Pratham � IIT Bombay�s journey into Space!

(Padakshep thanks Saptarshi Bandyopadhyay for arranging this article)

by Jhonny Santosh Jha

Pratham Team at IIT, Bombay

Have you ever imagined how it would feel to send something into space? What a wonderful feeling it would be to have a satellite circling the planet and beeping your name aloud every time it crossed your hometown! It all started with a bunch of students dreaming exactly this. Pratham, the first student satellite project of IIT Bombay, started 4 years ago as the brainchild of a few space technology enthusiasts at IIT Bombay.

The idea was to build a small satellite from scratch, learn the basics of space technology, and in the process make IIT Bombay a centre respected for Space Research. We started off in a small classroom with zero funding! Five years down the line we have created a specialized lab replete with clean room facilities to assemble an entire satellite and Pratham has become the largest technical student project that IIT Bombay has witnessed till date.

Pratham: IITB's first student satellite project

My role at Pratham when I first joined was as a team member of the communication subsystem. I was responsible to ensure that the satellite was heard (remember the beep that I talked about!). However, as the project grew, so did my responsibilities.  I was soon made the team leader of the communication subsystem and later the Project Manager. The technical complexity of the project can be gauged from the fact that it took 40 IITians 4 years to get the perfect design for the satellite. During this time, we created 30 versions of the satellite model, over 100 versions of the functional modules, visited Europe and Africa to represent Pratham in 6 international conferences and created almost 20000 pages of documentation! And the beauty is we started from scratch and did it all by ourselves.

Exploded view of Pratham

However, Pratham for me has gone beyond a college project. We started with what we call our social goal. We wanted to share all the knowledge that we had gathered among universities across the globe. We made our documents available in public domain and conducted workshops to help people get acquainted with satellite technology. Currently, we have 10 universities across India and 1 university in France participating in that social goal. In fact, two are from Bhopal and some others have started their own social goals.

Pratham for me was an opportunity of a lifetime and it taught me a great deal, however, if there is one thing you could take away from this, it should be, �You can engineer great things if you dream big�.

Author Jhonny Santosh Jha is the project manager (along with Sanyam Suhas Mulay) of Pratham, IITB's first student satellite project. Pratham website can be found at http://www.aero.iitb.ac.in/pratham/

Indian Roots of Modern Mathematics - Contributions of a Pioneer

by Krishnamurthi Ramasubramanian

Mathematics in India has a very long and hallowed history. Sulvasutras, the oldest extant texts (prior to 800 BCE) that deal with mathematics, explicitly state and make use of the so-called Pythagorean theorem apart from giving various interesting approximations to surds, in connection with the construction of altars and fire-places of different sizes and shapes. By the time of Aryabhata (c.499 CE), the Indian mathematicians were fully conversant with most of the mathematics that we currently teach in our schools, which includes the methods for extracting square root, cube root, and so on. Among other things, Aryabhata also presented the differential equation of sine function in its finite-difference form and a method for solving linear indeterminate equation. The `bhavana' law of Brahmagupta (c.628) and the `cakravala' algorithm described by Jayadeva and Bhaskaracarya (12th cent.) for solving quadratic indeterminate equation are some of the important landmarks in the evolution of algebra in India.

The Kerala School of Astronomy pioneered by Madhava (c.1340--1420) extends well into the 19th century. The mathematicians and astronomers residing on the banks of the river Nila in the south Malabar region of Kerala -- stumbling upon the problem of finding the exact relationship between the arc and the corresponding chord of a circle, and problems associated with that -- came very close to inventing what goes by the name of infinitesimal calculus today. Particularly, Madhava of Sangamagrama, around the end of 14th century, seems to have blazed a trail in the study of a specific branch of mathematics that goes by the name of analysis today. He enunciated the infinite series for pi/4 (the so-called Gregory-Leibniz series) and other trigonometric functions. The series for pi/4 being an excruciatingly slowly converging series, Madhava had also given several fast convergent approximations to it. Interesting proofs of these results are presented in the famous Malayalam text Ganita-Yuktibhasa (c.1530) of Jyesthadeva as well as in the works of Sankara Variyar, who was a contemporary of Jyesthadeva.

Though Madhava's works containing these series are not extant today, by way of the abundant citations that are to be found in the later works, we come to know that it was Madhava who was responsible for the efflorescence of the galaxy of brilliant astronomers and mathematicians that the Kerala School was to produce over the next three centuries. The works of the later astronomers and mathematicians of the Madhava school contain several interesting results that include the derivative of inverse trigonometric functions as well as the ratio of two trigonometric functions.

There is a perception that mathematics in India has just been a handmaiden to astronomy which in turn has been a handmaiden employed in fixing the appropriate times of religious rites. Though it had its modest beginning that way,  if the purpose of mathematics is not broadened to include sheer intellectual excitement, it may be difficult to explain as to why Nilakantha cogitated on the irrationality of pi -- a beautiful discussion of which is to be found in his Aryabhatiya-bhasya -- and Madhava evolved elegant methods to obtain the value of pi correct to almost 14 decimal places.

It is quite interesting to note that almost all these discoveries are succinctly coded in the form of metrical compositions in Sanskrit. To the present day reader, having got so much accustomed to the use of symbols, it may be rather difficult to imagine a recursion relation, or an infinite series, or the derivative of a function being expressed in the form of terse verses. But astonishingly, that is how it has been presented to us at least from the time of Aryabhata (5th cent.) till late 19th century. It is truly remarkable that all the different branches of mathematics in India, including the sophisticated infinitesimal calculus, have been developed ingeniously without `formal' notation in a completely indigenous way!

Further readings:

Madhava of Sangamagrama

Ganita-Yukti-Bhasa

Author Krishnamurthi Ramasubramanian is a professor at the department of humanities and social sciences of the Indian Institute of Technology, Bombay. He is a co-author of the book named "Ganita-Yukti-Bhasa of Jyesthadeva".