Aryabhata - Astronomer and Mathematician of Ancient India answers questions
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Who was Aryabhata?

Nalanda University
Ruins of Nalanda University, Patna

Aryabhata was born about 476 AD in India, probably in central India, though nobody knows for sure. When Aryabhata was a teenager, he left his hometown and went to Kusumapura (modern Patna) in north-eastern India, on the banks of the Ganges river, to study at Nalanda university there. At this time, just after the collapse of the Guptan Empire, the Buddhist institution Nalanda University was already hundreds of years old, but it was still a very good university. Nalanda was a Buddhist school, and King Ashoka paid for some of its buildings. One of the buildings was an astronomical observatory. Students came from far away, even from China, to study at Nalanda.

Aryabhata must have worked hard in college, because by the time he was 23 years old, in 499 AD, he was already writing an important book about math and astronomy of his own. It is a very short book, summarizing important new ideas in 108 short poems.

For the astronomy part of the book, Aryabhata seems to have thought that the earth spun around on its axis (as it really does). But he also thought that the stars moved around the sky, not realizing that they only seem to move because of the movement of the earth.

Because Aryabhata believed that the earth was at the center of the universe and the sun and the planets and the stars all moved around the earth in different orbits, he saw astronomy as a process of calculating distances and movements from the earth to these orbits. To calculate these distances, you needed trigonometry, and Arya Bhata used the trigonometry developed by Hipparchus and Ptolemy for this purpose. Aryabhata defined the concept of the sine and cosine, which he called jya and kojya, meaning "chord" and "perpendicular chord", and wrote down a table of sines. He took trigonometry further than Ptolemy had by working with half-chords.

At the same time, Aryabhata was also working on defining tangents and cotangents.

In another math section of his book, Aryabhata was inspired by recent work on using place values to help add and multiply large numbers. Zero had not yet been invented, but Aryabhata took some more steps along the path from place values towards the idea of zero.

Arya Bhata also wrote several other books about math and astronomy, but we no longer have copies of some of them. One of these lost books is the Arya-siddhanta. In this book, Aryabhata described ways of measuring time, like sundials and water clocks. Although we may not think of sundials and clocks and sines and tangents as all being related now, to Aryabhata and other scientists of his time, all of these were things that you needed in order to understand the movements of the stars and the planets around the Earth.

Learn by doing: make a sundial
More about Indian mathematics

Bibliography and further reading about Indian science:

Science in Ancient India Eyewitness India Ancient India

Science in Ancient India, by Melissa Stewart (2002). Written for kids.

Eyewitness India, by Manini Chatterjee (2002). Written for kids.

Ancient India, by Virginia Schomp (2005). Written for teens. Very good for reports.

Indian Mathematics
Indian Science
More about India home

Professor Carr

Karen Eva Carr, PhD.
Assoc. Professor Emerita, History
Portland State University

Professor Carr holds a B.A. with high honors from Cornell University in classics and archaeology, and her M.A. and PhD. from the University of Michigan in Classical Art and Archaeology. She has excavated in Scotland, Cyprus, Greece, Israel, and Tunisia, and she has been teaching history to university students for a very long time.

Professor Carr's PSU page

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