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Mahāvīra or Mahāvīrācārya was a 9th-century Jain mathematician born in Mysore, in Southern India. He was born in the year 815 AD<ref>{{Cite web|title=Mahāvīra|url=https://vedicmathschool.org/mahavira/}}</ref>. ''Gaṇitasārasan̄graha'' was authored by Mahāvīra.  He was in the royal court of  king Amoghavarṣa of Rāṣṭrakūṭa  dynasty.
Mahāvīra or Mahāvīrācārya was a 9th-century Jain mathematician born in Mysore, in Southern India. He was born in the year 815 AD<ref>{{Cite web|title=Mahāvīra|url=https://vedicmathschool.org/mahavira/}}</ref>. ''[[Gaṇitasārasan̄graha]]'' was authored by Mahāvīra.  He was in the royal court of  king Amoghavarṣa of Rāṣṭrakūṭa  dynasty.


''Gaṇitasārasan̄graha''  has the following  chapters<ref>{{Cite web|title=Gaṇitasārasan̄graha|url=https://en.wikipedia.org/wiki/Ganita_sar_sangrah}}</ref>
''Gaṇitasārasan̄graha''  has the following  chapters<ref>{{Cite web|title=Gaṇitasārasan̄graha|url=https://en.wikipedia.org/wiki/Ganita_sar_sangrah}}</ref>


# '''Saṃjñādhikāraḥ''' (Terminology)
# '''Saṃjñādhikāraḥ''' (Terminology)
# '''Parikarmavyahāraḥ''' (Arithmetical operations)
# '''Parikarmavyavahāraḥ''' (Arithmetical operations)
# '''Kalāsavarṇavyahāraḥ''' (Fractions)
# '''Kalāsavarṇavyavahāraḥ''' (Fractions)
# '''Prakīrṇakavyahāraḥ''' (Miscellaneous problems)
# '''Prakīrṇakavyavahāraḥ''' (Miscellaneous problems)
# '''Trairāśikavyavahāraḥ''' (Rule of three)
# '''Trairāśikavyavahāraḥ''' (Rule of three)
# '''Miśrakavyahāraḥ''' (Mixed problems)
# '''Miśrakavyavahāraḥ''' (Mixed problems)
# '''Kṣetragaṇitavyahāraḥ''' (Measurement of Areas)
# '''Kṣetragaṇitavyavahāraḥ''' (Measurement of Areas)
# '''Khātavyahāraḥ''' (calculations regarding excavations)
# '''Khātavyavahāraḥ''' (calculations regarding excavations)
# '''Chāyāvyahāraḥ''' (Calculations relating to shadows)
# '''Chāyāvyavahāraḥ''' (Calculations relating to shadows)


: Mahāvīrācārya has praised mathematics in ''Gaṇitasārasan̄graha''
: Mahāvīrācārya has praised mathematics in ''Gaṇitasārasan̄graha''
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:व्यापारस्तत्र सर्वत्र संख्यानमुपयुज्यते॥
:व्यापारस्तत्र सर्वत्र संख्यानमुपयुज्यते॥
: Meaning : Where there is business in worldly, Vedic and contemporary, only numbers are used everywhere.
: Meaning : Where there is business in worldly, Vedic and contemporary, only numbers are used everywhere.
:It was Mahāvīra  who first treats the series in [[Geometric progressions]] and gives almost all the formulae required therein.
:गुणसङ्कलितान्त्यधनं विगतैकपदस्य गुणधनं भवति ।
:तद्गुणगुणं मुखोनं व्येकोत्तर भाजितं सारम् ॥
:अन्त्यधन - the value of the last term. गुण - common ratio.
:The verse states that <math>S_n =\frac{ar^{n-1} X \ { r-a }  }{r-1} 
</math>
:<math>=\frac{a(r^n-1)}{r-1} 
</math> where a is the first term and r is the common ratio and S<sub>n</sub> is the sum to n terms.
:Mahāvīra's work differs <ref>{{Cite book|last=Gurjar|first=L V|title=Ancient Indian Mathematics and Vedha|year=1947|location=Pune|pages=102-103}}</ref>from that of others in respect of the definitions he introduced of various figures. He has given the definitions of a triangle-equilateral, isosceles and scalene-a square, a rectangle, [[isosceles trapezium]], trapezium with three sides equal, a quadrilateral, a circle, a semicircle, an ellipse, a hollow hemisphere and the lune. It is true that the results he derived regarding the area of an ellipse and the length of the curve of an ellipse are not accurate; but as a pioneer in this line his place stands high. Almost all the properties of the [[cyclic quadrilateral]] derived by [[Brahmagupta]], have been more lucidly explained by him.
== Contributions of Mahāvīra in Mathematics ==
* Separated astrology from mathematics<ref>{{Cite web |title=Mahāvīra |url=https://vedicmathschool.org/mahavira/}}</ref>
* Created the terms equilateral and isosceles triangle, rhombus , circle and semicircle
* Created formula that calculated the area and perimeters of ellipses.
* devised methods to calculate the square of a number and cube roots of a number.
* worked on the works of Āryabhaṭa and refined it.


