Imaginary Interest Rates - Lockdown Live Math
Explore compound interest, e, and their relation to circles in this engaging mathematical journey, connecting complex concepts to real-world applications like springs and rotations.
Visualizing Quaternions - 4D Numbers With Stereographic Projection
Explore 4D quaternions through stereographic projection, visualizing complex mathematical concepts in 3D space and understanding their geometric implications.
Quaternions for Rotation, Axis-Angle, Euler Parameters - MATLAB Examples - Rodrigues Rotation Formula
Explore quaternions, axis-angle representation, and Euler parameters for 3D rotations. Learn to calculate and convert between different rotation formats using MATLAB examples and tutorials.
Math for Game Devs - Abstract Algebra, Procedural Animation & Splines
Explore advanced math concepts for game development, including abstract algebra, procedural animation, and splines. Learn about complex numbers, quaternions, and geometric algebra for enhanced game design and animation techniques.
Quaternions and Fundamental Physics
Explore quaternions in physics, their role in fundamental constants, and potential for unifying theories, including variable speed of light and emergent phenomena.
Hypercomplex Numbers - Math History - NJ Wildberger
Explore hypercomplex numbers, their historical development, and connections to geometry and number theory. Discover quaternions, octonians, and their surprising links to ancient mathematical formulas.
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.
The Rotation Problem and Hamilton's Discovery of Quaternions - Famous Math Problems
Explore complex numbers and their connection to plane rotations, laying the groundwork for understanding quaternions and 3D rotations. Emphasizes a logical, algebraic approach without relying on transcendental functions.
The Rotation Problem and Hamilton's Discovery of Quaternions - Famous Math Problems
Explore quaternions and their connection to 3D rotations using 2x2 complex matrices. Learn key formulas and visual models for this algebraic structure without relying on transcendental concepts.
Representations of Finite Groups - A Few More Common Examples
Explore representations of finite groups including cyclic, dihedral, quaternions, and symmetric groups. Gain insights into advanced abstract algebra concepts and their applications.
A Quaternion Version of Euler's Formula
Explore a quaternion extension of Euler's formula, connecting complex numbers to 3D rotations and expanding mathematical understanding beyond traditional complex analysis.
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.
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.
The Rotation Problem and Hamilton's Discovery of Quaternions - Part 4
Practical implementation of quaternions for 3D rotations, focusing on half-turns and vector trigonometry. Explores quaternion multiplication and its geometric interpretation for rotations.
The Rotation Problem and Hamilton's Discovery of Quaternions - Part 2 - Famous Math Problems 13b
Explore 3D rotations, their composition, and algebraic representation. Learn about Euler's theorem, vector operations, and the foundations for understanding quaternions in graphics and rocket science.
Central Polynumber Algebra and Baby Weyl Character Formula - Math Foundations 236
Explores central polynumber algebra and Weyl character formula, focusing on SU(2) and SU(3) representations. Connects to particle physics and quaternions, emphasizing polynumbers over complex exponentials.
The Only Real Cross Product is Three-Dimensional
Explore the unique properties of 3D cross products, their mathematical significance, and why they don't exist in other dimensions. Gain insights into vector algebra and spatial geometry.
The Duality Between Quaternions and Vectors
Explore the fascinating relationship between quaternions and vectors, uncovering their dual nature and applications in mathematics and physics.
Qp Spaces for Hyperholomorphic Functions in the Unit Ball of R4
Explore Qp spaces for hyperholomorphic functions in R4's unit ball. Delve into properties of related spaces, extending classical concepts to quaternionic analysis.
Lie Group Quaternion Attitude Reconstruction of Quadrotor UAV
Explore quaternion-based attitude reconstruction for quadrotor UAVs using Lie group theory, enhancing control and navigation capabilities.
Quaternionic Non-Selfadjoint Operators and Their Spectral Theory
Explore spectral theory for quaternionic operators, focusing on S-spectrum, Volterra operators, and triangular representations. Gain insights into non-commutative settings and spectral localization.