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.
Addition in Practice - Elementary Mathematics Explained
Explore addition laws, even/odd numbers, and their geometric representations. Learn associative and commutative properties, and discover practical applications in arithmetic and counting problems.
Hyperbolic Geometry Is Projective Relativistic Geometry - Full Lecture
Explore hyperbolic geometry as projective relativistic geometry, covering key concepts, models, and theorems. Gain insights into quadrance, spread, trigonometry, and unique results like the Jumping Jack theorem.
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.
Calculus on a Cubic - The Folium of Descartes - Arithmetic and Geometry Math Foundations
Explore the Folium of Descartes through algebraic calculus, examining its parametrization, Taylor expansions, tangents, and unique properties in both 2D and 3D space.
An Introduction to Algebraic Curves - Arithmetic and Geometry Math Foundations
Explore the history and concepts of algebraic curves, from ancient Greek spirals to modern polynomial approaches, setting the stage for generalizing algebraic calculus beyond functions.
Object-Oriented Versus Expression-Oriented Mathematics - Arithmetic and Geometry Math Foundations
Exploring the shift from object-oriented to expression-oriented mathematics, focusing on the unit circle as a key example and discussing various interpretations and approaches in modern mathematics.
Triangle Geometry Old and New - An Introduction to Hyperbolic Triangle Geometry
Explore classical and hyperbolic triangle geometry, covering perpendicularity, midpoints, and bilines. Learn about orthocenters, incenters, circumcenters, and more through visual illustrations without complex formulas.
Cubics and the Prettiest Theorem in Calculus - Arithmetic and Geometry Math Foundations
Explore cubic polynomials, their calculus, and tangent conics. Learn about Etienne Ghys' theorem, considered one of the most beautiful in calculus, with an elegant proof provided.
Lines and Parabolas I - Arithmetic and Geometry Math Foundations
Explore lines and parabolas using algebraic calculus, covering y-intercepts, slopes, x-intercepts, quadratic polynomials, Taylor expansions, derivatives, and tangent lines in elementary mathematics.
Translating Polynumbers and the Derivative - Arithmetic and Geometry Math Foundations
Explore polynomials and derivatives algebraically, introducing Taylor polynomials and sub-derivatives. Challenges traditional calculus views, shifting towards Euler and Lagrange's approach to mathematical foundations.
Laurent Polynumbers - The New Years Day Lecture - Arithmetic and Geometry Math Foundations
Explore Laurent polynumbers, their arithmetic, and relation to rational polynumbers. Learn about the foundational importance of rational numbers and polynumbers in mathematics.
Row and Column Polynumbers - Arithmetic and Geometry Math Foundations
Explore two-dimensional arithmetic with polynumbers, introducing bipolynumbers and their associated polynomials in alpha and beta variables. Learn simplified arithmetic and multiplication techniques.
Decimal Numbers - Arithmetic and Geometry Math Foundations
Explore decimal numbers, their representation in the Hindu-Arabic system, and conversion between fractions and decimals. Learn about notation, structure, and practical applications in mathematics.
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.
Menelaus, Ceva and the Laws of Proportion - Universal Hyperbolic Geometry
Explore classical theorems of Menelaus and Ceva in universal hyperbolic geometry, along with new results on triangle proportions and alternate spreads. Learn about ratios, distances, and quadrances in triangular geometry.
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.
Thales' Theorem, Right Triangles + Napier's Rules - Universal Hyperbolic Geometry
Explores Thales' theorem and Napier's rules in universal hyperbolic geometry, focusing on right triangles. Covers key concepts like quadrea, spreads, and proofs, with practical exercises for deeper understanding.
The Fundamental Group - Algebraic Topology
Explore the fundamental group in algebraic topology, covering homotopic paths, loop multiplication, and equivalence classes. Understand key concepts for surfaces like disks and circles.
Knots and Surfaces I - Algebraic Topology - NJ Wildberger
Explore knot theory's origins, basic concepts, and key invariants in this introductory lecture on algebraic topology, covering Reidemeister moves, crossing numbers, and the Alexander-Conway polynomial.
The Two-Holed Torus and 3-Crosscaps Surface - Algebraic Topology - NJ Wildberger
Explore hyperbolic geometric structures of two-holed torus and 3-crosscaps surface through tessellations, hexagons, and the Beltrami Poincare model in this advanced algebraic topology lecture.