The Śrī Yantra, constructed exactly
Nine interlocking triangles, twenty-four triple intersections, forty-three chambers — and a figure that almost nobody draws correctly.
Anyone can sell a picture of a Śrī Yantra. Most contain geometric errors a measurement finds in seconds. What nobody else can do is prove theirs closes.
Every figure this platform produces ships with a certificate: the five parameters, the concurrency and concentricity residuals, the chamber count, and the engine version. Reproducible by anyone, impossible to fake.
The default figure
Concurrency and concentricity imposed exactly; the remaining freedom fixed by least squares against all twenty-seven numbers of the traditional construction.
| b | 0.489032362600 |
| c | 0.249533013554 |
| d | 0.273011999025 |
| e | 0.465372418465 |
| g | 0.098643819684 |
| concurrency residual | 3.80e-13 |
| concentricity residual | 1.88e-13 |
| chambers | 1 + 8 + 10 + 10 + 14 = 43 |
| misfit to the traditional construction | 2.2960% |
| the tradition’s own internal inconsistency | 2.675% |
The misfit is below the noise floor — the reconstruction explains the tradition’s numbers better than those numbers explain each other, which is the signature of noisy measurements of an exact underlying object.
Studio
Generate any figure, move the five parameters and watch it stop closing, recolour it, turn the Meru, and export to 23 formats.
Library
9 published figures — Huet, Kulaichev, Rao, the tradition — in one coordinate system, measured and drawn side by side.
Sources
27 sources with a status each, and for 14 of them what happened when the claim was tested against the engine.
Colour
8 records of what the tradition attests about colour and material — who says it, and how far it goes. No claims about effect.
Kūrma
The figure on a sphere — where the construction has a floor, the optimum is a shallow dome, and the plate can be exported as a carvable solid.
The Book
Thirty-two chapters and five appendices on the geometry, the tradition, and the search for the true figure.
Licences
Reading is free, permanently. The studio and every file it produces — print, CAD, three dimensions — open with a licence.
How the engine is verified
| check | agreement |
|---|---|
| the source implementation, all 54 triangle coordinates | 1.1 × 10⁻¹⁶ |
| Huet 2002 — his fifth parameter recovered from concurrency alone | 7 × 10⁻⁵ |
| Rao 1998 — all seven published parameter sets | 1 × 10⁻⁷ |
| the spherical engine against Rao’s r = 10° optimum | 1 × 10⁻⁸ |
| the spherical engine at r = 0.5°, against the plane engine | 4 decimals |
The last is the one worth noticing: two independently written engines agreeing on a quantity neither was tuned to reproduce.
Two things this work found
The forty-three chambers do not tile the figure. They are edge-disjoint — all 129 of their edges are distinct, and adjacent chambers meet only at vertices. They cover 57.2% of the area the nine triangles enclose. Both things are true at once: there are exactly forty-three, and they do not fill it. So a Meru’s tier is a level whose outline is the outer envelope of its chambers, not their union.
Swept for that envelope, the five inner enclosures return 28, 20, 20, 16, 3 vertices — a fourteen-pointed star, two ten-pointed, an eight-pointed, and the trikoṇa. Nothing told the sweep to expect that. It is what every drawing has always shown, recovered from the five parameters alone.
The Meru is a 45° pyramid. Put the apex over the centre and run the face down to the mid-side of the bhūpura, and one angle fixes the whole elevation. At 45° — rise equal to run — the height comes out at exactly half the base width. The Sahasrākṣī Meru at Devipuram is 108 feet square on 54 feet: that ratio to the digit, with the cast bronzes at 0.481 and 0.525 either side. At that angle and no other, the cap closing the summit is a true hemisphere.