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
A journal and laboratory for mathematics
Mathematics worth
returning to.
Articles, notes and interactive investigations that make mathematical ideas visible without sanding away their depth.
Latest publication 1 October 2026 · 2 active projects · 6 live interactives
Featured investigation
From 16! possibilities to 51 kolams
Begin with the published exposition, take the classroom investigation further, then build and move the tiles in the Lab.
Beginning with From 16! possibilities to 51 kolams, this investigation continues through the Kolam Tiles project hub.
Explore the investigationRecently published
New articles
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
Study material
Recent notes
Expository noteUndergraduate
What Row Reduction Remembers
A geometric reading of row reduction: why RREF remembers the row space, how elimination moves through a pencil of lines, and what survives for arbitrary linear systems.
Course resourceGeneral · Undergraduate
Sixteen Tiles, One Kolam Puzzle
A classroom-ready investigation using binary tiles to explore local constraints, connectivity and sliding-puzzle invariants.
From the laboratory
Project hubs
Active now2 interactives
Tessellations
Interactive investigations in which periodic patterns turn area identities into movable geometric proofs.
Active now4 interactives
Kolam Tiles
Binary kolam tiles on square boards and polyhedral surfaces: local matching, global connectivity, graph structure, symmetry, puzzles, and interactive constructions.