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#Rational Geometry

Showing: 16 courses
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
On-Demand
Free-Video
Insights into Mathematics

The Projective Quadruple Quad Formula - Rational Geometry Math Foundations

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Explore the projective Quadruple quad formula and its connection to cyclic quadrilateral geometry, advancing beyond classical trigonometry to a more powerful approach applicable to general fields.
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7 Lesons
31 minutes
On-Demand
Free-Video
Insights into Mathematics

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

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

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

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Exploring Paul Miller's protractor for efficient spread measurement in projective geometry, linking projective and affine measurements through core circles and the Triple quad formula.
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5 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

The Projective Triple Quad Formula - Rational Geometry Math Foundations

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Explores the projective Triple Quad Formula in rational geometry, relating three projective quadrances formed by projective 1-points. Highlights similarities to the Triple spread formula and its mathematical significance.
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9 Lesons
26 minutes
On-Demand
Free-Video
Insights into Mathematics

NJ's Pizza Model for Organizing Geometry - Rational Geometry Math Foundations

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Explore a systematic approach to organizing metrical geometry using a pizza-making analogy. Learn about various geometries, their interconnections, and key concepts in this comprehensive overview.
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10 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

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

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

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

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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.
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9 Lesons
31 minutes
On-Demand
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

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

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

The Cyclic Quadrilateral Quadrea Theorem - Rational Geometry Math Foundations

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Explores the Cyclic Quadrilateral Quadrea theorem, combining Brahmagupta's and Robbins' formulas for cyclic quadrilateral areas. Includes examples, tips, and a critical look at real number thinking in geometry.
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6 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

Brahmagupta's Formula and the Quadruple Quad Formula - Rational Geometry Math Foundations

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Explore Brahmagupta's formula and the Quadruple Quad Formula, connecting classical geometry with modern insights. Learn about cyclic quadrilaterals, factorization, and rational number precision in geometry.
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9 Lesons
41 minutes
On-Demand
Free-Video
Insights into Mathematics

Brahmagupta's Formula and the Quadruple Quad Formula - Rational Geometry Math Foundations

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Explore Brahmagupta's formula for cyclic quadrilateral areas and the Quadruple Quad Formula, delving into algebraic manipulations and rational geometry concepts for a deeper understanding of quadrilateral properties.
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10 Lesons
41 minutes
On-Demand
Free-Video
Insights into Mathematics

Heron's Formula, Archimedes' Function, and the TQF - Rational Geometry Math Foundations

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Explore Heron's formula and Archimedes' theorem for triangle area calculation using rational quantities, revealing connections between one-dimensional and higher-dimensional geometry.
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8 Lesons
46 minutes
On-Demand
Free-Video
Insights into Mathematics

Relativistic Velocity and Core Circles in Rational Geometry - Lecture 4

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

Affine One-Dimensional Geometry and the Triple Quad Formula - Math Foundations 123

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Explore the Triple Quad Formula, a fundamental theorem in mathematics, through affine geometry. Learn its derivation, significance, and applications in measuring point separation and collinearity.
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8 Lesons
27 minutes
On-Demand
Free-Video