India’s first satellite was launched on 19th April 1975. It was built by the ISRO but launched by the erstwhile Soviet Union as a part of their friendship program. The satellite was polyhedron in shape with 26 sides, most of which was covered by solar panels. It was carrying instruments to measure X-ray astronomy, aeronomics and solar physics. The satellite worked for four days sending data till a power failure disrupted communications. It finally entered in the Earth’s atmosphere on 10th February 1992. An artistic impression of the satellite is permanently etched in our memory on the reverse of the Rs 2 note introduced into circulation in 1976. The satellite was named after the most famous Indian mathematician Aryabhata.
Bakhshali Manuscript
In 1881 near Peshawar, Pakistan an ancient mathematical text was discovered in a village called Bakhshali. It was discovered by a farmer while working on his field. It was studied in detail by Rudolf Hoernle who was working with the Indian Education Service. He was the known expert at that time in Indo-Aryan Languages. After the first detailed study he discovered that the 70 page document is actually an incomplete mathematical manual. Carbon dating has attempted to establish the origin of the document. Even the script used provides a clue as to who wrote it. But despite research and debate, till date it has not been established who has written it and when. The date ranges from 224 AD to 993 AD based on carbon dating. A study of contents and script used however leads to the conclusion that it is a copy of an earlier text or maybe an adaptation. Here is where things get interesting.
At around 500 AD lived Aryabhata who was the most influential mathematician of his time. So any mathematical text written in that era or after it has to have his influence. What scholars have discovered that the Bakhshali manuscript uses terminology earlier from that what was prevalent during that era. But other set of scholars find some similarity with the works of Bhaskara I who mathematical work was heavily influenced by the works of Aryabhata. The Bakhshali manuscript uses a dot in place of zero. This place holder in place of a null value was extensively used by Aryabhata.
Discovery and use of Zero
Though the concept of zero or null value began in almost all ancient civilisations like Egypt, Babylon, Mayan and China. But the use of zero as a placeholder began in India. It is believed that Aryabhata brought in zero for use of merchants. Inspired by the work of Aryabhata, Bhaskara I started using a circle in place of zero. The knowledge of zero then moved to Persia where it got developed into Hindu-Arabic numeral system which later reached Europe and came to be known as modern maths.
Calculating the approximated value of π
Aryabhata describes the concept of π in his work Aryabhatiyam and worked out the value of π till four decimal places. He was also able to establish that π is an irrational number.
Trigonometry
In another mathematical work named Ganitapada, he explains area of a triangle.
tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ
Which translates to “for a triangle, the result of a perpendicular with the half-side is the area.
Contribution to Algebra
Although the word Algebra is of Persian origin, the history of Algebra begins much prior to that. Aryabhatiya provides a series of questions with solutions on Algebra.
Astronomy
Mathematics those days was also used for the study of stars. Aryabhata studied the solar system and discovered that the earth rotates round its axis. He was able to calculate the position of stars and planets. Eclipses was explained by Aryabhata too. The methodology of calculation of timing of eclipse were founded by Aryabhata.
Contributions of Aryabhata can be summarised below
- Aryabhatiya – A compendium of maths and astronomy which covers arithmetic, algebra, trigonometry and astronomy.
- Calculation of π correctly upto 4 decimal places.
- Calculation of diameter of Earth.
- Calculation of timing and prediction of eclipse.
- Contributed to the evolution of use of Zero.