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#Euclidean Geometry

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METUopencouseware

Geometry I - Prof. Dr. Cem Tezer

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Comprehensive exploration of fundamental geometric concepts, covering various topics over 16 weeks. Ideal for students seeking in-depth understanding of geometry principles and applications.
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25 Lesons
16 hours
On-Demand
Free-Video
Professor Dave Explains

Geometry

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Explore shapes, angles, and theorems in this comprehensive geometry overview, covering 2D and 3D concepts from basic principles to advanced calculations.
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15 Lesons
1 hour 30 minutes
On-Demand
Free-Video
Mathologer

Why Is Doubling Cubes and Squaring Circles Impossible?

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Explore the 2000-year journey to prove the impossibility of doubling cubes, trisecting angles, constructing regular heptagons, and squaring circles using only a ruler and compass, from ancient Greece to modern mathematics.
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8 Lesons
40 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

PROLÍMPICO - 6° Edição 2023 - Geometria - Aula 02

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Aprofunde-se em geometria olímpica com técnicas avançadas e resolução de problemas complexos para aprimorar suas habilidades em competições matemáticas.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
BIMSA

Degeneration of Singular Circle Patterns

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Explore singular Euclidean circle patterns, cone-angle maps, and degeneration schemes. Analyze the structure of cone-angle polytopes and their relationship to admissible partial edge orientations.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Insights into Mathematics

The Language of Geometry - Math Terminology

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Comprehensive review of geometry terminology for university students, covering Euclidean concepts, shapes, transformations, 3D geometry, and coordinate systems. Includes subtitles and supplementary materials.
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9 Lesons
41 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

Euclid Book 1 Props I - V - A Critical Review - Sociology and Pure Mathematics - N J Wildberger

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Critical review of Euclid's Book 1 Propositions I-V, examining logical foundations and constructions. Explores historical significance and questions modern interpretations of Euclidean geometry.
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8 Lesons
29 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

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

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

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Explores core circles in rational geometry, connecting projective and Euclidean geometry. Covers parametrization, quadrances, and theorems, bridging abstract concepts with practical applications.
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8 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

Isometry Groups of the Projective Line - Rational Geometry Math Foundations

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Exploring finite field geometry: isometries, rotations, and reflections on the projective line, revealing connections to relativistic geometry and offering a new perspective on Euclidean concepts.
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8 Lesons
35 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

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 Remarkable Platonic Solids I - Universal Hyperbolic Geometry

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Explore the fascinating world of Platonic solids, their symmetry, history, and mathematical properties. Learn about Euclid's contributions and Euler's fundamental relation for polyhedra.
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9 Lesons
26 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

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

Spherical and Elliptic Geometries - An Introduction

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Explore spherical geometry fundamentals: great circles, antipodal points, triangles, and circles. Learn key concepts and visualize ideas with physical models, connecting to 3D space and Euclidean geometry.
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8 Lesons
32 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Branching Random Walks - Two Conjectures and a Theorem by Parthanil Roy

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Explore branching random walks, their applications, and long-term behavior. Delve into conjectures and theorems with mathematician Parthanil Roy in this engaging lecture on probability theory.
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30 Lesons
1 hour 53 minutes
On-Demand
Free-Video
Fields Institute

Donald Coxeter and Geometry

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Explore Donald Coxeter's contributions to geometry, including non-Euclidean geometries, higher dimensions, and connections to art and music in this engaging mathematical journey.
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11 Lesons
55 minutes
On-Demand
Free-Video
Mathemaniac

What if We Define 1-0 = Infinity - Möbius Transformations Visualized

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Explore Möbius transformations and their connection to defining 1/0 = ∞, with insights on circular inversion, Riemann sphere, and applications in geometry and complex analysis.
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5 Lesons
25 minutes
On-Demand
Free-Video
The Royal Institution

How Geometry Created Modern Physics

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Explore the evolution of geometry from Euclid to Einstein, uncovering how post-Euclidean concepts revolutionized our understanding of spacetime and laid the foundation for modern physics.
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24 Lesons
1 hour 2 minutes
On-Demand
Free-Video
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

Inconvenient Truths About the Square Root of 2 - Real Numbers and Limits

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Explores the concept of sqrt(2), its historical significance, and modern approaches, challenging traditional views on irrational numbers and highlighting logical issues in mathematical analysis.
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10 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

The Geometry of Surfaces - Algebraic Topology Lecture 20

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Explore the connection between 2D surfaces and classical geometries, focusing on isometries and introducing hyperbolic geometry through circle inversions in the Beltrami Poincare disk model.
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1 Lesons
44 minutes
On-Demand
Free-Video
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
Free-Video
Insights into Mathematics

Isometry Groups of the Projective Line - Rational Geometry Math Foundations 138

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Explore isometry groups of the projective line, focusing on rotations and reflections. Learn about symmetry, group theory, and their algebraic relationships in a concrete, accessible way.
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7 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Algebraic Structure on the Euclidean Projective Line - Rational Geometry Math Foundations 137

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Explores algebraic structure on the Euclidean projective line, covering projective formulas, isometries, rotations, and their compositions. Connects to chaos theory and complex number multiplication.
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9 Lesons
41 minutes
On-Demand
Free-Video
Insights into Mathematics

