When Law Met Mathematics

He was a lawyer, a qualified lawyer and had studied law at Poitiers, graduating in 1559. He began his career as an attorney at a quite high level, with cases involving the widow of King Francis I of France and also Mary, Queen of Scots. He generally pleaded important cases of royal families and won also. He was always logical in his dealings and practice. He argued his cases on logics and never hid any facts irrespective these went against him.

But law was not his cup of tea. He was always curious solving mathematical problems. What makes a circle round, a rectangle cornered and a line straight? Can a polygon be a circle? He used to ponder over such problems sitting on his desk with elbow on the study table, taking food with other hand and constantly concentrating on the same problem even for as many as three days. He was François Viète of France, a Lawyer and Mathematician, a combination that is uncommon and he was uncommon.

Nonetheless, he was highly successful in law. By 1590 he was working for King Henry IV. The king admired his mathematical talents, and Viète soon confirmed his worth by cracking a Spanish cipher, thus allowing the French to read all the Spanish communications they were able to obtain.

He did not abandon his passion for mathematics and In 1591, François Viète came out with an important book, introducing what is called the new algebra: a symbolic method for dealing with polynomial equations.

How I came to know of this great Mathematician, is also worth telling. A few months back, it was Pie (written as π) day and there was a great hustle and bustle and magazines full of articles on Pi. This inspired me though late to contribute something to Pi which is considered the great mathematical constant.

For a person like me who had studied mathematics from the point of view of its applicability to Engineering, writing on Pi by me with contents noticeable among mathematics fraternity was analogous to passing post graduation by a school primer. With passing of each day, celebrations of Pi were dimming but my determination remained bright. Specially during morning walk when neurones were upbeat, different description of Pi focussed on my mental screen and finally I took this shining and glassy device in my hand and typed my notions about pie with title,”Pi Is Sweeter Than Pie.”

It was my whole hearted effort aimed at revealing something new which was not known earlier about Pi.I had already gone through various description evaluating Pi by means of infinite series and infinite products. Why I can’t give something alike of these, was the voice of my inner self.

Writing sine of an angle, I started sub dividing it infinitely into sines and cosines of an angle. Equating sin x as x where x diminished to very small quantity, Lo, there appeared an identity not seen by me. And I substituted x as Pi/2 and there appeared the value of Pi in nested form.

Immediately, I checked the identity on google search engine, yes it was correct, no one had done it the way I did. But still there was a lurking doubt in my mind, if I could do, others would have also done it. It were Eureka moments till my further search led me to Viete Formula for Pi. I looked at it intently, final formula of Viete had more or less the resemblance with my formula but his method was altogether different. There was a geometrical drawing, certain perpendiculars, triangles, everything was different but the result had the resemblance. Derivation done by me was based upon the trigonometry and calculus whereas great Mathematician Viete has derived it from geometry. This assuaged my feelings a bit, after all my approach was independent unguided by any help. An idea had cropped up in my mind and that led me to this derivation. “There are different ways to reach a destination and journey by each route had its own pleasures. Those who discover new ways, enjoys the beauty of virgin paths,” said I to myself.

Lifting my morales, I completed, “Pie is sweeter than pie,” which have many formulae to ponder and there one can find a bit of mathematician in oneself. Later on I found, it indeed proved sweeter than pie to many readers to whom I am indebted for showing interest in my works. Now whenever, I attempt any mathematical derivation, similarity of the result with Viete formula keeps me on tenter hooks. I am writing a paper on golden ratio and there too appears a nested function (similar to Viete Pi formula) to determine value of  φ^1/k where k = 2^n, φ = (1+ 5^1/2)/2 and n is 0, 1, 2, 3, ……. any number. But great Mathematician Viete has not done, according to me, work on golden ratio  φ and I feel secure.

Besides this, I find, attempting a mathematical derivation without having any knowledge of previous works in that field, gives one great satisfaction on knowing later on that ones approach was unique and undefiled. I am benefitted in this regard, there is an ocean of mathematics to attempt and derive independently. Do you endorse, books bias ones thinking? Whatsoever your answer may be, I am certain, it is one of the most difficult question to answer.

All said and done, Francoise Viete will remain great Mathematician in the annals of history. He was the first one from Europe to give formula in nested radicals of Pi to the world.

(Viete Beautiful Formula For Pi, see only integer 2 is used.)

If you happen to see this formula, it uses only one integer 2 to calculate Pi. One wonders if 2 was sufficient to evaluate Pi, what are then other integers meant for? Such great men will always be remembered like Benjamin Jonson said in poem, “In Short Measure Life May Perfect Be.” It is virtue that never dies, it is like a wood that is seasoned to last for ever.

References:

1. Image Pi courtesy Pi visualized. Saw it over at /r/dataisbeautiful and had to make it. – View on Imgur: https://m.imgur.com/r/wallpapers/ZCUW7js

2. Pi and Golden ratio by John Baez at https://johncarlosbaez.wordpress.com/2017/03/07/pi-and-the-golden-ratio/amp/

3. “Pi Is Sweeter Than Pie,” at https://narinderkw.wordpress.com/2017/04/10/pi-is-sweeter-than-pie/

4. Viete’s Formula for Pi at World Of Pi http://www.pi314.net/eng/viete.php

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About Author

Writer is an Electronics and Electrical Communication Engineering graduate and was earlier Scientist, then Instrument Maintenance Engineer, then Civil Servant in Indian Administrative Service (IAS). After retirement, he writes on subjects, Astronomy, Mathematics, Yoga, Humanity etc.