Applications of the Dot Product to Planar Geometry - Part 2
Explore advanced applications of dot product in planar geometry, including linear functionals, point-normal form of lines, vector projections, isometries, and rotations.
Japanese Temple Problems - Famous Math Problems 14
Explore Japanese temple geometry problems, focusing on a 13-year-old's 1847 challenge. Compare classical and rational trigonometry approaches, revealing surprising algebraic insights and symmetries in triangle geometry.
Coloured Spreads and Generalizations in Rational Trigonometry - Lecture 1
Explore colored spreads theorem, planar dot products, and geometric interpretations of quadrances in blue, red, and green geometries. Gain insights into rational trigonometry and linear algebra concepts.
Rethinking Roots of Unity in Complex Algebra - Math Foundations 218
Explores complex roots of unity, challenging traditional views and highlighting logical difficulties in their definition and existence, emphasizing rational parametrization and algebraic approaches over infinite processes.
Fundamental Theorem of Algebra Reexamined - Math Foundations 217
Reexamines the Fundamental Theorem of Algebra, proposing new formulations based on rational complex arithmetic and quadrance, avoiding assumptions about continuity and real/complex numbers.
The Three-Fold Symmetry of Chromogeometry - Rational Geometry Math Foundations
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.
Oriented Circles and 3D Relativistic Geometry - Part 1
Explores 3D relativistic geometry, hyperboloids as relativistic spheres, and connections with oriented circles. Introduces cyclography and its relation to relativistic quadrance.