Why Can't You Multiply Vectors? - A Mathematical Journey into Vector Multiplication
Een wiskundige reis door vectorvermenigvuldiging, complexe getallen en geometrische algebra, met toepassingen in game-ontwikkeling en nieuwe perspectieven op wiskundige constructies.
Complex Multiplication: Past, Present, Future - Lecture 1
Explore the historical and contemporary aspects of complex multiplication in mathematics, with insights into its future applications and developments.
Calculus on the Unit Circle - Arithmetic and Geometry Math Foundations 78
Explore algebraic calculus on unit circles, covering subderivatives, Taylor expansions, tangents, and 3D visualizations. Gain insights into foundational mathematics with a unique approach to this fundamental topic.
Algebraic Structure on the Euclidean Projective Line - Rational Geometry Math Foundations 137
Explores algebraic structure on the Euclidean projective line, covering projective formulas, isometries, rotations, and their compositions. Connects to chaos theory and complex number multiplication.
The Projective Line, Circles and the CQQ Theorem - Part 2
Explores advanced geometry concepts including general circles, complex numbers, and the Cyclic Quadrilateral Quadrea theorem, emphasizing projective parametrization and transformations in the complex plane.
The Chromatic Algebra of 2x2 Matrices - Part 2
Explores chromatic algebra of 2x2 matrices, focusing on subalgebras, complexions, dot products, and the four-dimensional Dihedrons algebra. Compares to quaternions and highlights unique properties.
Relativistic Dot Products and Complex Numbers in Linear Algebra - Part 2
Exploring triality of dot products and associated complex numbers in chromogeometry, organized within 2x2 matrices. Delves into interactions between three geometries.
Complex Numbers and Curves in 19th Century Mathematics
Explore complex numbers, algebraic curves, and their intersection with projective geometry and topology. Discover how these concepts revolutionized 19th-century mathematics and laid the foundation for modern algebraic geometry.
Rethinking Roots of Unity in Complex Algebra - Math Foundations 218
Explores complex roots of unity, challenging traditional views and highlighting logical difficulties in their definition and existence, emphasizing rational parametrization and algebraic approaches over infinite processes.
Fundamental Theorem of Algebra Reexamined - Math Foundations 217
Reexamines the Fundamental Theorem of Algebra, proposing new formulations based on rational complex arithmetic and quadrance, avoiding assumptions about continuity and real/complex numbers.
The Geometry of Euclidean Reflections and Rotations - Grounded Case
Explore Euclidean reflections and rotations using rational geometry. Learn about complex number multiplication, group structures, and a visual notation for describing transformations.
Central Polynumbers and SL(2)/SU(2) Characters - Math Foundations 235
Explore a novel algebraic approach to SL(2) and SU(2) representation theory, emphasizing central polynumbers and mset arithmetic, with implications for Lie theory and modern physics.
Solving Quintic Equations - Mathematical Misconceptions
Discover the method to solve any quintic equation in this engaging tutorial. Learn advanced algebraic techniques and expand your mathematical problem-solving skills.
Complex Numbers in Fourier Series and Quantum Mechanics
Explore complex numbers in harmonic analysis, focusing on the unit circle. Learn about Laplacian operators, harmonic polynomials, and integration theory, with applications to quantum mechanics and physics.
Number Systems - Foundations and Applications in Mathematics
Explore the foundations of mathematics through an in-depth examination of number systems, presented by Kevin Hare from the University of Waterloo.
A Great Proof of the Euler-Mascheroni Constant Identity
Explore a captivating proof of a fascinating mathematical identity, delving into elegant reasoning and surprising connections that illuminate the beauty of number theory.
The Duality Between Quaternions and Vectors
Explore the fascinating relationship between quaternions and vectors, uncovering their dual nature and applications in mathematics and physics.
An Integral Connection Between Trigonometry and Logarithms
Explore the fascinating link between trigonometry and logarithms through an integral, revealing unexpected mathematical connections and deepening understanding of both concepts.
The Fundamental Theorem of Algebra - Challenging Mathematical Orthodoxy
Challenging the Fundamental Theorem of Algebra: Exploring its limitations, implications for calculus and linear algebra, and the need for a more accurate formulation in rational numbers.
Real and Complex Number Systems - Lecture 1
Explore real and complex numbers, their properties, and applications in mathematical analysis and problem-solving.
Noncommutative Elliptic Poisson Structures on Projective Spaces
Explore noncommutative Poisson structures on affine and projective spaces, focusing on examples in complex projective spaces and their connections to elliptic Poisson algebras.