life history of your favourite mathematics
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Aryabhata was an acclaimed mathematician-astronomer. He was born in Kusumapura (present day Patna) in Bihar, India. His contribution to mathematics, science and astronomy is immense, and yet he has not been accorded the recognition in the world history of science. At the age of 24, he wrote his famed “Aryabhatiya”. He was aware of the concept of zero, as well as the use of large numbers up to 1018. He was the first to calculate the value for ‘pi’ accurately to the fourth decimal point. He devised the formula for calculating areas of triangles and circles. He calculated the circumference of the earth as 62,832 miles, which is an excellent approximation, and suggested that the apparent rotation of the heavens was due to the axial rotation of the earth on its axis. He was the first known astronomer to devise a continuous counting of solar days, designating each day with a number. He asserted that the planets shine due to the reflection of sunlight, and that the eclipses occur due to the shadows of moon and earth. His observations discount the “flat earth” concept, and lay the foundation for the belief that earth and other planets orbit the sun.
A verse mentions that Aryabhata was the head of an institution (kulapa) at Kusumapura. Since, the University of Nalanda was in Pataliputra, and had an astronomical observatory; it is probable that he was its head too.
Direct details of his work are known only from the Aryabhatiya. His disciple Bhaskara I calls it Ashmakatantra (or the treatise from the Ashmaka).
The Aryabhatiya is also occasionally referred to as Arya-shatas-aShTa (literally, Aryabhata’s 108), because there are 108 verses in the text. It also has 13 introductory verses, and is divided into four pādas or chapters.
Aryabhatiya’s first chapter, Gitikapada, with its large units of time — kalpa, manvantra, and Yuga — introduces a different cosmology. The duration of the planetary revolutions during a mahayuga is given as 4.32 million years.
Ganitapada, the second chapter of Aryabhatiya has 33 verses covering mensuration (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon or shadows (shanku-chhAyA), simple, quadratic, simultaneous, and indeterminate equations.
Aryabhatiya’s third chapter Kalakriyapada explains different units of time, a method for determining the positions of planets for a given day, and a seven-day week with names for the days of week.
The last chapter of the Aryabhatiya, Golapada describes Geometric/trigonometric aspects of the celestial sphere, features of the ecliptic, celestial equator, shape of the earth, cause of day and night, and zodiacal signs on horizon.
He did not use a symbol for zero; its knowledge was implicit in his place-value system as a place holder for the powers of ten with null coefficients.
He did not use the Brahmi numerals, and continued the Sanskritic tradition from Vedic times of using letters of the alphabet to denote numbers, expressing quantities in a mnemonic form.
He worked on the approximation for pi thus — add four to 100, multiply by eight, and then add 62,000, the circumference of a circle with a diameter of 20,000 can be approached.
It is speculated that Aryabhata used the word āsanna (approaching), to mean that not only is this an approximation, but that the value is incommensurable or irrational.
In Ganitapada, he gives the area of a triangle as: “for a triangle, the result of a perpendicular with the half-side is the area”. He discussed ‘sine’ by the name of ardha-jya or half-chord.
Like other ancient Indian mathematicians, he too was interested in finding integer solutions to Diophantine equations with the form ax + by = c; he called it the kuṭṭaka (meaning breaking into pieces) method.
Aryabhata’s major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature, and has survived to modern times. The Aryabhatiya covers arithmetic, algebra, and trigonometry.