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## Paramesvara – The Mathematician Who Gave the World Cyclic Quadrilaterals 350 Years Before Lhuilier!

Where do you find the brightest minds of our time? The idealist in me likes to believe they are hidden amongst the everyday hustle and grind; But a very reasonable person will tell you to find a reputed university for them. But as old as universities may be, there was a time when brilliant minds walked among us not as academic elites, but as ordinary people. They are not removed from our everyday reality, but used to fuel their ideas and theories. One such person lived in South India and his name was Parameshwar.

It is not uncommon to hear of mathematics’ undying love affair with India; After all it was here that the zero was invented. Then there was Aryabhatta – many of whose teachings and interpretations still hold relevance and validity from the 5th century AD. Names like Bhaskar and Ramanujan also gain respect and recognition. But little is known about another great Indian mathematician who lived at the end of the 15th century.

Born amidst the lush green landscape of God’s own country – Kerala – Parameshwar was a renowned mathematician and astronomer. He wrote a series of commentaries on contemporary and ancient Indian mathematical and astronomical texts during his lifetime, which is estimated to be over 55 years. He is revered for his eclipse observations, as well as for modifying planetary parameters to create greater coherence between theoretical models and direct observations. Perhaps, the real proof of his skill lies in the fact that he proposed methods and principles that were unheard of in India but all over the world. In fact it was two hundred years before the West made similar or parallel discoveries.

For example his work Siddhantadipika – a commentary on Govindaswami’s commentary on the Mahabhaskariya by Bhaskara I – includes eclipse observations, a mean value type formula for calculating the inverse trajectory of a sine and a point iteration technique for calculating any sine. the angle It also includes a two-point iterative logarithm, similar to the modern secant method.

Furthermore, God also proposed a technique for calculating the radius of a circle circumscribing a cyclic quadrilateral, using the sides of the quadrilateral to calculate the same. According to the technique, the radius of a circle (r) can be calculated by the formula

r2 = x/y, where

x= (ab+cd) (ac+bd) (ad+bc) and

y = (a+b+cd) (b+c+da)(c+d+ab)(d+a+bc)

where a, b, c and d are the four sides of the cyclic quadrilateral.

The formula is usually attributed to the Swiss mathematician Simon Antoine Jean Lahuiler, who lived and worked only at the end of the 19th century – exactly 350 years after Paramesvara first promulgated the formula.

The lack of information about Parameswara, or any knowledge of his thoughts and works, can be attributed to the wide communication gaps that existed at the time, as well as the turbulent history of the Indian subcontinent over the next two centuries. But having entered the twenty-first century, we have the luxury of acknowledging the unsung heroes of ancient and medieval India and their pioneering visions and ideas and sharing their stories across the globe. Why not start with God?!

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