Birth and Early Life: Aryabhata was born in 476 CE in the ancient kingdom of Magadha, in present-day Bihar, India. Not much is known about his early life or family background.2.Education: Aryabhata received his education at the ancient university of Nalanda, which was renowned for its excellence in mathematics, astronomy, and other sciences. He studied various mathematical and astronomical texts of his time, as well as the works of Greek mathematicians and astronomers.
Works and ContributionsAryabhatiya: Aryabhata’s most famous work is the “Aryabhatiya,” a Sanskrit astronomical treatise that provides a comprehensive overview of mathematics and astronomy as understood during his time. It consists of 121 verses divided into four chapters, covering topics such as arithmetic, algebra, trigonometry, and planetary motion.
Contribution of Aryabhatta to Astronomy
Aryabhatta’s system of astronomy was called the audAyaka system (days are reckoned from uday, dawn at Lanka, equator).
Principle of Rotation: The discovery, recorded in the Aryabhatiya, that the Earth rotates around its own axis from west to east is significant.
Aryabhatta also declared that the Earth rotates around the sun and the moon moves round the earth.
Eclipses: In Aryabhatiya he introduces the idea of shadows, cast by and falling on earth, moon, and planets, and states that the lunar eclipse is caused by the entering of the moon into the earth’s shadow.
Aryabhatta gives formulas for the length and diameter of the earth’s shadow, the timing and duration of the eclipses, and or the size of the eclipsed part of the sun or moon.
Circumference of the Earth: Aryabhatta also revealed that the circumference of the Earth is 39,968km.
It is 40,072 km according to modern scientific calculations.
Mathematical Contributions: Aryabhata made significant contributions to the fields of algebra and trigonometry. He introduced the concept of zero (0) as a placeholder and developed algorithms for arithmetic operations. He also provided trigonometric tables for sine and cosine functions.
Decimal places: Aryabhatta invented the decimal system and used zero as a placeholder.
He names the first 10 decimal places and gives algorithms for obtaining square and cubic roots, using the decimal.
Value of ‘pi’: He treats geometric measurements employing 62,832/20,000 (= 3.1416) for π, very close to the actual value of 3.14159.
Aryabhatta’s value of ‘pi’ is very close to the modern value and the most accurate among the ancients.
Furthermore, it is also considered that Aryabhata knew that the value of ‘pi’ is irrational.
Area of Triangle: Aryabhatta correctly calculated the areas of a triangle and of a circle.
For example, in Ganitapadam, he mentioned that “for a triangle, the result of a perpendicular with the half-side is the area.”
Table of sines: Using the Pythagorean theorem, he obtained one of the two methods for constructing his table of sines.
Other contributions: Mathematical series, quadratic equations, compound interest (involving a quadratic equation), proportions (ratios), and the solution of various linear equations among the arithmetic and algebraic topics included.
Astronomical Contributions: Aryabhata proposed a heliocentric model of the solar system, where he suggested that the Earth rotates on its axis and orbits the Sun. He accurately calculated the duration of a solar year and explained the causes of eclipses.
Other Works: Apart from the Aryabhatiya, Aryabhata is also believed to have written other treatises on mathematics and astronomy, although many of them have been lost over time
Legacy:
Aryabhata’s works had a profound influence on the development of mathematics and astronomy in India and beyond. His ideas laid the foundation for further advancements in these fields, and his contributions were studied and built upon by later scholars, both in India and in other parts of the world.
Aryabhata’s legacy continues to be celebrated, and he is regarded as one of the greatest mathematicians and astronomers of ancient India. His insights and methodologies have left an indelible mark on the history of science.
