The library

Every published figure in one coordinate system, with measured residuals.

The field has no shared frame. Kulaichev states his figure as the root of an eighth-degree polynomial, Huet as eleven coordinates on a unit diameter, Rao as nonlinear-programming output, the tradition as integers on a diameter of forty-eight. None can be compared with any other as published.

This table is that comparison. Concurrency is how far the three lines that should meet at each of the twenty-four triple points actually miss. Concentricity is how far the central triangle’s incentre sits from the centre of the circle. Both should be zero. Misfit is the distance from the traditional construction’s twenty-seven numbers — and those numbers disagree with each other by 2.675% of R, so a figure closer than that is nearer to the tradition than the tradition is to itself.

figure	b	c	d	e	g	concurrency	concentricity	misfit	chambers
The Reconstruction This study, Chapter 19	0.489032	0.249533	0.273012	0.465372	0.098644	closes	closes	2.296% below noise	43
The Reconstruction, equilateral centre This study, Chapter 19 §19.4	0.472585	0.261282	0.306197	0.479117	0.120693	closes	closes	4.425%	43
The Tradition — 12 : 6 : 7 : 11 : 3 in twenty-fourths Vyāse devīkṛte… verse	0.500000	0.250000	0.291667	0.458333	0.125000	2.21e-2	3.63e-3	2.675%	43
Huet 1990 / 2002 Huet, Gérard	0.466074	0.204000	0.336000	0.438000	0.074000	closes	4.19e-2	4.941%	43
Kulaichev 1984 Kulaichev, A. P.	0.560659	0.279461	0.279461	0.513999	0.101410	closes	closes	3.953%	43
Rao 1998 — plane optimum Rao, C. S.	0.482391	0.261039	0.287454	0.467384	0.108463	closes	closes	3.129%	43
Rao 1998 — {1,2,5,6,19} Indian Journal of History of Science 33(3), 1998, Table 3	0.467298	0.261224	0.304553	0.471512	0.120134	closes	closes	4.437%	43
Rao 1998 — {1,2,6,14,19} Indian Journal of History of Science 33(3), 1998, Table 3	0.468710	0.257071	0.308200	0.480582	0.121790	closes	closes	4.436%	43
The “Optimal” figure sriyantraresearch.com	0.476092	0.269564	0.300965	0.470340	0.118093	closes	closes	4.475%	43

“Closes” means the condition holds to the precision of the published values. Where a number appears instead, the figure does not close — and the drawings below show where.

The same figures, drawn

Without the lotuses and the bhūpura, because the ornament is identical in all of them and would hide the only thing that differs: the nine triangles and where their apexes land.

The ReconstructionConcurrency and concentricity exact; the remaining freedom fixed by least squares against all 27 traditional numbers. Misfit 2.2960% against a 2.675% noise floor — it explains the tradition better than the tradition explains itself.

The Reconstruction, equilateral centreAs above with the equilateral condition imposed. Worse on the data (misfit 4.425%) but its bindu is unambiguous, since incentre and centroid coincide only for an equilateral triangle.

The Tradition — 12 : 6 : 7 : 11 : 3 in twenty-fourthsThe traditional construction read directly into the five parameters. Not concurrent — error 2.208% of R, about the resolution of its own integer scale. Three of the five values are dyadic.

Huet 1990 / 2002Concurrency only. Not concentric — residual 4.19e-2, the largest deviation in the literature. Huet fixed the remaining four parameters by aesthetic judgment and said so.

Kulaichev 1984Concurrent, concentric, with the two largest triangles equal (c = d). Reproduced independently by Rao fourteen years later. Note b exceeds the source implementation’s default bound.

Rao 1998 — plane optimumThe source of the five-variable parameterisation used throughout the modern literature, generally uncredited.

Rao 1998 — {1,2,5,6,19}Satisfies all three of the later “optimal” criteria — eight years before they were proposed, and uncited by that account.

Rao 1998 — {1,2,6,14,19}Also satisfies all three criteria, and is a different figure from the row above — which is how we know three conditions leave two degrees of freedom.

The “Optimal” figureConcurrency, concentricity and an equilateral central triangle. One of infinitely many figures satisfying those three; the account presents it as unique.

Colour

Every palette in the studio carries the object or text that attests it, and none of them claims a colour does anything. The evidence, and how far each piece of it goes, is set out on the colour page.