Geometry I - Prof. Dr. Cem Tezer
Comprehensive exploration of fundamental geometric concepts, covering various topics over 16 weeks. Ideal for students seeking in-depth understanding of geometry principles and applications.
Geometry
Explore shapes, angles, and theorems in this comprehensive geometry overview, covering 2D and 3D concepts from basic principles to advanced calculations.
Why Is Doubling Cubes and Squaring Circles Impossible?
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.
PROLÍMPICO - 6° Edição 2023 - Geometria - Aula 02
Aprofunde-se em geometria olímpica com técnicas avançadas e resolução de problemas complexos para aprimorar suas habilidades em competições matemáticas.
Degeneration of Singular Circle Patterns
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.
The Language of Geometry - Math Terminology
Comprehensive review of geometry terminology for university students, covering Euclidean concepts, shapes, transformations, 3D geometry, and coordinate systems. Includes subtitles and supplementary materials.
Geometry with Linear Algebra - Wild Linear Algebra A - NJ Wildberger
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.
Euclid Book 1 Props I - V - A Critical Review - Sociology and Pure Mathematics - N J Wildberger
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.
How Chromogeometry Transcends Klein's Erlangen Program for Planar Geometries - N J Wildberger
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.
Isometry Groups in Planar Geometry - WildTrig: Intro to Rational Trigonometry - N J Wildberger
Explore isometry groups in Euclidean and relativistic geometries, focusing on grounded isometries, reflections, and rotations using an algebraic approach without infinite operations.
Relativistic Velocity, Core Circles, and Paul Miller's Protractor - Rational Geometry
Explores core circles in rational geometry, connecting projective and Euclidean geometry. Covers parametrization, quadrances, and theorems, bridging abstract concepts with practical applications.
Isometry Groups of the Projective Line - Rational Geometry Math Foundations
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.
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.
Absolute Versus Relative Measurements in Geometry - Rational Geometry Math Foundations
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.
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 Remarkable Platonic Solids I - Universal Hyperbolic Geometry
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.
The Cross Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger
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.
Quadrance and Spread - Universal Hyperbolic Geometry
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.
Spherical and Elliptic Geometries - An Introduction
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.
Branching Random Walks - Two Conjectures and a Theorem by Parthanil Roy
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.
Donald Coxeter and Geometry
Explore Donald Coxeter's contributions to geometry, including non-Euclidean geometries, higher dimensions, and connections to art and music in this engaging mathematical journey.