The Circumquadrance of a Cyclic Quadrilateral - Rational Geometry Math Foundations - NJ Wildberger
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.
The Projective Quadruple Quad Formula - Rational Geometry Math Foundations
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.
The Curvature of a Parabola, Without Calculus - Rational Geometry Math Foundations
Algebraic approach to calculate parabola curvature without calculus, using circle circumquadrance and triangle properties. Demonstrates wider applicability to various algebraic curves.
Relativistic Velocity, Core Circles and Paul Miller's Protractor - Rational Geometry
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.
The Projective Triple Quad Formula - Rational Geometry Math Foundations
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.
NJ's Pizza Model for Organizing Geometry - Rational Geometry Math Foundations
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.
Higher Dimensions and the Roles of Length, Area, and Volume - Rational Geometry Math Foundations
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.
The Bretschneider Von Staudt Formula for a Quadrilateral - Rational Geometry Math Foundations
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.
Ptolemy's Theorem and Generalizations - Rational Geometry Math Foundations
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.
The Projective Line, Circles and a Proof of the CQQ Theorem - Rational Geometry Math Foundations
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.
The Cyclic Quadrilateral Quadrea Theorem - Rational Geometry Math Foundations
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.
Brahmagupta's Formula and the Quadruple Quad Formula - Rational Geometry Math Foundations
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.
Brahmagupta's Formula and the Quadruple Quad Formula - Rational Geometry Math Foundations
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.
Heron's Formula, Archimedes' Function, and the TQF - Rational Geometry Math Foundations
Explore Heron's formula and Archimedes' theorem for triangle area calculation using rational quantities, revealing connections between one-dimensional and higher-dimensional geometry.
Relativistic Velocity and Core Circles in Rational Geometry - Lecture 4
Exploring relativistic velocity and core circles in rational geometry, extending Paul Miller's protractor concept to projective quadrance and comparing Euclidean and relativistic geometries.
Affine One-Dimensional Geometry and the Triple Quad Formula - Math Foundations 123
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.