Mahāvīra: Difference between revisions
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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. | |||
== External Links == | == External Links == |
Revision as of 13:10, 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]
- Saṃjñādhikāraḥ (Terminology)
- Parikarmavyavahāraḥ (Arithmetical operations)
- Kalāsavarṇavyavahāraḥ (Fractions)
- Prakīrṇakavyavahāraḥ (Miscellaneous problems)
- Trairāśikavyavahāraḥ (Rule of three)
- Miśrakavyavahāraḥ (Mixed problems)
- Kṣetragaṇitavyavahāraḥ (Measurement of Areas)
- Khātavyavahāraḥ (calculations regarding excavations)
- 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.