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.
Triangle Geometry Problem: Proving z²/(x²+y²) = 1/2 Using the Sine Rule
Reidemeister Moves: Transforming a Trefoil Knot Step by Step
Reidemeister Theorem: How Knots Became Rigorous Mathematics
The Coastline Paradox: Why the Length of a Coastline Cannot Be Measured
Archimedes’ Sphere Slicing Theorem: Why Every Slice Has Equal Surface Area
Imagine putting a spherical loaf of bread into a bread slicer. No matter where you cut, every single slice comes…
The Law of Sines: Beauty, History, and Applications in Geometry
The First Trigonometric Proof of the Pythagorean Theorem Explained
Remember, a week ago I wrote about a new proof of the Pythagorean theorem — the first trigonometric proof in…
The “Impossible” Trigonometric Proof of the Pythagorean Theorem Explained
Fields Medal Winners and the Depths of Algebraic Geometry: From Hironaka to Mumford
I've been reading Modern Mathematics in the Glow of the Fields Medals by Monastyrsky — a book dedicated to the…