discuss aryabhatt's contribution in the spheres of mathematics and astronomy
Answers
#1 HE WROTE THE HUGELY INFLUENTIAL ARYABHATIYA
Aryabhatiya (510 CE)
Aryabhatiya (510 CE) – Aryabhatta
Although Aryabhatta wrote several treatises, Aryabhatiya is his only known surviving work and it is widely regarded as his magnum opus. It is primarily an astronomical treatise written in 121 verses. Its mathematical section contains 33 verses giving 66 mathematical rules. Aryabhatiya is divided into four chapters: Gitikapada (13 verses), Ganitapada (33 verses), Kalakriyapada (25 verses) and Golapada (50 verses). Among other things, Aryabhatiya contains a systematic treatment of the position of the planets in space; the nature of the Solar System; and the causes of eclipses of the Sun and the Moon. The mathematical part of the
#2 ARYABHATTA WAS THE FIRST KNOWN PERSON TO SOLVE DIOPHANTINE EQUATIONS
A Diophantine equation is an equation that has more than one unknown integer. A simple Diophantine equation would be ax + by = c. In this equation a, b and c are given integers; and x and y unknown integers. Aryabhatiya is the earliest known work which examines integer solutions to Diophantine equations of the form by = ax + c and by = ax – c. For this purpose, Aryabhata promptly introduced a new and popular method, known as the Kuttaka method. The word kuttaka means “to pulverise” and Aryabhata’s method was based around a recursive algorithm which involved writing the original factors in smaller numbers.
#3 HE MADE MAJOR CONTRIBUTIONS TO TRIGONOMETRY AND ALGEBRA
Aryabhatiya provides simple solutions to complex mathematical problems of the time like summing the first n integers, the squares of these integers and also their cubes. Furthermore, Aryabhatta correctly calculated the areas of a triangle and of a circle. For example in Ganitapadam his writings can be translated as “for a triangle, the result of a perpendicular with the half-side is the area.” In trigonometry, Aryabhatta gave a table of sines calculating the approximate values at intervals of 90°/24 = 3° 45′. In order to do this he used a formula for sin(n + 1)x – sin nx in terms of sin nx and sin (n – 1)x. He was also the one to introduce the versine (versin = 1 – cosine) into trigonometry.
#4 HE MOST PROBABLY UNDERSTOOD THE CONCEPT OF ZERO AND THE PLACE VALUE SYSTEM
In Aryabhatiya, Aryabhatta introduced a system of numerals in which he used letters of the Indian alphabet to denote numbers. His numeral system allowed numbers up to 1018 to be represented with an alphabetical notation. It is considered that Aryabhatta was familiar with the concept of zero and the place value system. Ifrah based his supposition on the following two facts: “first, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the place-value system and zero.” This is an incredible achievement for the time and one of the earliest proper understanding of the concept of zero, which is fundamental to mathematics.
#5 HE CALCULATED THE CLOSEST APPROXIMATE VALUE OF PI TILL THAT TIME
One of the most important achievements of Aryabhatta is giving an approximate value of Pi (π). An account of this is found in the second part of Aryabhatiyam where he explains “Add four to 100, multiply by eight, and then add 62,000. By this rule, the circumference of a circle with a diameter of 20,000 can be approached.” This calculation gives the vale of pi to be 62832/20000 = 3.1416, reflecting an accuracy of 5 significant digits. In fact π = 3.14159265 correct to 8 places. Aryabhatta’s value of π is a very close approximation to the modern value and the most accurate among those of the ancients. Furthermore, it is also considered that Aryabhata knew that the value of Pi was irrational. This was an amazing discovery since the value of Pi was proved to be irrational only in the year 1761 by Swiss mathematician Johann Heinrich Lambert.