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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 that they are hidden in the hustle and bustle of everyday life; but someone more practical will tell you to look for a reputable college for them. But no matter how old universities are, there was a time when the brightest minds among us walked not as academic elites, but as common people. They were not removed from our everyday realities, but used to strengthen their ideas and theories. Such a man lived in southern India, and his name was Paramesvara.

It is not surprising to hear of an eternal love affair with India on mathematics; after all it was here that copper was invented. Then there was Aryabhata – many of whose teachings and reflections from the 5th century AD are still relevant and valid. Names like Bhaskara and Ramanujan also receive respect and approval. But few people know about another great Indian mathematician who lived in the early 15th century.

Born in the lush green landscapes of God’s own country – Kerala – in the south, Paramesvara was a brilliant mathematician and astrologer. He wrote a series of commentaries on contemporary and ancient Indian mathematical and astronomical treatises during his lifetime, estimated to be more than 55 years old. He is credited for his observations of obscurity, as well as the change in the parameters of the planets to create a greater consistency between theoretical models and live observations. However, perhaps, the true testimony of his genius lies in the fact that he proposed methods and theories that were previously unseen in India but throughout the world. In fact it was a good few 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 – contains discoveries of closure, a mean-value type formula for calculating the reciprocal of the sine interval and a one-point iterative technique for calculating the sine of any given sine. bump It also includes a two-point iterative logarithm, which is essentially the same as the modern constant method.

In addition, Paramesvara also presented a technique to calculate the radius of a circle enclosed by a circumscribed rectangle, using the sides of the rectangle to calculate the same. According to the technique, the radius of a circle (r) can be calculated using 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 & d are the dimensions of the four sides of the circle.

This formula is generally attributed to the Swiss mathematician Simon Antoine Jean L’huiler, who lived and worked only at the beginning of the 19th century – a good 350 years after Parmesvara first derived the formula.

The paucity of information about Parmesvara, or lack of knowledge of his thoughts and work, may be attributed to the vast communication gaps that existed at the time, as well as the turbulent history of the Indian subcontinent over the next two centuries. But after entering the twenty-first century, we have the good fortune to acknowledge the unsung heroes of ancient and medieval India and their pioneering visions and ideas, and share their stories around the world. Why not start with Parmesvara?!

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