The Golden Ratio Spiral - Visual Infinite Descent
Explore number-associated spirals, infinite descent proofs, and continued fractions. Debunk golden ratio myths while gaining insights into number properties through visual representations.
Pi Is Irrational - Animation of a Gorgeous Proof
Explore a visually stunning animation of Lambert's proof of pi's irrationality, delving into infinite fractions and mathematical concepts in an engaging, accessible manner.
Sex and Marriage Theorems
Explore mathematical theorems on stable marriages and debunk sex statistics myths. Discover how mathematicians can earn Nobel-like recognition through innovative problem-solving.
The Area of a Triangle and Archimedes' Formula - Famous Math Problems
Novel approach to calculating triangle area using rational trigonometry, avoiding unnecessary irrationalities in Heron's formula. Presents a clearer solution based on Pythagoras' theorem and Triple quad formula, with practical applications.
The Realm of Natural Numbers - Data Structures in Mathematics
Explore natural numbers through multisets, examining addition, union, and intersection operations. Discover unique properties, including a new distributive law that forms the basis for tropical calculus.
Naming and Ordering Numbers for Students - Data Structures in Mathematics Math Foundations
Explores naming, ordering, and using natural numbers, focusing on their fundamental nature as expressions of marks. Discusses counting, cardinal vs ordinal usage, and the successor operation.
Rational Trigonometry, Generalized Triangle Geometry and Four-Fold Incenter Symmetry
Explores rational trigonometry and generalized triangle geometry, introducing quadrances, spreads, and chromogeometry. Discusses Euler lines, incenters, and various triangle centers, culminating in a novel result on colored incenters.
The SDP Relaxation for Max-Cut - Lecture 19b of CS Theory Toolkit
Explore SDP relaxation for Max-Cut, transforming a quadratic program into a semidefinite program solvable by the Ellipsoid Algorithm. Part of CMU's graduate-level CS Theory Toolkit course.
Isosceles Triangles in Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger
Explore isosceles triangles in hyperbolic geometry, including special formulas, midpoint construction, and related theorems. Gain insights through proofs, exercises, and applications of the cross law.
Polyhedra and Euler's Formula - Algebraic Topology
Explore Platonic solids, Euler's formula, and spherical geometry in this engaging lecture on algebraic topology, featuring proofs and insights into fundamental mathematical concepts.
The Spread Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry
Explores the Spread law in universal hyperbolic geometry, including its definition, relation to Euclidean geometry, proof, and implications. Covers key concepts like quadrance, spread duality, and quadrea.
Pythagoras' Theorem in Universal Hyperbolic Geometry
Explore the hyperbolic version of Pythagoras' theorem, its importance in geometry, and the concept of quadrance. Learn about planar coordinates, formulas, and proofs in Universal Hyperbolic Geometry.
Complex Numbers and Algebra - Math History - NJ Wildberger
Explore complex numbers' history, applications in cubic equations, and geometric representations. Delve into the Fundamental Theorem of Algebra and its proofs by d'Alembert and Gauss.
Apollonius and Polarity Revisited - Universal Hyperbolic Geometry
Explores Apollonius' polarity in hyperbolic geometry, focusing on null points, quadrangles, and the relationship between poles and polars. Includes explicit formulas and computational examples.
Sums of Squares - Number Theory
Explore number theory concepts focusing on sums of squares, including a theorem and its proof, enhancing mathematical understanding and problem-solving skills.
Square Roots Mod P - Number Theory
Explore square roots in modular arithmetic, a key concept in number theory. Learn proofs, work through examples, and gain practical problem-solving skills in this engaging mathematical exploration.
Quadratic Reciprocity Proof - Number Theory
Explore an in-depth proof of quadratic reciprocity in number theory, covering Legendre symbols, Gauss limits, and key concepts essential for understanding this fundamental theorem.
Wilson's Theorem - Number Theory
Explore Wilson's Theorem in number theory, including its proof, examples, and applications. Gain insights into this fundamental concept and its significance in mathematical reasoning.
Multivariable Calculus - Stoke's Theorem
Explore Stoke's Theorem in multivariable calculus, including its description and a proof outline, enhancing understanding of vector calculus and its applications in physics and engineering.
Abstract Algebra - Eisenstein's Criterion
Proof and examples of Eisenstein's criterion in abstract algebra, demonstrating its application in determining polynomial irreducibility over rational numbers.
Pi Is Irrational
Explore a simple proof demonstrating pi's irrationality, delving into mathematical concepts and reasoning behind this fundamental property of the famous constant.