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#Affine Geometry

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Hausdorff Center for Mathematics

Floating Bodies and Duality in Spaces of Constant Curvature

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Explores p-affine surface area and floating bodies in curved spaces, extending Meyer & Werner's Euclidean results to spherical and hyperbolic geometries. Examines limiting behavior as curvature approaches zero.
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1 Lesons
30 minutes
On-Demand
Free-Video
Conference GSI

Virtual Affine Nonholonomic Constraints

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Explore virtual affine nonholonomic constraints in mechanical systems, examining their mathematical foundations and practical applications in robotics and control theory.
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1 Lesons
21 minutes
On-Demand
Free-Video
Insights into Mathematics

Calculus and Affine Geometry of the Magical Parabola - Algebraic Calc and DCB Curves 3 - Wild Egg

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Explore affine geometry and the parabola's unique properties in algebraic calculus, focusing on parallelism and linear algebra concepts without relying on traditional Euclidean definitions.
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6 Lesons
37 minutes
On-Demand
Free-Video
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

Affine and Projective Geometry, and the Problem of Lines

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Explore affine and projective geometry, focusing on points, vector spaces, and lines in 2D. Learn to solve geometric problems using projective coordinates and understand curve representation.
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9 Lesons
51 minutes
On-Demand
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

Seminar - Some Fundamental Formulas from Metrical Algebraic Geometry

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Explore fundamental formulas in metrical algebraic geometry, connecting classical theorems to modern discoveries. Gain insights into affine and projective variants applicable across various fields.
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7 Lesons
50 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

Absolute Versus Relative Measurements in Geometry - Rational Geometry Math Foundations

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Explore the distinction between absolute and relative measurements in geometry, focusing on proportions and ratios. Learn about ancient Greek approaches and their relevance to modern mathematics.
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8 Lesons
31 minutes
On-Demand
Free-Video
Insights into Mathematics

Area and Volume - Wild Linear Algebra A | NJ Wildberger

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Explore area and volume in linear algebra using bi-vectors and tri-vectors. Learn algebraic formulations, geometric proofs, and applications in physics and electromagnetism.
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15 Lesons
56 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

The Circle and Projective Homogeneous Coordinates - Universal Hyperbolic Geometry Lecture 7a

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Introduction to projective geometry and its relation to universal hyperbolic geometry, exploring concepts like affine spaces, perspective, and one-dimensional projective geometry.
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1 Lesons
38 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
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
Insights into Mathematics

Mathematical Space and Basic Duality in Geometry - Rational Geometry Math Foundations 122

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Exploring fundamental concepts of mathematical space, including the duality between affine and projective views, Cartesian geometry, and the relationship between affine and projective lines.
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1 Lesons
33 minutes
On-Demand
Free-Video
Insights into Mathematics

The Rational Number Line and Irrationalities - Famous Math Problems 19b

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Geometric approach to modeling the continuum using the rational number line. Explores properties, projective view, and introduces irrationalities through Euclidean geometry and polynomial equations.
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7 Lesons
38 minutes
On-Demand
Free-Video
Insights into Mathematics

The Geometry of Euclidean Reflections and Rotations - Grounded Case

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Explore Euclidean reflections and rotations using rational geometry. Learn about complex number multiplication, group structures, and a visual notation for describing transformations.
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7 Lesons
24 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Dylan Langharst: Higher-Order Affine Isoperimetric Inequalities

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Explores extensions of geometric inequalities to higher-order bodies, including projection, centroid, LYZ, and radial mean bodies, with proofs of associated inequalities in convex geometry.
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1 Lesons
27 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The Funk Metric in Convex Geometry and Related Fields

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Explore the Funk metric's connections to convex geometry, affine geometry, and combinatorics. Discover its projective invariance and relations to various conjectures and theorems.
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1 Lesons
53 minutes
On-Demand
Free-Video
Centrum Fizyki Teoretycznej PAN

Affine and Euclidean Geometry - The Modern Approach

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Explore modern approaches to affine and Euclidean geometry, with applications to electrodynamics and relativity theory in this advanced physics lecture.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video