Sliding Between Kolams
Turn a square kolam into a sliding puzzle, discover the parity invariant, and see why 408 valid boards divide into two equally sized reachability classes.
KolamsCombinatoricsGraph theorySymmetryInteractive
Essays & explanations
Articles
Mathematical stories developed through examples, visuals, computation and proof.
Starting Later: Geometric Bounds for Stirling’s Formula
Beginning with a chord-and-tangent proof for log x, we move the starting point and uncover a nested family of bounds for the normalized factorial.
Stirling’s formulaAsymptotic analysisInequalitiesInteractive
The Law of Cosines
An interactive tessellation proof of the law of cosines, organised over the two-dimensional moduli space of triangle shapes.
GeometryTessellationsInteractive
Kolams on Octahedron
An expository graph-theoretic classification of triangular binary kolam tiles on an octahedron.
KolamsGraph theoryPolyhedraSymmetry
Infinitely many ‘proofs’ of Pythagoras’ theorem
An interactive common-lattice proof of Pythagoras’ theorem, with historical anchor positions from a medieval dissection to Perigal and beyond.
GeometryTessellationsInteractive
From 16! possibilities to 51 kolams
An interactive exposition connecting square kolam tiles, graph theory, Boolean satisfiability, exhaustive enumeration, and Burnside’s lemma.
KolamsCombinatoricsGraph theoryBoolean satisfiabilityBurnside's lemmaSymmetry