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#Universal Hyperbolic Geometry

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Insights into Mathematics

The Classification of Platonic Solids I - Universal Hyperbolic Geometry

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Exploring the classification of Platonic solids using modern notation and turn angles. Examines planar, spherical, and higher-dimensional cases, highlighting mathematical constructions and challenges in Euclid's proof.
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7 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

Trigonometric Dual Laws and the Parallax Formula - Universal Hyperbolic Geometry

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Explore trigonometric dual laws and the Right parallax formula in Universal Hyperbolic Geometry. Learn about Pythagoras' theorem, Cross dual law, and zero quadrance/spread theorems.
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7 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Menelaus, Ceva and the Laws of Proportion - Universal Hyperbolic Geometry

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

Thales' Theorem, Right Triangles + Napier's Rules - Universal Hyperbolic Geometry

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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.
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11 Lesons
43 minutes
On-Demand
Free-Video
Insights into Mathematics

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

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

The Spread Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry

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Explores the Spread law in universal hyperbolic geometry, including its definition, relation to Euclidean geometry, proof, and implications. Covers key concepts like quadrance, spread duality, and quadrea.
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7 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Visualizing Quadrance with Circles - Universal Hyperbolic Geometry - NJ Wildberger

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

The Triple Quad Formula in Universal Hyperbolic Geometry

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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.
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9 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

Pythagoras' Theorem in Universal Hyperbolic Geometry

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Explore the hyperbolic version of Pythagoras' theorem, its importance in geometry, and the concept of quadrance. Learn about planar coordinates, formulas, and proofs in Universal Hyperbolic Geometry.
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9 Lesons
36 minutes
On-Demand
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

Parallels and the Double Triangle - Universal Hyperbolic Geometry

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Explores parallels, double triangles, and perspective centers in Universal Hyperbolic Geometry, offering new insights into Euclid's parallel postulate and its historical implications.
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8 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

Medians, Midlines, Centroids and Circumcenters - Universal Hyperbolic Geometry

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Explore triangle geometry in universal hyperbolic geometry, covering medians, midlines, centroids, and circumcenters. Discover unique properties and connections in this algebraic framework.
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8 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Apollonius and Polarity Revisited - Universal Hyperbolic Geometry

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Explores Apollonius' polarity in hyperbolic geometry, focusing on null points, quadrangles, and the relationship between poles and polars. Includes explicit formulas and computational examples.
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8 Lesons
27 minutes
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Free-Video
Insights into Mathematics

Theorems Using Perpendicularity - Universal Hyperbolic Geometry

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Explore perpendicularity in hyperbolic geometry, including duality, triangles, and the Base center point. Learn a general theorem approach and investigate concepts using Standard Triangle 1.
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8 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

Orthocenters Exist - Universal Hyperbolic Geometry

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Explores orthocenters in universal hyperbolic geometry, introducing key concepts like triangles, altitudes, and Desargues' theorem. Culminates in defining orthic line, orthostar, and ortho-axis in hyperbolic triangle geometry.
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10 Lesons
44 minutes
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Insights into Mathematics

Duality and Perpendicularity - Universal Hyperbolic Geometry

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Explore perpendicularity in universal hyperbolic geometry, including duality, altitudes, and key theorems. Learn about unique aspects like perpendicular points and their applications in geometric analysis.
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9 Lesons
33 minutes
On-Demand
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Insights into Mathematics

Apollonius and Harmonic Conjugates - Universal Hyperbolic Geometry 2 - NJ Wildberger

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Explore harmonic conjugates in geometry, including their relation to circles, conics, and quadrangles. Learn about harmonic ranges, pencils, and vector combinations in this advanced mathematical discussion.
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7 Lesons
38 minutes
On-Demand
Free-Video
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Null Points and Null Lines in Universal Hyperbolic Geometry - Lecture 12

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Explore null points and null lines in universal hyperbolic geometry, including rational and projective parametrization, joins and meets theorems, and a triply nil triangle.
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7 Lesons
36 minutes
On-Demand
Free-Video
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The Circle and Projective Homogeneous Coordinates in Universal Hyperbolic Geometry - Lecture 7b

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Explores projective geometry as the foundation of universal hyperbolic geometry, focusing on the circle in projective homogeneous coordinates and its significance in mathematics and physics.
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1 Lesons
24 minutes
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Insights into Mathematics

The Circle and Cartesian Coordinates in Universal Hyperbolic Geometry - Lecture 5

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Explore Cartesian coordinates and the unit circle, covering key theorems on lines, points, and circles. Learn about determinants, parametrization, and the intersection of lines and circles in geometry.
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7 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Geometer's Sketchpad and Circles in Universal Hyperbolic Geometry - Lecture 25

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Explore Geometer's Sketchpad for dynamic illustrations in universal hyperbolic geometry. Learn custom tools, construct point duals, and discover various circles, including equidistant curves, in hyperbolic space.
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1 Lesons
25 minutes
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Insights into Mathematics

Reflections in Hyperbolic Geometry - Universal Hyperbolic Geometry Lecture 14

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Explore reflections in hyperbolic geometry, comparing with Euclidean counterparts. Discover unique properties and surprising connections to circle geometry in this advanced mathematical exploration.
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8 Lesons
31 minutes
On-Demand
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Insights into Mathematics

Duality, Polarity and Projective Linear Algebra - Differential Geometry Lecture 11

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Explores projective geometry, quadratic forms, and pole-polar duality in relation to the unit circle. Connects these concepts to Lorentz/Einstein/Minkowski geometry and Apollonius' work.
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1 Lesons
48 minutes
On-Demand
Free-Video