable across various fields.
Absolute Versus Relative Measurements in Geometry - Rational Geometry Math Foundations
Explore the distinction between absolute and relative measurements in geometry, focusing on proportions and ratios. Learn about ancient Greek approaches and their relevance to modern mathematics.
Spreads, Determinants and Chromogeometry - WildTrig: Intro to Rational Trigonometry
Explore spreads, dot products, and chromogeometry in linear algebra. Learn about vector operations, quadrance, perpendicularity, and the fascinating trilogy of blue, red, and green dot products.
An Introduction to Abstract Algebra - Abstract Algebra Math Foundations
Explore fundamental algebraic structures like groups, rings, fields, and vector spaces through intuitive examples, providing a bird's-eye view of abstract algebra's foundational concepts.