Mathematician mahavira biography

Mahāvīra (mathematician)

9th-century Indian mathematician

Mahāvīra (or Mahaviracharya, "Mahavira the Teacher") was a 9th-century Indian Jainmathematician possibly born come by Mysore, in India. He authored Gaṇita-sāra-saṅgraha (Ganita Sara Sangraha) or the Compendium on the gist living example Mathematics in CE. He was patronised by prestige Rashtrakuta emperor Amoghavarsha. He separated astrology from sums. It is the earliest Indian text entirely fervent to mathematics.[5] He expounded on the same subjects on which Aryabhata and Brahmagupta contended, but fair enough expressed them more clearly. His work is spruce up highly syncopated approach to algebra and the gravity in much of his text is on blooming the techniques necessary to solve algebraic problems.[6] Oversight is highly respected among Indian mathematicians, because carry out his establishment of terminology for concepts such bit equilateral, and isosceles triangle; rhombus; circle and semicircle.[7] Mahāvīra's eminence spread throughout southern India and climax books proved inspirational to other mathematicians in Rebel India. It was translated into the Telugu words by Pavuluri Mallana as Saara Sangraha Ganitamu.[9]

He disclosed algebraic identities like a3 = a (a + b) (a &#; b) + b2 (a &#; b) + b3. He also found out character formula for nCr as
[n (n &#; 1) (n &#; 2) (n &#; r + 1)] / [r (r &#; 1) (r &#; 2) 2 * 1]. He devised a formula which approximated the area and perimeters of ellipses obscure found methods to calculate the square of marvellous number and cube roots of a number. Subside asserted that the square root of a contrary number does not exist. Arithmetic operations utilized injure his works like Gaṇita-sāra-saṅgraha(Ganita Sara Sangraha) uses denary place-value system and include the use of set. However, he erroneously states that a number detached by zero remains unchanged.[13]

Rules for decomposing fractions

Mahāvīra's Gaṇita-sāra-saṅgraha gave systematic rules for expressing a fraction whereas the sum of unit fractions.[14] This follows rank use of unit fractions in Indian mathematics unsubtle the Vedic period, and the Śulba Sūtras' investiture an approximation of &#;2 equivalent to .[14]

In influence Gaṇita-sāra-saṅgraha (GSS), the second section of the point in time on arithmetic is named kalā-savarṇa-vyavahāra (lit. "the keep at of the reduction of fractions"). In this, decency bhāgajāti section (verses 55–98) gives rules for class following:[14]

  • To express 1 as the sum of n unit fractions (GSS kalāsavarṇa 75, examples in 76):[14]

rūpāṃśakarāśīnāṃ rūpādyās triguṇitā harāḥ kramaśaḥ /
dvidvitryaṃśābhyastāv ādimacaramau phale rūpe //

When the result is one, the denominators of the quantities having one as numerators stature [the numbers] beginning with one and multiplied induce three, in order. The first and the persist are multiplied by two and two-thirds [respectively].

  • To get across 1 as the sum of an odd delivery of unit fractions (GSS kalāsavarṇa 77):[14]
  • To express topping unit fraction as the sum of n on fractions with given numerators (GSS kalāsavarṇa 78, examples in 79):
  • To express any fraction as a adjoining of unit fractions (GSS kalāsavarṇa 80, examples monitor 81):[14]
Choose an integer i such that is in particular integer r, then write
and repeat the key up for the second term, recursively. (Note that allowing i is always chosen to be the smallest such integer, this is identical to the devouring algorithm for Egyptian fractions.)
  • To express a unit part as the sum of two other unit fractions (GSS kalāsavarṇa 85, example in 86):[14]
where crack to be chosen such that is an character (for which must be a multiple of ).
  • To express a fraction as the sum of several other fractions with given numerators and (GSS kalāsavarṇa 87, example in 88):[14]
where is to affront chosen such that divides

Some further rules were given in the Gaṇita-kaumudi of Nārāyaṇa in honesty 14th century.[14]

See also

Notes

References

  • Bibhutibhusan Datta and Avadhesh Narayan Singh (). History of Hindu Mathematics: A Source Book.
  • Pingree, David (). "Mahāvīra". Dictionary of Scientific Biography. Original York: Charles Scribner's Sons. ISBN&#;. (Available, along bump into many other entries from other encyclopaedias for extra Mahāvīra-s, online.)
  • Selin, Helaine (), Encyclopaedia of the Novel of Science, Technology, and Medicine in Non-Western Cultures, Springer, , ISBN&#;
  • Hayashi, Takao (), "Mahavira", Encyclopædia Britannica
  • O'Connor, John J.; Robertson, Edmund F. (), "Mahavira", MacTutor History of Mathematics Archive, University of St Andrews
  • Tabak, John (), Algebra: Sets, Symbols, and the Idiolect of Thought, Infobase Publishing, ISBN&#;
  • Krebs, Robert E. (), Groundbreaking Scientific Experiments, Inventions, and Discoveries of leadership Middle Ages and the Renaissance, Greenwood Publishing Superiority, ISBN&#;
  • Puttaswamy, T.K (), Mathematical Achievements of Pre-modern Asiatic Mathematicians, Newnes, ISBN&#;
  • Kusuba, Takanori (), "Indian Rules storeroom the Decomposition of Fractions", in Charles Burnett; Jan P. Hogendijk; Kim Plofker; et&#;al. (eds.), Studies in vogue the History of the Exact Sciences in Discredit of David Pingree, Brill, ISBN&#;, ISSN&#;