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
Essays & explanations
Articles
Mathematical stories developed through examples, visuals, computation and proof.
Kolams on Octahedron
An expository graph-theoretic classification of triangular binary kolam tiles on an octahedron.
KolamsGraph theoryPolyhedraSymmetry
The Law of Cosines
An interactive tessellation proof of the law of cosines, organised over the two-dimensional moduli space of triangle shapes.
GeometryTessellationsInteractive
From Sixteen Tiles to Fifty-One Kolams
An interactive exposition connecting square kolam tiles, graph theory, Boolean satisfiability, exhaustive enumeration, and Burnside’s lemma.
KolamsCombinatoricsGraph theoryBoolean satisfiabilityBurnside's lemmaSymmetry