The Chromatic Algebra of 2x2 Matrices - Part 2

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Explores chromatic algebra of 2x2 matrices, focusing on subalgebras, complexions, dot products, and the four-dimensional Dihedrons algebra. Compares to quaternions and highlights unique properties.
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1 Lesons
38 minutes
On-Demand
Free-Video
Insights into Mathematics

The Chromatic Algebra of 2x2 Matrices - Wild Linear Algebra B41

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Explore chromatic algebra in 2x2 matrices, covering subalgebras, complexions, trace, determinant, and characteristic polynomials. Introduces unique dot products on 2x2 matrices.
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8 Lesons
32 minutes
On-Demand
Free-Video
Insights into Mathematics

Circles and Spheres via Dot Products - Part 1

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Explore circles using dot products in linear algebra. Learn two approaches: quadratic and bilinear equations. Discover applications to tangents, pole/polar duality, and classical theorems in projective geometry.
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1 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

Applications of the Dot Product to Planar Geometry - Part 1

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Explore how the dot product shapes planar Euclidean geometry, introducing linear functionals, normal vectors for lines, and geometric projections in linear algebra.
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1 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Meusnier, Monge and Dupin - Differential Geometry - Lecture 32

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Explore Monge's contributions to differential geometry, including descriptive geometry, theorems, and studies on curves, surfaces, and lines of curvature in this advanced mathematics lecture.
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10 Lesons
48 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

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

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
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
The Royal Institution

Geometry in Everyday Life - Past, Present, and Future

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Explore the past, present, and future of geometry with Yang-Hui He and Madeleine Hall. Discover how geometric principles shape our world, from ancient postulates to modern applications in nature and science.
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1 Lesons
35 minutes
On-Demand
Free-Video
MindYourDecisions

Geometry Problem from the 2024 International Mathematical Olympiad - Explained

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Explore a challenging geometry problem from the 2024 International Mathematical Olympiad, with step-by-step analysis and proof techniques for advanced mathematical reasoning.
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5 Lesons
20 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
Schmid College, Chapman University

The Conundrum of the Fourth Postulate - Euclid's Geometry Revisited

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Explore the historical and philosophical aspects of Euclid's fourth postulate, examining its provability within a constructive setting and offering a novel perspective on this classical mathematical problem.
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1 Lesons
1 hour 57 minutes
On-Demand
Free-Video
Schmid College, Chapman University

A Possible Way to Read and Interpret Euclid's Elements

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Explore a novel approach to reading Euclid's Elements, focusing on fundamental theorems in Books I and II as a guide to understanding Euclidean geometry and its philosophical implications.
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1 Lesons
2 hours 3 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

The Steklov Spectrum of Convex Euclidean Polygons

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Explore upper bounds and inverse problems for Steklov eigenvalues of convex polygons. Discover how generic n-gons can be determined by their Steklov spectra using powerful spectral invariants.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Divisibility of Spheres with Measurable Pieces - Oleg Pikhurko

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Explore divisibility of spheres with measurable pieces, focusing on Euclidean (d-1)-dimensional sphere S^(d-1) and special orthogonal matrices. Examine impossibility of measurable divisibility for generic rotations.
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1 Lesons
48 minutes
On-Demand
Free-Video
Banach Center

Rigidity of Convex Surfaces in Space-Forms

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Explore rigidity properties of convex surfaces in space-forms, focusing on mathematical concepts and geometric analysis techniques.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Fields Institute

Maximally Dense Sphere Packings

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Explore optimal arrangements of disks in 2D and higher dimensions, focusing on recent findings for multiple disk sizes. Survey of results accessible to a broad audience.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Insights into Mathematics

The Three-Fold Symmetry of Chromogeometry - Rational Geometry Math Foundations

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Explore chromogeometry's three-fold symmetry, combining Euclidean and relativistic geometries. Discover new patterns and relations beyond traditional approaches, opening doors to 21st century geometric insights.
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8 Lesons
24 minutes
On-Demand
Free-Video
ICTP-SAIFR

Analog Model for Euclidean Wormholes Effects

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Explore an analog model for Euclidean wormholes effects, delving into quantum aspects of gravity and their potential laboratory observations.
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1 Lesons
48 minutes
On-Demand
Free-Video
VinAI

AlphaGeometry: Solving IMO Geometry Problems without Human Demonstrations

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Explore AlphaGeometry, a groundbreaking theorem prover for Euclidean plane geometry that outperforms previous methods and approaches IMO gold medallist level, solving complex problems without human demonstrations.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Michael Penn

Is This Triangle Even Possible? - A Geometric Problem Analysis

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Explore a fascinating geometric puzzle examining the possibility of constructing a specific triangle through step-by-step mathematical analysis and proof.
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1 Lesons
11 minutes
On-Demand
Free-Video
Michael Penn

Geometric Properties of Tumbling Squares in a Right Triangle

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Explore an intriguing geometric puzzle involving rotating squares within a right triangle, demonstrating mathematical relationships and properties through visual analysis.
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1 Lesons
17 minutes
On-Demand
Free-Video