Petrie Polygons of a Polyhedron - Universal Hyperbolic Geometry
Explore Petrie polygons on polyhedra, focusing on Platonic solids. Learn about tesselations, Schlafli symbols, and orthogonal projections in this geometric journey.
Canonical Structures Inside the Platonic Solids III - Universal Hyperbolic Geometry
Explore the rich symmetries of the dodecahedron through internal structures like handle sets, inscribed cubes, tetrahedra, and face diameters. Discover five-fold and six-fold symmetries in this fascinating Platonic solid.
Canonical Structures Inside Platonic Solids II - Universal Hyperbolic Geometry
Explore symmetries and canonical structures within the cube, including 2-fold, 3-fold, and 4-fold symmetries. Gain insights into rigid motions and even/odd symmetries using graph theory concepts.
The Remarkable Platonic Solids II- Symmetry - Universal Hyperbolic Geometry
Explore the symmetries of Platonic solids through rigid motions and rotations, examining tetrahedron, cube, and dodecahedron symmetries while connecting rotations to directed edges and discussing duality.
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.
Eight Ninths and the Geometry of A4 Paper - Universal Hyperbolic Geometry
Explore the fascinating geometry of A4 paper, its connection to the spread 8/9, and how Rational Trigonometry provides deeper insights into everyday objects and mathematical concepts.
Teaching Connections Between Algebra and Geometry I - A MANSW Presentation
Exploring connections between algebra and geometry, covering topics like Euclidean algorithm, continued fractions, and projective geometry. Aims to revitalize interest in geometry as a core subject for students.
Euclid's Construction Problems I - Famous Math Problems
Explore Euclid's fundamental geometric constructions using straight-edge and compass, enhancing understanding of mathematical logic and the importance of constructing objects before theorizing about them.
Steiner's Regions of Space Problem - Famous Math Problems
Exploration of Steiner's space division problem, analyzing how many regions n planes can create in space, with insights into the analogous 2D problem and mathematical reasoning.
Archimedes' Squaring of a Parabola - Famous Math Problems
Explore Archimedes' ingenious solution to calculating the area of a parabolic section, a foundational problem in calculus, through geometric insights and elegant proofs.
Visualizing the Folium Surface with GeoGebra - Differential Geometry
Explore the folium surface using GeoGebra, developing skills in 3D visualization and understanding tangent planes and quadrics through dynamic geometry.
Tangent Conics and Tangent Quadrics - Differential Geometry
Exploring advanced calculus concepts through algebraic methods, focusing on tangent conics and quadrics. Offers a fresh perspective on polynomial approximations and their geometric applications.
Parametrized Curves and Algebraic Curves - Differential Geometry
Explore parametrization of curves, from ancient Greek conics to 17th-century algebraic curves. Discover fascinating mechanisms generating curves, including four-bar and Watt's linkages.
Classical Curves - Differential Geometry
Explore classical curves in differential geometry, from conics to advanced constructions. Learn techniques for generating new curves and their applications in various fields.
Equations of Lines and Planes in 3D - Wild Linear Algebra A - NJ Wildberger
Explore parametric and Cartesian equations of lines and planes in 3D space, including novel concepts like describing all 2D lines as a Möbius band and using determinants for 3D analysis.
Applications of 3x3 Matrices - Wild Linear Algebra A
Explore 3x3 matrices and their applications in 3D space, covering dilations, reflections, rotations, and projections. Learn key concepts and formulas for linear transformations in three dimensions.
Area and Volume - Wild Linear Algebra A | NJ Wildberger
Explore area and volume in linear algebra using bi-vectors and tri-vectors. Learn algebraic formulations, geometric proofs, and applications in physics and electromagnetism.
Geometry with Vectors - Wild Linear Algebra A 2 - NJ Wildberger
Explore vector geometry, arithmetic, and affine combinations. Learn key theorems about parallelograms and triangles. Practice with exercises on vector properties and geometric relationships.
Introduction to Linear Algebra - Wild Linear Algebra A 1 - NJ Wildberger
Explore geometric approach to linear algebra, focusing on vectors, coordinate systems, and transformations. Learn essential concepts and problem-solving techniques in this foundational mathematics course.
The Geometry of a System of Linear Equations - Wild Linear Algebra A
Explore the geometry of linear equations through a novel approach using properties instead of infinite sets. Gain insights into subspaces, kernel, and linear transformations with practical examples.
Trigonometric Dual Laws and the Parallax Formula - Universal Hyperbolic Geometry
Explore trigonometric dual laws and the Right parallax formula in Universal Hyperbolic Geometry. Learn about Pythagoras' theorem, Cross dual law, and zero quadrance/spread theorems.