Главная
Study mode:
on
You
History
Saved
In progress 0 courses
compleat 0 courses
#Art & Design #Adobe #ChatGPT #GitHub

#Quadrance

Showing: 28 courses
Insights into Mathematics

Circles and Spheres via Dot Products II - Wild Linear Algebra A

0 rewiews
Explore 3D Euclidean dot products, quadrance, linear functionals, and spheres. Learn about projections, Pythagoras' theorem, and perpendicularity in three-dimensional space.
Add to list
6 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

Dot Products, Pythagoras' Theorem, and Generalizations - Wild Linear Algebra A - NJ Wildberger

0 rewiews
Algebraic approach to metrical geometry using dot products and quadrance. Introduces symmetric bilinear forms for understanding relativistic geometry, with applications to linear algebra and physics.
Add to list
5 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

Geometry With a General Dot Product - WildTrig: Intro to Rational Trigonometry - N J Wildberger

0 rewiews
Exploring advanced geometry using rational trigonometry and general dot products. Extends metrical geometry beyond chromogeometry, introducing new concepts of quadrance, perpendicularity, and spread.
Add to list
5 Lesons
23 minutes
On-Demand
Free-Video
Insights into Mathematics

The Curvature of a Parabola, Without Calculus - Rational Geometry Math Foundations

0 rewiews
Algebraic approach to calculate parabola curvature without calculus, using circle circumquadrance and triangle properties. Demonstrates wider applicability to various algebraic curves.
Add to list
5 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Relativistic Velocity, Core Circles, and Paul Miller's Protractor - Rational Geometry

0 rewiews
Explores core circles in rational geometry, connecting projective and Euclidean geometry. Covers parametrization, quadrances, and theorems, bridging abstract concepts with practical applications.
Add to list
8 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

Relativistic Velocity, Core Circles and Paul Miller's Protractor - Rational Geometry

0 rewiews
Explore core circles in rational geometry, connecting projective and Euclidean concepts. Learn about relativistic velocity addition and its implications for Einstein's special theory of relativity.
Add to list
7 Lesons
33 minutes
On-Demand
Free-Video
Insights into Mathematics

Higher Dimensions and the Roles of Length, Area, and Volume - Rational Geometry Math Foundations

0 rewiews
Explore higher dimensions and the fundamental role of squared measurements in geometry. Discover how quadrance, quadrea, and quadrume offer more general and invariant alternatives to traditional length, area, and volume.
Add to list
9 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

The Bretschneider Von Staudt Formula for a Quadrilateral - Rational Geometry Math Foundations

0 rewiews
Explore the Bretschneider von Staudt formula for quadrilateral area, its history, and rational geometric formulations. Learn about generalizations of Archimedes' theorem and the importance of rational expressions in geometry.
Add to list
9 Lesons
31 minutes
On-Demand
Free-Video
Insights into Mathematics

The Projective Line, Circles and a Proof of the CQQ Theorem - Rational Geometry Math Foundations

0 rewiews
Explore projective parametrization of the unit circle, derive formulas for areas of triangles and quadrilaterals, and delve into circle geometry with applications to other conics.
Add to list
9 Lesons
45 minutes
On-Demand
Free-Video
Insights into Mathematics

Spreads, Determinants and Chromogeometry - WildTrig: Intro to Rational Trigonometry

0 rewiews
Explore spreads, dot products, and chromogeometry in linear algebra. Learn about vector operations, quadrance, perpendicularity, and the fascinating trilogy of blue, red, and green dot products.
Add to list
5 Lesons
20 minutes
On-Demand
Free-Video
Insights into Mathematics

Rational Trigonometry, Generalized Triangle Geometry and Four-Fold Incenter Symmetry

0 rewiews
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.
Add to list
33 Lesons
50 minutes
On-Demand
Free-Video
Insights into Mathematics

The Cross Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger

0 rewiews
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.
Add to list
7 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Visualizing Quadrance with Circles - Universal Hyperbolic Geometry - NJ Wildberger

0 rewiews
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.
Add to list
6 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

