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#Rational Trigonometry

Showing: 30 courses
Insights into Mathematics

Geometry with Linear Algebra - Wild Linear Algebra A - NJ Wildberger

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Explore the connection between linear algebra and geometry, focusing on Pythagoras' theorem and perpendicularity. Learn how linear algebra provides a solid framework for understanding Euclidean and other geometries.
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8 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

The Area of a Triangle and Archimedes' Formula - Famous Math Problems

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Novel approach to calculating triangle area using rational trigonometry, avoiding unnecessary irrationalities in Heron's formula. Presents a clearer solution based on Pythagoras' theorem and Triple quad formula, with practical applications.
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7 Lesons
38 minutes
On-Demand
Free-Video
Insights into Mathematics

Trigonometry in Elliptic Geometry II - Universal Hyperbolic Geometry - NJ Wildberger

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Explore elliptic trigonometry laws, including Spread, Cross, and Dual cross, using linear algebra. Learn proofs for Thales', Pythagoras', and Triple Quad formulas in elliptic geometry.
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7 Lesons
41 minutes
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Free-Video
Insights into Mathematics

Trigonometry in Elliptic Geometry - Universal Hyperbolic Geometry

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Explore elliptic geometry's trigonometry, including projective points, quadrances, and spreads. Learn key laws connecting triangles and their polar counterparts in this fundamental mathematical realm.
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6 Lesons
42 minutes
On-Demand
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
On-Demand
Free-Video
Insights into Mathematics

The Group of Blue Planar Isometries - WildTrig: Intro to Rational Trigonometry - N J Wildberger

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Explore Euclidean isometries from a rational perspective, focusing on grounded isometries and deriving formulas for projections, reflections, and compositions in planar geometry.
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5 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

Rational Trigonometry and Mathematics Education - WildTrig: Intro to Rational Trigonometry

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Innovative approach to teaching geometry and trigonometry, emphasizing rational methods for Year 9-10 students. Covers shapes, transformations, circle geometry, and challenges traditional concepts.
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6 Lesons
22 minutes
On-Demand
Free-Video
Insights into Mathematics

Maths Education and Rational Trigonometry - WildTrig: Intro to Rational Trigonometry

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Innovative approach to teaching geometry and trigonometry, emphasizing rational trigonometry for Year 9-10 students. Covers progression from basic shapes to advanced topics, including circle geometry and 'pi'.
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8 Lesons
31 minutes
On-Demand
Free-Video
Insights into Mathematics

Maths Education and Rational Trigonometry - WildTrig: Intro to Rational Trigonometry

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Exploring the challenges in trigonometry education and introducing rational trigonometry as a potential solution to improve mathematical understanding for students.
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6 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

The General Rational Laws of Trigonometry - WildTrig: Intro to Rational Trigonometry

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Explore general rational trigonometry laws in a planar setting, deriving elegant algebraic formulas without transcendental functions or real numbers. Learn key mathematical principles efficiently.
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5 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

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

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

Applications of Rational Spherical Trigonometry II - Universal Hyperbolic Geometry

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Explore spherical trigonometry to calculate distance and bearing between two points on Earth, comparing classical and modern rational methods for solving real-world navigation problems.
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7 Lesons
43 minutes
On-Demand
Free-Video
Insights into Mathematics

The Circumquadrance of a Cyclic Quadrilateral - Rational Geometry Math Foundations - NJ Wildberger

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Explore a rational approach to cyclic quadrilateral geometry, avoiding transcendental quantities and extending to other fields and geometries. Learn Parameshvara's formula and its non-convex counterpart.
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5 Lesons
36 minutes
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Free-Video
Insights into Mathematics

The Triple Spread Formula, Circumcircles and Curvature - Rational Geometry Math Foundations

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Explores the Triple spread formula in Rational Trigonometry, relating it to circumcircles and curvature. Connects projective geometry with one and two-dimensional geometries through core circles and quadratic curvature.
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8 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

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

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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.
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5 Lesons
20 minutes
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Free-Video
Insights into Mathematics

Eight Ninths and the Geometry of A4 Paper - Universal Hyperbolic Geometry

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Explore the fascinating geometry of A4 paper, its connection to the spread 8/9, and how Rational Trigonometry provides deeper insights into everyday objects and mathematical concepts.
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5 Lesons
25 minutes
On-Demand
Free-Video
Insights into Mathematics

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

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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.
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33 Lesons
50 minutes
On-Demand
Free-Video
Insights into Mathematics

Towards a More Computational Mathematics - Rational Trigonometry and New Foundations for Geometry

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Explores a computational approach to mathematics using rational numbers, introducing rational trigonometry and its laws. Covers applications in geometry, spread polynomials, and projective trigonometry.
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33 Lesons
56 minutes
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Free-Video
Insights into Mathematics

Quadrance and Spread - Universal Hyperbolic Geometry

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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.
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8 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Three Dimensional Geometry, ZOME, and the Elusive Tetrahedron

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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.
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35 Lesons
59 minutes
On-Demand
Free-Video
Insights into Mathematics

Rational Trigonometry in Three Dimensions - Universal Hyperbolic Geometry

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Extending rational trigonometry to 3D using vectors and dot products. Explores quadrance, spread, and key trigonometric laws. Introduces solid spread and determinants for three vectors.
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8 Lesons
31 minutes
On-Demand
Free-Video
Insights into Mathematics

Rational Trigonometry - An Overview - Universal Hyperbolic Geometry

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

Rational Curvature, Winding, and Turning in Algebraic Topology - Lecture 11

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Explores rational curvature, turn angles, and winding numbers in algebraic topology. Introduces new geometric concepts for describing polygons and planar curves, emphasizing practical applications in mathematics.
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14 Lesons
48 minutes
On-Demand
Free-Video
Insights into Mathematics

Teaching Connections Between Algebra and Geometry - Part 2

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Exploring connections between algebra and geometry, including Cartesian geometry, conics, projective geometry, triangle geometry, and rational trigonometry for a fresh approach to math education.
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1 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

Meusnier, Monge and Dupin - Differential Geometry - Lecture 1

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Explores the contributions of French geometer Meusnier to differential geometry, focusing on curvature, asymptotic directions, and umbilic points, with applications of Rational Trigonometry.
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10 Lesons
49 minutes
On-Demand
Free-Video
Insights into Mathematics

Examples of Curvatures of Surfaces - Differential Geometry Lecture 30

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Explore curvature formulas for surfaces through examples like spheres, ellipsoids, and cubic surfaces. Learn to calculate mean and Gaussian curvatures using linear algebra and characteristic coefficients.
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9 Lesons
43 minutes
On-Demand
Free-Video
Insights into Mathematics

Japanese Temple Problems - Famous Math Problems 14

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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.
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11 Lesons
46 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

Coloured Spreads and Generalizations in Rational Trigonometry - Lecture 1

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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.
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8 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

Half-Slope and the Full Group of Euclidean Isometries - WildTrig: Intro to Rational Trigonometry

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Explore half-slopes in planar reflections and rotations, circle sums, and translations to understand Euclidean isometries. Gain insights into rational trigonometry and algebraic approaches to geometry.
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1 Lesons
21 minutes
On-Demand
Free-Video