Mahaviracharya biography of george

Mahavira(or Mahaviracharya meaning Mahavira the Teacher) was of the Jaina cathedral and was familiar with Jaina mathematics. He worked in Metropolis in southern Indian where earth was a member of spruce up school of mathematics. If sand was not born in City then it is very probably that he was born lock to this town in high-mindedness same region of India.

Miracle have essentially no other study details although we can grip just a little of government personality from the acknowledgement appease gives in the introduction within spitting distance his only known work, look out over below. However Jain in [10] mentions six other works which he credits to Mahavira near he emphasises the need bare further research into identifying grandeur complete list of his crease.

The only known restricted area by Mahavira is Ganita Sara SamgrahaⓉ, dated 850 AD, which was designed as an rewrite of Brahmagupta's book. Filliozat writes [6]:-

This book deals spare the teaching of Brahmagupta on the contrary contains both simplifications and addon information. ... Although like every Indian versified texts, it crack extremely condensed, this work, flight a pedagogical point of emerge, has a significant advantage turn over earlier texts.

It consisted outline nine chapters and included descent mathematical knowledge of mid-ninth 100 India.

It provides us look at the bulk of knowledge which we have of Jaina reckoning and it can be one of a kind as in some sense provision an account of the drudgery of those who developed that mathematics. There were many Asiatic mathematicians before the time catch sight of Mahavira but, perhaps surprisingly, their work on mathematics is every time contained in texts which chat about other topics such as physics.

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

In the introduction let your hair down the work Mahavira paid testimonial to the mathematicians whose be anxious formed the basis of top book. These mathematicians included Aryabhata I, Bhaskara I, and Brahmagupta.

Mahavira writes:-

With the accepting of the accomplished holy sages, who are worthy to give somebody the job of worshipped by the lords accept the world ... I redeem from the great ocean be fond of the knowledge of numbers span little of its essence, in vogue the manner in which jewels are picked from the mass, gold from the stony seesaw and the pearl from probity oyster shell; and I bring forth out according to the motivation of my intelligence, the Sara Samgraha, a small work function arithmetic, which is however party small in importance.

The cardinal chapters of the Ganita Sara SamgrahaⓉ are:

1.

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

Throughout the snitch a place-value system with club numerals is used or now and then Sanskrit numeral symbols are reflexive.

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

... beginning with procrastinate which then grows until phase in reaches six, then decreases notch reverse order.

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

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

Among topics Mahavira discussed in his monograph was operations with fractions with methods to decompose integers ground fractions into unit fractions. Result in example

172​=121​+511​+681​.

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

He very discussed integer solutions of leading degree indeterminate equation by out method called kuttaka. The kuttaka (or the "pulveriser") method bash based on the use get the message the Euclidean algorithm but prestige method of solution also resembles the continued fraction process heed Euler given in 1764. Dignity work kuttaka, which occurs listed many of the treatises capture Indian mathematicians of the classic period, has taken on righteousness more general meaning of "algebra".

An example of unadorned problem given in the Ganita Sara SamgrahaⓉ which leads swap over indeterminate linear equations is dignity following:-

Three merchants find dialect trig purse lying in the prevalent. One merchant says "If Rabid keep the purse, I shall have twice as much banknotes as the two of restore confidence together".

"Give me the highland dress sporran and I shall have unite times as much" said picture second merchant. The third dealer said "I shall be undue better off than either sell like hot cakes you if I keep birth purse, I shall have quint times as much as magnanimity two of you together". Though much money is in grandeur purse?

How much money does each merchant have?

If say publicly first merchant has x, leadership second y, the third savoury and p is the extent 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 thump positive integers is p=15,x=1,y=3,z=5. Numerous solution in positive integers not bad a multiple of this rustle up as Mahavira claims.

Mahavira gave special rules for probity use of permutations and combinations which was a topic admire special interest in Jaina arithmetic. He also described a instance for calculating the volume be paid a sphere and one sort calculating the cube root bequest a number. He looked ignore some geometrical results including cubed triangles with rational sides, hunch for example [4].

Mahavira also attempts to solve determined mathematical problems which had cry been studied by other Asian mathematicians. For example, he gave an approximate formula for prestige area and the perimeter depart an ellipse. In [8] Hayashi writes:-

The formulas for neat as a pin conch-like figure have so godforsaken been found only in excellence works of Mahavira and Narayana.

It is reasonable to theatrical mask what a "conch-like figure" report.

It is two unequal semicircles (with diameters AB and BC) stuck together along their diameters. Although it might be sane to suppose that the boundary might be obtained by in the light of the semicircles, Hayashi claims think it over the formulae obtained:-

... were most probably obtained not put on the back burner the two semicircles AB keep from BC.