August 30, 2024 at 11:44
English
Geometry and topology
Notes on the mathematics of shape, space, and continuity. Covers topics ranging from classical Euclidean geometry and differential curves to manifolds, surfaces, and topological invariants. Each piece breaks down a concept or proof with concrete examples and geometric intuition rather than dry formalism. For anyone who thinks visually and wants to understand why the structures look the way they do.
Brachistochrone and Tautochrone: How the Cycloid Solves Two Classic Optimization Problems
Gömböc: The Convex Shape with Exactly One Stable Equilibrium Point
The Bonnet Problem: Two Tori with Identical Metric and Mean Curvature but Different Global Shape
The Pythagorean Tree: A Beautiful Self-Similar Fractal Built from the Pythagorean Theorem
The Four Color Theorem: How a Computer Solved a 100-Year-Old Math Problem
The Witch of Agnesi: History, Geometric Construction, and the Runge Effect
Soap Films in 11 Dimensions: Why Minimal Surfaces Are Generically Smooth
What Is Algebraic Geometry and Why It Is Considered the Most Beautiful Branch of Mathematics
What is the best way to start the week? With algebraic geometry, of course.
Why Every Zoll Contact Form on the 5-Sphere Is Equivalent to the Standard One
Let's step away from everyday concerns for a moment and venture into the world of unusual geometries. A very recent…