The Sporadic Nature of Big Numbers - Data Structures in Mathematics
Explores how arithmetic breaks down with large numbers, revealing most "numbers" are invisible to us. Challenges conventional number theory and questions the nature of natural numbers.
The Chaotic Complexity of Natural Numbers - Data Structures in Mathematics
Exploring the complex nature of arithmetic with large numbers, focusing on exponential and triangular complexity, and examining the role of powers in mathematical computations.
Maxel Algebra I - Data Structures in Mathematics Math Foundations
Explore maxel algebra, a new matrix theory focusing on idempotent diagonal maxels and sets of natural numbers. Learn about multiplication, identity maxels, and key propositions in this mathematical foundation.
Teaching Connections Between Algebra and Geometry I - A MANSW Presentation
Exploring connections between algebra and geometry, covering topics like Euclidean algorithm, continued fractions, and projective geometry. Aims to revitalize interest in geometry as a core subject for students.
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.
Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations
Explore interval arithmetic, its laws for natural numbers and integers, and the challenges with real number arithmetic. Gain insights into measurement, approximation, and foundational mathematical concepts.
Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations
Explores interval arithmetic for natural numbers and integers, covering definitions, inequalities, arithmetic operations, and applications in measurement and counting. Lays foundations for mathematical reasoning.
The Division Algorithm for Polynumbers - Arithmetic + Geometry Math Foundations | N J Wildberger
Explore the division algorithm for polynumbers, covering integral and rational polynumbers, and different approaches to division. Learn foundational concepts in mathematics with a focus on logical rigor.
The Cross Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger
Explores the Cross law in Universal Hyperbolic Geometry, proving it with a polynomial identity and demonstrating its application to equilateral triangles. Includes exercises and comparisons to Euclidean geometry.
Visualizing Quadrance with Circles - Universal Hyperbolic Geometry - NJ Wildberger
Explore quadrance in universal hyperbolic geometry through circles, examining their appearance as ellipses, parabolas, or hyperbolas with different centers, enhancing understanding of this fundamental concept.
The Triple Quad Formula in Universal Hyperbolic Geometry
Explores the Triple quad formula in hyperbolic geometry, its proof, and related concepts. Compares with Euclidean geometry and discusses algebraic challenges, providing exercises for deeper understanding.
Quadrance and Spread - Universal Hyperbolic Geometry
Introduces algebraic definitions of quadrance and spread in Universal Hyperbolic Geometry, comparing with Rational Trigonometry and exploring main laws and exercises in this advanced mathematical framework.
Factoring Large Numbers into Primes - Famous Math Problems
Explore prime factorization of large numbers, modular arithmetic, and theorems by Fermat and Euler. Learn techniques to tackle complex mathematical problems and improve number theory skills.
Challenges With Higher On-Sequences - Real Numbers and Limits Math Foundations
Explores challenges in extending polynumber sequences, discussing exponomials and recursive sequences. Highlights logical issues and the need for clearer definitions in mathematical foundations.
Three Dimensional Geometry, ZOME, and the Elusive Tetrahedron
Explore three-dimensional geometry using rational trigonometry and ZOME construction, focusing on tetrahedron trigonometry and new algebraic relations for a deeper understanding of spatial structures.
The Deep Structure of the Rational Numbers - Real Numbers and Limits Math Foundations
Explores the deep structure of rational numbers, focusing on their layered nature within [0,1]. Covers key concepts like Farey sequences and Ford circles, emphasizing rationals' importance in modern mathematics.
Fractions and P-Adic Numbers - Real Numbers and Limits Math Foundations
Explore 10-adic numbers and repeating reversimals, a playful alternative to decimal arithmetic. Learn addition, multiplication, and conversion of fractions in this number theory adventure.
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.
Number Theory and Algebra in Asia - Math History - NJ Wildberger
Explores number theory, algebra, and astronomy in ancient Chinese, Indian, and Arab mathematics, highlighting key figures and their contributions to mathematical development.
Infinity in Greek Mathematics - Math History - NJ Wildberger
Explore ancient Greek mathematics, focusing on Eudoxus and Archimedes' groundbreaking work in calculus, geometry, and mechanics. Discover their ingenious formulas and principles that laid the foundation for modern mathematics.
Greek Number Theory - Math History - NJ Wildberger
Explore ancient Greek number theory, including primes, perfect numbers, and the Fundamental Theorem of Arithmetic. Learn about Euclidean algorithms, continued fractions, and Pell's equation.