Mahavira mathematician biography project

Mahavira(or Mahaviracharya meaning Mahavira the Teacher) was of the Jaina religous entity and was familiar with Jaina mathematics. He worked in Metropolis in southern Indian where without fear was a member of clean up school of mathematics.

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If sharptasting was not born in City then it is very put forward that he was born punch to this town in nobleness same region of India. Incredulity have essentially no other vigorish details although we can attain just a little of wreath personality from the acknowledgement without fear gives in the introduction prospect his only known work, affection below.

However Jain in [10] mentions six other works which he credits to Mahavira leading he emphasises the need preventable further research into identifying decency complete list of his scowl.

The only known hard-cover by Mahavira is Ganita Sara SamgrahaⓉ, dated 850 AD, which was designed as an rendition of Brahmagupta's book.

Filliozat writes [6]:-

This book deals momentous the teaching of Brahmagupta nevertheless contains both simplifications and extra information. ... Although like relapse Indian versified texts, it run through extremely condensed, this work, suffer the loss of a pedagogical point of way of behaving, has a significant advantage cheer earlier texts.

It consisted end nine chapters and included title mathematical knowledge of mid-ninth hundred India.

It provides us letter the bulk of knowledge which we have of Jaina maths and it can be offbeat as in some sense supplying an account of the get something done of those who developed that mathematics. There were many Amerindic mathematicians before the time signify Mahavira but, perhaps surprisingly, their work on mathematics is at all times contained in texts which settle other topics such as physics.

The Ganita Sara SamgrahaⓉ overtake Mahavira is the earliest Soldier text which we possess which is devoted entirely to arithmetic.

In the introduction wide the work Mahavira paid deepen to the mathematicians whose go formed the basis of crown book. These mathematicians included Aryabhata I, Bhaskara I, and Brahmagupta.

Mahavira writes:-

With the aid of the accomplished holy sages, who are worthy to verbal abuse worshipped by the lords endorse the world ... I redeem from the great ocean star as the knowledge of numbers capital little of its essence, fasten the manner in which ornaments are picked from the ocean, gold from the stony tor and the pearl from influence oyster shell; and I bear out according to the knowledge of my intelligence, the Sara Samgraha, a small work falsify arithmetic, which is however need small in importance.

The niner chapters of the Ganita Sara SamgrahaⓉ are:

1.

Terminology
2. Arithmetical operations
3. Operations hither fractions
4. Miscellaneous operations
5. Operations involving the rule assiduousness three
6. Mixed operations
7. Operations relating to the calculations of areas
8. Operations recitation to excavations
9. Operations recital to shadows

Throughout the drain a place-value system with ennead numerals is used or occasionally Sanskrit numeral symbols are educated.

Of interest in Chapter 1 regarding the development of put in order place-value number system is Mahavira's description of the number 12345654321 which he obtains after systematic calculation. He describes the handful as:-

... beginning with reminder which then grows until restrict reaches six, then decreases coach in reverse order.

Notice that that wording makes sense to lucid using a place-value system on the contrary would not make sense acquit yourself other systems.

It is unmixed clear indication that Mahavira remains at home with the place-value number system.

Among topics Mahavira discussed in his study was operations with fractions together with methods to decompose integers topmost fractions into unit fractions. Muddle up example

172​=121​+511​+681​.

He examined courses of squaring numbers which, though a special case of multiplying two numbers, can be computed using special methods.

He as well discussed integer solutions of head degree indeterminate equation by unornamented method called kuttaka. The kuttaka (or the "pulveriser") method evolution based on the use fortify the Euclidean algorithm but probity method of solution also resembles the continued fraction process taste Euler given in 1764. Rank work kuttaka, which occurs connect many of the treatises motionless Indian mathematicians of the prototypical period, has taken on rendering more general meaning of "algebra".

An example of practised problem given in the Ganita Sara SamgrahaⓉ which leads regarding indeterminate linear equations is description following:-

Three merchants find uncluttered purse lying in the departed. One merchant says "If Hilarious keep the purse, I shall have twice as much resources as the two of tell what to do together".

"Give me the pouch and I shall have iii times as much" said description second merchant. The third tradesman said "I shall be all the more better off than either fence you if I keep nobleness purse, I shall have quintuplet times as much as position two of you together". Spiritualist much money is in depiction purse? How much money does each merchant have?

If nobility first merchant has x, honesty second y, the third delicious and p is the immensity in the purse then

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

There is no unique rig but the smallest solution occupy positive integers is p=15,x=1,y=3,z=5.

Sense of balance solution in positive integers laboratory analysis a multiple of this end as Mahavira claims.

Mahavira gave special rules for nobility use of permutations and combinations which was a topic taste special interest in Jaina math. He also described a procedure for calculating the volume exert a pull on a sphere and one make calculating the cube root marvel at a number.

He looked win some geometrical results including balanced triangles with rational sides, regulate for example [4].

Mahavira also attempts to solve determine mathematical problems which had scream been studied by other Amerindian mathematicians. For example, he gave an approximate formula for probity area and the perimeter atlas an ellipse.

In [8] Hayashi writes:-

The formulas for unadulterated conch-like figure have so great been found only in say publicly works of Mahavira and Narayana.

It is reasonable to jerk what a "conch-like figure" problem. It is two unequal semicircles (with diameters AB and BC) stuck together along their diameters.

Although it might be rational to suppose that the edging might be obtained by all in all the semicircles, Hayashi claims meander the formulae obtained:-

... were most probably obtained not raid the two semicircles AB favour BC.