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#Relativistic Geometry

Showing: 15 courses
Insights into Mathematics

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

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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.
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5 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

Metrical Structure and Curvature of a Parabola - Differential Geometry

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Explore metrical structures and curvature in differential geometry, focusing on parabolas. Learn about symmetric bilinear forms, relativistic geometries, and their applications in physics.
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7 Lesons
44 minutes
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Free-Video
Insights into Mathematics

The Geometry of the Dihedrons and Quaternions - Famous Math Problems

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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.
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7 Lesons
39 minutes
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Free-Video
Insights into Mathematics

How Chromogeometry Transcends Klein's Erlangen Program for Planar Geometries - N J Wildberger

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Discover chromogeometry's three-fold symmetry in planar geometry, unifying Euclidean and relativistic geometries. Explore rational trigonometry, colored Pythagoras theorems, Euler lines, and novel perspectives on conic sections.
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24 Lesons
48 minutes
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Free-Video
Insights into Mathematics

Isometry Groups in Planar Geometry - WildTrig: Intro to Rational Trigonometry - N J Wildberger

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Explore isometry groups in Euclidean and relativistic geometries, focusing on grounded isometries, reflections, and rotations using an algebraic approach without infinite operations.
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5 Lesons
26 minutes
On-Demand
Free-Video
Insights into Mathematics

Isometry Groups of the Projective Line - Rational Geometry Math Foundations

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Exploring finite field geometry: isometries, rotations, and reflections on the projective line, revealing connections to relativistic geometry and offering a new perspective on Euclidean concepts.
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8 Lesons
35 minutes
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Free-Video
Insights into Mathematics

Ptolemy's Theorem and Generalizations - Rational Geometry Math Foundations

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Explores Ptolemy's theorem in rational geometry, extending it to finite fields and relativistic planar geometry. Demonstrates how classical results can yield broader insights when formulated without infinite processes.
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9 Lesons
46 minutes
On-Demand
Free-Video
Insights into Mathematics

First Steps in Hyperbolic Geometry - Universal Hyperbolic Geometry

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Explore fundamental concepts of universal hyperbolic geometry, including perpendicularity, quadrance, spread, and key theorems, with a focus on projective study of circles and relativistic geometry.
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9 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

Barycentric Coordinates and Subtractive Arithmetic of Vectors - Algebraic Calculus and dCB Curves 9

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Explore barycentric coordinates and vector arithmetic in affine geometry, enhancing understanding of de Casteljau Bezier polygons and curves. Gain insights into advanced mathematical concepts and their applications.
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1 Lesons
34 minutes
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Free-Video
Insights into Mathematics

The Chromatic Algebra of 2x2 Matrices - Part 2

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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.
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1 Lesons
38 minutes
On-Demand
Free-Video
Insights into Mathematics

The Chromatic Algebra of 2x2 Matrices - Wild Linear Algebra B41

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Explore chromatic algebra in 2x2 matrices, covering subalgebras, complexions, trace, determinant, and characteristic polynomials. Introduces unique dot products on 2x2 matrices.
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8 Lesons
32 minutes
On-Demand
Free-Video
Insights into Mathematics

Colored Spreads and Generalizations in Rational Trigonometry - Lecture 2

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Explore colored spreads in planar geometries, visualizing red and green spreads using cross products and determinants. Learn about generalized dot products and Pythagoras' theorem in different geometries.
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8 Lesons
27 minutes
On-Demand
Free-Video
Insights into Mathematics

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

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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.
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8 Lesons
24 minutes
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Free-Video
Insights into Mathematics

Oriented Circles and Relativistic Geometry II - Wild Linear Algebra

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Explores oriented circles in plane geometry and their connection to relativistic geometry, covering homothetic centers, Monge's theorem, and the Apollonius problem using algebraic approaches.
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7 Lesons
51 minutes
On-Demand
Free-Video
Insights into Mathematics

Oriented Circles and 3D Relativistic Geometry - Part 1

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