== External Links ==
== External Links ==


* [https://mathshistory.st-andrews.ac.uk/Biographies/Mahavira/ Mahāvīra]  
* [https://mathshistory.st-andrews.ac.uk/Biographies/Mahavira/ Mahāvīra]  
*[http://www.chaturpata-atharvan-ved.com/spiritual-books-section/spiritual-books/acharya-literature/scientist-acharya-of-ancient-india/Ganit-Sara-Sangraha-MahavirAcharya-Jain-EN.pdf Ganit-Sara-Sangraha-MahavirAcharya-Jain-EN.pdf]


== See Also ==
== See Also ==
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== References ==
== References ==
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Latest revision as of 15:43, 1 December 2022

Mahāvīra or Mahāvīrācārya was a 9th-century Jain mathematician born in Mysore, in Southern India. He was born in the year 815 AD[1]. Gaṇitasārasan̄graha was authored by Mahāvīra. He was in the royal court of king Amoghavarṣa of Rāṣṭrakūṭa dynasty.

Gaṇitasārasan̄graha has the following chapters[2]

  1. Saṃjñādhikāraḥ (Terminology)
  2. Parikarmavyavahāraḥ (Arithmetical operations)
  3. Kalāsavarṇavyavahāraḥ (Fractions)
  4. Prakīrṇakavyavahāraḥ (Miscellaneous problems)
  5. Trairāśikavyavahāraḥ (Rule of three)
  6. Miśrakavyavahāraḥ (Mixed problems)
  7. Kṣetragaṇitavyavahāraḥ (Measurement of Areas)
  8. Khātavyavahāraḥ (calculations regarding excavations)
  9. Chāyāvyavahāraḥ (Calculations relating to shadows)
Mahāvīrācārya has praised mathematics in Gaṇitasārasan̄graha
लौकिके वैदिके वापि तथा सामयिकेऽपि यः।
व्यापारस्तत्र सर्वत्र संख्यानमुपयुज्यते॥
Meaning : Where there is business in worldly, Vedic and contemporary, only numbers are used everywhere.
It was Mahāvīra who first treats the series in Geometric progressions and gives almost all the formulae required therein.
गुणसङ्कलितान्त्यधनं विगतैकपदस्य गुणधनं भवति ।
तद्गुणगुणं मुखोनं व्येकोत्तर भाजितं सारम् ॥
अन्त्यधन - the value of the last term. गुण - common ratio.
The verse states that
where a is the first term and r is the common ratio and Sn is the sum to n terms.
Mahāvīra's work differs [3]from that of others in respect of the definitions he introduced of various figures. He has given the definitions of a triangle-equilateral, isosceles and scalene-a square, a rectangle, isosceles trapezium, trapezium with three sides equal, a quadrilateral, a circle, a semicircle, an ellipse, a hollow hemisphere and the lune. It is true that the results he derived regarding the area of an ellipse and the length of the curve of an ellipse are not accurate; but as a pioneer in this line his place stands high. Almost all the properties of the cyclic quadrilateral derived by Brahmagupta, have been more lucidly explained by him.

Contributions of Mahāvīra in Mathematics

  • Separated astrology from mathematics[4]
  • Created the terms equilateral and isosceles triangle, rhombus , circle and semicircle
  • Created formula that calculated the area and perimeters of ellipses.
  • devised methods to calculate the square of a number and cube roots of a number.
  • worked on the works of Āryabhaṭa and refined it.

External Links

See Also

महावीर

References

  1. ↑ "Mahāvīra".
  2. ↑ "Gaṇitasārasan̄graha".
  3. ↑ Gurjar, L V (1947). Ancient Indian Mathematics and Vedha. Pune. pp. 102–103.{{cite book}}: CS1 maint: location missing publisher (link)
  4. ↑ "Mahāvīra".
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