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Aryabhatta: Aryabhatta was an acclaimed mathematician astronomer. He was born in Kusumapura (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 62832 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 eclipses occur due to the shadows of the moon and earth. His observations account for the ‘flat earth concept and lay the foundation for the belief that earth and other planets orbit the Sun.

Scientific works and achievements:

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 or chapters.

Aryabhatiya’s first chapter, Gitikapada, with its large units of timc-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, arithmetic and geometric progressions, gnomon or shadows, simple, quadratic, simultaneous, and indeterminate equations. Aiyabhatiya’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 the horizon.

(i) It is speculated that Aryabhata used the word (approaching), to mean that not only is this an approximation but that the value is incommensurable or irrational.

(ii) 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.

(iii) Like other ancient Indian mathematicians, he too was interested in finding integer solutions to Diophantine equations, with the form $$– ,+$$ by $$= ,c;$$ he called it the (meaning breaking into pieces) method.

(iv) His contribution to the study of Algebra is immense. In Aryabhatiya, Aryabhata provided elegant results for the summation of series of squares and cubes through well-tried formulae. (v) He correctly believed that the earth rotates about its axis daily.

(vi) In Aryabhatiya, he writes that ‘setting and rising of planets’ is a perception, similar to that of Someone in a boat going forward sees an object going backwards.

(vii) He correctly, asserted that the planets shine, due to the reflection of sunlight, and that the eclipses occur due to the shadows of moon and earth, and not caused by a demon called ‘Rahu’.

(viii) He correctly deduced that the orbits of the planets are ellipses.

Other Achievements:

The gave the knowledge of Algebra, Intermediate equations, Trigonometry, Place value system and zero and also the motions of the Solar system.