Mahāvīra: Difference between revisions

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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>
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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.
:It was Mahāvīra  who first treats the series in [[Geometric progressions]] and gives almost all the formulae required therein.
:गुणसङ्कलितान्त्यधनं विगतैकपदस्य गुणधनं भवति ।  
:गुणसङ्कलितान्त्यधनं विगतैकपदस्य गुणधनं भवति ।  
:तद्गुणगुणं मुखोनं व्येकोत्तर भाजितं सारम् ॥
:तद्गुणगुणं मुखोनं व्येकोत्तर भाजितं सारम् ॥
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</math> where a is the first term and r is the common ratio and S<sub>n</sub> is the sum to n terms.
</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.
: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.


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

Revision as of 19:53, 14 November 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.

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)
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