A kolam begins not with a line but with dots. The drawer sets out the pulli, a counted grid, five by five, seven by seven, or one of many rhombic and staggered arrangements, and only then draws, either joining dots with straight strokes or, in the kambi kolam, looping a continuous line around each dot without touching it. In the most admired kambi designs a single unbroken curve winds around every dot in the grid and closes on itself where it began. Practitioners judge a kolam by exactly the properties a geometer would name: symmetry, closure, the even weaving of the line, the fit of the figure to its grid. This is mathematics done by hand and memory, without instruments, at speed, before breakfast.
The rigour is real enough to have drawn formal study. Nagarajan devotes a chapter of her ethnography to the encounter between the kolam and the sciences: computer scientists in the tradition of Gift Siromoney treated kolam designs as picture languages, writing array grammars whose production rules generate legitimate figures, and the single-loop designs have been analysed as closed paths on lattices, kin to problems in graph theory. The kolam thus sits in both worlds at once. For the woman drawing it, it is an offering, a discipline and an inheritance; for the mathematician, a corpus of algorithms preserved in daily practice, a reminder that sophisticated geometry has flourished, anonymously and for centuries, on the thresholds of ordinary houses.