Ancient Indian Mathematics GANIT

Behold the man who shields his family from all suffering

Behold the man who shields his family from all suffering. Has not his body become a willing vessel for affliction. Without good men to hold it up, the family house will fall when misfortune descends. — Tirukkural 103: 1029-1030

गणित 

Ganita (Sanskrit: for mathematics; is derived from the root ‘gana’, which means to count or to enumerate.)

 

Mathematics in Ancient India

Mathematics in India has been cultivated in connection with Astronomy. Like the other streams of knowledge, the early references of mathematics, are also found in the vedic literature. The word ‘Rashividya’ is used for mathematics in Chhandogya Upanishad (7.1.2). Some hymns of Shuklayajureda reveal the knowledge of odd numbers and tables (18/24,25). The Brahmana texts like ; ‘ekaya svaha, dvabhyam svaha, tribhyah svaha’ reflect the vedic concept of arithmetical progressions. In Pingal Sutra there is a discourse on the calculation of squares and square roots.

The Indians; earlier than other nations; became familiar with the system of place value of numerals. Undoubtedly the Europian system of enumeration is of Indian origin. India is the birth place of several mathematical concepts including zero, the decimal system, algebra, algorithm, square root and cube root etc. The origin of calculus was in India, even more than three centuries before Leibnitz and Newton introduced their own theorems.

 

The concept of zero, i.e. shunya, which means ‘void’, a figure to indicate the absence of a position of number is virtually void. A round figure, symbol for zero, i.e. ‘0’ had emerged to represent the philosophical concept of void.

 

Mathematics in India might have started more than five thousand years ago. Since 1000 B.C. almost for a period of two thousand years, many a number of mathematical works were produced in India. Since the 5th centruay A.D., the method of graduated calculation had been introduced in India. By that time, the geometric theories were known to the Indians. We may see some displays of motifs on the walls of ancient temples. Those motifs ideally reflect the patterns available in Indian architecture, as we see the admixture of floral and wall pattern of geometric method. These concepts, were collected and developed further by the mathematicians like Aryabhata who flourished in the 5th Century A.D. His work Aryabhatiyam is equally important for Mathematics and Astronomy. The first part of the book explains the special system of writing numerals that was introduced by Aryabhata alone. The Second part gives a small anthology of mathematical teachings of Aryabhatta. He deals in his work with evolution and revolution, area and volumes, progressions and algebraic identities.

 

Brahmagupta’s work ‘Brahma-sphuta-siddhanta’ covers very briefly the arithmetical operations, square and cube roots, interest, progressions, geometry and simple algebraic identities.

 

Bhaskaracharya the great astronomer, enjoys high reputation as a mathematician also. His work Lilavati, in which a lovely maiden is addressed and problems set to her, is a famous book on mathematics. The second book Bijaganita, is the fullest and most systematic account of Indian algebra

Ganitasarasangraha of Mahaviracharya, Trishati of Shridhara, Bijaganita of Narayan are some prominent Sanskrit treatises on Indian Mathematics.

34000th of a Second to 4.32 Billion Years

The ancient Hindus had given the world the idea of the smallest and largest measuring units of Time. Astonishingly, the ancient Hindus used the following units of time:

 

 

Unit	Equivalent		Equivalent
Krati			34,000th of a second
1 Truti			300th of a second
2 Truti	1 Luv
2 Luv	1 Kshana
30 Kshana	1 Vipal
60 Vipal	1 Pal
60 Pal	1 Ghadi		24 minutes
2.5 Gadhi	1 Hora		1 Hour
24 Hora	1 Divas		1 Day
7 Divas	1 Saptaah		1 Week
4 Saptaah	1 Maas		1 Month
2 Maas	1 Rutu (season)
6 Rutu	1 Varsh		1 Year
100 Varsh	1 Shataabda		1 Century
10 Shataabda	1 Sahasraabda		10 Centuries or 1000 Years
432 Sahasraabda	1 Yuga		4320 Centuries or 432000 Years
10 Yuga	1 Mahayuga		43200 Centuries or 4320000 Years
1000 Mahayuga	1 Kalpa		43200000 Centuries or 4.32 Billion Years

 

 

India gave the largest measurement of time as 8.64 billion years.

The Gregorian calendar on your desk simply adds on one day for every 4 years and is not in coherence with the movement of sun. But, Hindu calendar is in coherence as the short fall is corrected in the month itself by adding Adhikamasa as postulated by Maharshi Vishwamitra. Rig Veda 1.164.1, 2, 14 and 15 describe sun's motion, ritus and colours of spectrum. Kalyana varma, Varahamihira, Jaimini, Vidyanatha Deekshita, Kalidasa, Mantreshwara, Satyacharya, Venkatadri, Parashara, Ramadayalu and Garga have immensely contributed for the development of Hindu astrology.