Perunthachan Connections

I often refer here to the great cycle of Keralan myths called 'Parayipetta Panthirukulam' - the lives and adventures of 12 divinely gifted siblings of antiquity. Some of the siblings were historical figures but were not all contemporaries in any strict sense - the poet/sage Tiruvalluvar ('Vallon') who lived around the time of Christ was one of the brothers and so was Uppukoottan, who was a Muslim and hence could not have lived before 7th century AD. It was clear to me from a long time back that several members of this legendary fraternity were non-Keralan or non-Mallu - the aforementioned Tiruvalluvar, Tiruppan Alwar (Pananar) of Srirangam, Karaikal Matha (the 'lady' of Karaikal, a place on the Tamil coast)... were all clearly Tamil. But I was quite sure that Perunthachan, master craftsman and practical trickster, was out and out Mallu. And now, I have to correct myself.

'The Hindu' recently had an article on Vettuvan Koil, a rock-cut temple deep in Tamil Nadu. A significant Pandyan achievement along with the more famous paintings at Sittannavasal, the site has a mix of Jain and Hindu sculpture and architecture. Some superb details have been captured on this page: http://madraswanderer.blogspot.com/2010/02/vettuvankovil-at-peruneccuram-aka.html

Therein lies a Perunthachan connection. 'Vettuvan' in Tamil could mean either 'carver' or 'slasher (killer)' and refers to a local legend about the master architect/sculptor who built this koil (temple). While work was in progress, this guy murdered his even more gifted son in a fit of jealousy. As penalty, he had to leave the project unfinished; Vettuvan koil was never consecrated. This story line faithfully echoes (or anticipates) the (Keralan) myth of Perunthachan dropping a heavy chisel to sever his brilliant son's head. Note: While the Tam version of the legend is somewhat obscure, the Keralan counterpart is well-known.

I recall that near Chennai there is a place called Vettuvankeni (Vettuvan's tank/pond). I have not been there but I suspect it might have been the site of another of Perunthachan's achievements. Here is the story: a temple management hired Perunthachan to dig a ceremonial tank but the project soon ran into serious trouble as the trustees were totally divided on the shape the tank ought to have - some wanted a square, some a circle and others a rectangle .... Perunthachan worked out a complex, "egg-like" geometric shape which could indeed (!) look like all of these specified shapes - when viewed from suitable vantage points. The tank was soon ready but in a final twist, it was never used - most rituals need to be performed with reference to the cardinal directions and the tank was so disorienting that even east and west could not be made out!

Personal: I spent several months last year searching for the convex planar shape P with the property: if two mutually identical (congruent) convex shapes of largest area possible are cut out from P, the largest fraction of P's area goes waste. I could not solve the problem properly ... but I am tempted to christen the mysterious shape of P, the 'Perunthachan Oval'. Some details are here: http://arxiv.org/abs/1012.3106

The name I propose is aided by this bit from Wiki: an oval is any curve resembling an egg or an ellipse, but not an ellipse. Unlike other curves, the term 'oval' is not well-defined and many distinct curves are commonly called ovals.