RESHEL BRETNY FERNANDES, STUDENT SDM LAW COLLEGE MANGALURU
“Mathematics is not just the count of numbers but the legacy which uproots from the pages of history .” It is a enhancing moment and setup to notice that India had been rich in the glory of the contributions towards the mathematical fields that was the base for the development and create a star mark in the prominence of the fields through history . We can understand that the development of mathematics is not just the aspect which arose suddenly but it is the chain that finds it’s origin from past. One among such great mathematician , scholar and astronomer is Aryabhata who lived during the tenure of Guptan age creating the foundation for the mathematics that led to new thinking dimensions marking greatest contributions.
Aryabhata was the major mathematician from the classical age who had called himself the native of Pataliputra born in 476 CE. Certain sources find that from Asmaka, he went to Kusumapura for the studies . Later , he was made as the head of the instiution at Kusumapura during the 6th century CE which he even worked at Nalanda university being kulapathi. His major work is Aryabhatia and Aryasiddhnatika , where Aryabhatia contains the detailed knowledge on arithmetic , algebra , plane trigonometry and trigonometry of spherical . . This text consists of 108 verses and 13 introductory verses and divided into four chapters .
1.Gitikapada – 13 verses
2.Ganitapada- 33 verses
3. kalakriyapada- 25 verses
4.Golapada- 50 verses
The Arya –sidhantika which has the matters of certain astronomical elements and explantaions that were provided in new ways and forms. The mathematical contributions implied:
- Aryabhata was first to solve the Diophitine equations that has more than one unknown integer . A simple equation is : ax=by=c where x and y are unknown and a,b c are integers with values given . With this regard , Aryabhata introduced new method called Kuttaka method that has its meaning ‘pulverise’ which was in the recursive algorithm involving the factors of the small numbers . The Kuttaka method made the easy solve of the equations which is standard and popular though they were tough.
- Aryabhatta contributed the numericals systems in which he utilized the letters to denote numbers of Indian alphabet . The number system denoted had the numbers upto 10to power 18 with alphabetical notations. Even certain evidences prove that Aryabhatta was familiar with the place value and concept of zero , although there is no mention of 0. A famous French mathematics scholar opines: “ The existence of zero were implicit in place value of Aryabhata with powers of 10 in null coefficients . It would not be possible to continue numerical system without zero. The analyazation of square and cubic roots cannot be possible without zero.
- The greatest achievement denoted is that of value of PI (π) . The book Aryabhatiam denotes : Add 4 to 100 , multiply 8 , add 62000 . With this the diameter of circle can be attained which is 20000. Hereby , the PI value is the outcome – 62832/20000=3.1416 . Aryabhatta’s value of π is very close to the accuracy. Here the PI was considered as irrational.
- The simple solutions to the complex problems were given like sum of integers. Even the area of triangle was correctly calculated . In the writings of Ganitapadam , it is found that , for triangle its perpendicular result is half side area.” In trigonometry , he gave tables of sines at 90 deegre / 24= 3 deegre 45 . The formula used was , sin(n=1) x- sin nx in terms of sin nx and sin (n-1) x by which attained (versin=1- cosine). • The calculations of the length of day and year was made with sidereal rotation with year to be 365.258 days considering as an accurate results and his algorithms are used in cryptographic community securing passwords. From the above description , it can be noted that Aryabhata’s inventions had made the highest contribution signifying the knowledge possessed . These have made the medieval and modern thinkers to make certain modifications creating the accuracy which promotes interest in constant working. We find that , the various ideas given have remained fruitful at the working systems creating realities at the field of Mathematics presently using it in modern sciences with his school in Kerela that successfully works . “ The richness of contributions has the move towards turning the spokes of evolution into accuracy.”
