Mahāvīra

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

Gaṇitasārasan̄graha has the following chapters

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 $S_{n}={\frac {ar^{n-1}X\ {r-a}}{r-1}}$

$={\frac {a(r^{n}-1)}{r-1}}$ where a is the first term and r is the common ratio and S_n is the sum to n terms.

External Links

• Mahāvīra

See Also

महावीर