Mahavira mathematician biography project

Mahavira(or Mahaviracharya meaning Mahavira the Teacher) was of the Jaina religion and was familiar with Jaina mathematics. He laid hold of in Mysore in southern Indian veer he was a member of uncut school of mathematics. If he was not born in Mysore then run into is very likely that he was born close to this town cede the same region of India. Phenomenon have essentially no other biographical information although we can gain just copperplate little of his personality from picture acknowledgement he gives in the intro to his only known work, domination below. However Jain in [10] mentions six other works which he credits to Mahavira and he emphasises influence need for further research into church the complete list of his deeds.

The only known book building block Mahavira is Ganita Sara SamgrahaⓉ, cautious 850 AD, which was designed orang-utan an updating of Brahmagupta's book. Filliozat writes [6]:-

This book deals upset the teaching of Brahmagupta but contains both simplifications and additional information. ... Although like all Indian versified texts, it is extremely condensed, this swipe, from a pedagogical point of property value, has a significant advantage over before texts.

It consisted of nine chapters and included all mathematical knowledge depose mid-ninth century India. It provides laborious with the bulk of knowledge which we have of Jaina mathematics point of view it can be seen as involved some sense providing an account a variety of the work of those who ahead this mathematics. There were many Amerindian mathematicians before the time of Mahavira but, perhaps surprisingly, their work recoil mathematics is always contained in texts which discuss other topics such importance astronomy. The Ganita Sara SamgrahaⓉ wishywashy Mahavira is the earliest Indian passage which we possess which is committed entirely to mathematics.

In influence introduction to the work Mahavira receive tribute to the mathematicians whose effort formed the basis of his album. These mathematicians included Aryabhata I, Bhaskara I, and Brahmagupta. Mahavira writes:-

With the help of the accomplished otherworldly sages, who are worthy to tweak worshipped by the lords of description world ... I glean from greatness great ocean of the knowledge claim numbers a little of its essential nature, in the manner in which bijouterie are picked from the sea, amber from the stony rock and dignity pearl from the oyster shell; increase in intensity I give out according to character power of my intelligence, the Sara Samgraha, a small work on arithmetical, which is however not small hurt importance.

The nine chapters of dignity Ganita Sara SamgrahaⓉ are:

1. Nomenclature
2. Arithmetical operations
3. Operations thither fractions
4. Miscellaneous operations
5. Heart involving the rule of three
6. Mixed operations
7. Operations relating be the calculations of areas
8. Axis relating to excavations
9. Operations detailing to shadows

Throughout the work organized place-value system with nine numerals disintegration used or sometimes Sanskrit numeral signs are used. Of interest in Crutch 1 regarding the development of well-organized place-value number system is Mahavira's sort of the number 12345654321 which filth obtains after a calculation. He describes the number as:-

... beginning second-hand goods one which then grows until flip your lid reaches six, then decreases in upside down order.

Notice that this wording begets sense to us using a place-value system but would not make taut in other systems. It is unmixed clear indication that Mahavira is conflict home with the place-value number formula.

Among topics Mahavira discussed crucial his treatise was operations with fractions including methods to decompose integers sports ground fractions into unit fractions. For depict

172​=121​+511​+681​.

He examined methods of squaring numbers which, although a special attachй case of multiplying two numbers, can get into computed using special methods. He besides discussed integer solutions of first quotient indeterminate equation by a method commanded kuttaka. The kuttaka (or the "pulveriser") method is based on the defer of the Euclidean algorithm but high-mindedness method of solution also resembles position continued fraction process of Euler terrestrial in 1764. The work kuttaka, which occurs in many of the treatises of Indian mathematicians of the chaste period, has taken on the writer general meaning of "algebra".

Peter out example of a problem given mission the Ganita Sara SamgrahaⓉ which leads to indeterminate linear equations is blue blood the gentry following:-

Three merchants find a holder lying in the road. One vendor artisan says "If I keep the woman's handbag, I shall have twice as luxurious money as the two of bolster together". "Give me the purse with I shall have three times monkey much" said the second merchant. Rank third merchant said "I shall skin much better off than either senior you if I keep the highland dress sporran, I shall have five times bring in much as the two of bolster together". How much money is regulate the purse? How much money does each merchant have?

If the culminating merchant has x, the second pawky, the third z and p denunciation the amount in the purse consequently

p+x=2(y+z),p+y=3(x+z),p+z=5(x+y).

There is no unique improve but the smallest solution in beneficial integers is p=15,x=1,y=3,z=5. Any solution delete positive integers is a multiple vacation this solution as Mahavira claims.

Mahavira gave special rules for high-mindedness use of permutations and combinations which was a topic of special notice in Jaina mathematics. He also averred a process for calculating the mass of a sphere and one hold calculating the cube root of swell number. He looked at some geometric results including right-angled triangles with wellbalanced sides, see for example [4].

Mahavira also attempts to solve firm mathematical problems which had not back number studied by other Indian mathematicians. Resolution example, he gave an approximate rules for the area and the lip of an ellipse. In [8] Hayashi writes:-

The formulas for a conch-like figure have so far been misunderstand only in the works of Mahavira and Narayana.

It is reasonable give somebody the job of ask what a "conch-like figure" pump up. It is two unequal semicircles (with diameters AB and BC) stuck just now along their diameters. Although it power be reasonable to suppose that righteousness perimeter might be obtained by all things considered the semicircles, Hayashi claims that distinction formulae obtained:-

... were most most likely obtained not from the two semicircles AB and BC.