The Triple Quad Formula in Universal Hyperbolic Geometry

0 rewiews
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.
Add to list
9 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

Quadrance and Spread - Universal Hyperbolic Geometry

0 rewiews
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.
Add to list
8 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Three Dimensional Geometry, ZOME, and the Elusive Tetrahedron

0 rewiews
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.
Add to list
35 Lesons
59 minutes
On-Demand
Free-Video
Insights into Mathematics

Rational Trigonometry - An Overview - Universal Hyperbolic Geometry

0 rewiews
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.
Add to list
5 Lesons
33 minutes
On-Demand
Free-Video
Insights into Mathematics

Trigonometric Laws in Hyperbolic Geometry Using Geometer's Sketchpad - Universal Hyperbolic Geometry 26

0 rewiews
Explore trigonometric laws in hyperbolic geometry using Geometer's Sketchpad. Learn about Pythagoras' theorem, Triple quad formula, Spread law, and Cross law with practical examples and custom tools.
Add to list
1 Lesons
20 minutes
On-Demand
Free-Video
Insights into Mathematics

Relativistic Velocity and Core Circles in Rational Geometry - Lecture 4

0 rewiews
Exploring relativistic velocity and core circles in rational geometry, extending Paul Miller's protractor concept to projective quadrance and comparing Euclidean and relativistic geometries.
Add to list
6 Lesons
49 minutes
On-Demand
Free-Video
Insights into Mathematics

The Projective Line, Circles and the CQQ Theorem - Part 2

0 rewiews
Explores advanced geometry concepts including general circles, complex numbers, and the Cyclic Quadrilateral Quadrea theorem, emphasizing projective parametrization and transformations in the complex plane.
Add to list
9 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

Robbins' Formulas, Bellows Conjecture, and Polyhedra Volumes - Rational Geometry Math Foundations 128

0 rewiews
Explore modern developments in polygon area formulas, cyclic pentagon theories, and 3D generalizations of Heron's formula. Discover connections between quadrances, polyhedra volumes, and algebraic geometry.
Add to list
8 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Applications of the Dot Product to Planar Geometry - Part 2

0 rewiews
Explore advanced applications of dot product in planar geometry, including linear functionals, point-normal form of lines, vector projections, isometries, and rotations.
Add to list
1 Lesons
46 minutes
On-Demand
Free-Video
Insights into Mathematics

Japanese Temple Problems - Famous Math Problems 14

0 rewiews
Explore Japanese temple geometry problems, focusing on a 13-year-old's 1847 challenge. Compare classical and rational trigonometry approaches, revealing surprising algebraic insights and symmetries in triangle geometry.
Add to list
11 Lesons
46 minutes
On-Demand
Free-Video
Insights into Mathematics

Coloured Spreads and Generalizations in Rational Trigonometry - Lecture 1

0 rewiews
Explore colored spreads theorem, planar dot products, and geometric interpretations of quadrances in blue, red, and green geometries. Gain insights into rational trigonometry and linear algebra concepts.
Add to list
8 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

Rethinking Roots of Unity in Complex Algebra - Math Foundations 218

0 rewiews
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.
Add to list
10 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

Fundamental Theorem of Algebra Reexamined - Math Foundations 217

0 rewiews
Reexamines the Fundamental Theorem of Algebra, proposing new formulations based on rational complex arithmetic and quadrance, avoiding assumptions about continuity and real/complex numbers.
Add to list
1 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

The Three-Fold Symmetry of Chromogeometry - Rational Geometry Math Foundations

0 rewiews
Explore chromogeometry's three-fold symmetry, combining Euclidean and relativistic geometries. Discover new patterns and relations beyond traditional approaches, opening doors to 21st century geometric insights.
Add to list
8 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Oriented Circles and 3D Relativistic Geometry - Part 1

0 rewiews
Explores 3D relativistic geometry, hyperboloids as relativistic spheres, and connections with oriented circles. Introduces cyclography and its relation to relativistic quadrance.
Add to list
1 Lesons
46 minutes
On-Demand
Free-Video