Friday, May 21, 2010

Aryabhata आर्यभटः

Aryabhata (IAST: Āryabhaṭa; Sanskrit: आर्यभटः) (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Aryabhatiya (499 CE, when he was 23 years old) and the Arya-siddhanta.

“Chaturadhikam Shatamashtagunam Dvashashtistatha Sahasranam Ayutadvayavi Shkambhasyasanno Vrttaparinahah”
  – Ganita Pada, 10 – Aryabhatiya.

Roughly translated: “Add 4 to 100, multiply by 8 and add to 62000. 
This is approximately the circumference of a circle whose diameter is 20000”

Implying PI = 62832/20000 = 3.1416

  • One of his most important legacies is his accurate knowledge of the value of Pi. Especially when Pi could be expressed only as a whole number ratio as there was no system for decimal fractions back then.
  • Prior to him, Vedic Sutras had expounded on geometric relationships for religious purposes such as altar construction and keeping track of calendars. Jain mathematicians also excelled at mathematics prior to Aryabhata.
  • One of his works, “Aryabhatiya” has survived till today. It was written in Sanskrit and in poetic verse form containing 123 stanzas.
  • Aryabhata provides methods to find out square roots and cube roots (Though the square roots have been thought of being found out before him)
  •  Since the value of Pi was known to him, he also gave the formulae to calculate the area of a circle and volume of sphere.
  • One of his more complicated works was his derivation of the Sine Table. In fact, the modern  trigonometric names ‘Sine’ and ‘Cosine’ are a mis-transcription of the words ‘jya’ and ‘kojya’ as introduced by Aryabhata. These were transcribed as Jiba and KoJiba in Arabic. They were then misinterpreted by Gerard of Cremona while translating an Arabic Geometry text into Latin. He took Jiba to be the Arabic word Jaib, which means fold in a garment, ie. Sinus.
  • Aryabhata’s astronomical calculation methods were also very influential. Calendric calculations worked out by Aryabhata and followers have been in continuous use in India for the practical purposes of fixing the Panchangam or the Hindu calendar.
  • Aryabhata was the first astronomer to make an attempt at measuring the earth’s circumference accurately. His estimation of 24,835 miles was a deviation of just 0.2% from the actual value.

So, the next time you hear the name of the first satellite launched by India to be “Aryabhata”, the Lunar Crater “Aryabhata”, Aryabhata Maths Competition or of the Aryabhata Research Institute of Observational Sciences (Near Nainital), you know who the great person was and why they are all named after him – After all, calculating the value of Pi when there was no decimal fraction system was like thinking of a car when the wheels were not invented!

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