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Mathematician Aryabhata



Birth (476 AD – 550 AD)

(Devanagari: आर्यभट ) One of the most famous mathematicians of ancient India. India’s first satellite was named “Aryabhatta” in honor of this great Indian historian and the government of Bihar built a university in Patna called “The Aryabhata Knowledge University”.

His Contribution at a Glance :


He was the first to use zero in mathematical pie (pie , π ),  sine , COS and decimal methods. In his book ” Aryabhatiya ” he describes the circumference and diurnal motion of the earth, the method of determining the period of lunar eclipses and solar eclipses, mathematical geometry, orbits of the planets etc.



According to the first sculptor, one of the commentators of Aryabhata, he was born in a place called Ashmaka. In ancient Buddhist and Hindu tradition, this place is identified as a place between the rivers Narmada and Godavari, in the vicinity of South Gujarat and North Maharashtra . Aryabhata mentions in his Aryabhatiya text that he was 23 years old in the 3600th year of Kali Yuga. And based on this information, various scholars have come up with an accurate idea about the year of Aryabhata’s birth!

Higher education :


According to some sources, he went to Kusumpura for higher education. He lived in Kusumpura, the first sculptor of his commentary called this place Pataliputra Nagari. He was known as Aryav of Kusumpur. He did most of his work at Nalanda University. It was here that he received his higher education. After graduation, he joined the university as a teacher. Some say that Aryabhata also served as the head of Nalanda University.

Major Contributions :


The Classical Age (or Golden Age) begins with the hand of Aryabhata in the history of ancient Indian mathematics. Aryabhata’s various works on mathematics and astronomy are said to have been compiled in two main texts. Among them ‘Aryabhattiya’ is the one who has been rescued. It is composed in four volumes, with a total of 118 hymns. The other work that is known about is the ‘Aryan-decision’. No manuscript of the Aryan decision has been found, but it is mentioned in the works of Brahmihir, Brahmagupta and the first sculptor. Aryabhata wrote the book in the form of a phrase.

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Mathematician Aryabhata

Aryabhatti / Aryabhatiya :


Aryabhata compiled this book when he was only 23 years old. These four chapters are: Dasgitika, Ganitapada, Kalkriyapada and Golpada. The ten chapters, Kalkriya and Golpada chapters deal with spherical trigonometry and astronomy. Mathematical terms, on the other hand, include arithmetic, algebra, plane trigonometry, quadratic equations, the sum of the squares and cubes of the exponents of the first n natural numbers, and a table of sine ratios. Moreover, this chapter describes the 33 mathematical processes required for the popular astrology of that time. In mathematics, Aryabhata identifies the value of pi as well as the circumference of a circle and its diameter as 3.1416 . He introduced zero in India.

Aryabhata’s contribution to mathematics :


Decimal number method and zero :


Aryabhata’s work makes full use of the decimal number system. Aryabhata, however, did not use the conventional Brahmi script in his work. He created his own method of presenting numbers by composing books in the form of phrases. There the numbers were presented in the form of words. He used the consonants as different numbers and with the help of vowels he could explain which number is in which position. In that sense, the decimal number system he uses is not exactly the same as today’s decimal number system, but is systematically compatible with today’s decimal numbers. There is controversy over whether his decimal number system was zero. An idea equivalent to zero was at work,It is called ‘B’ (meaning emptiness). There is controversy as to whether the concept of ‘b’ was a number or a sign indicating a space. In conventional books it is marked as a space sign, although Georges Ifrah claims that Aryabhata indirectly used it as a decimal number. However, he was the first to describe a complete mathematical process using the decimal system, which included determining the square root and cube root of a number. This was the most important factor in establishing the decimal number system, since the representation of this number in the coordinate system has been used in different civilizations at different times, but the use of mathematical processes in the coordinate system has not been established. The most important thing at that time was to ensure systematic generalizations using the decimal system,Which was first done by Aryabhata. That is why he is credited with introducing the complete decimal number system. In one of the works of Aryabhata in the year 498, in the statement of decimal number system, the phrase sthanam sthanam ten gunam is found which means – varies from place to place ten times. This clearly recognizes the key features of the current decimal number system.

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Trigonometry :


Aryabhata’s second important mathematical contribution was the introduction of modern trigonometry. In trigonometry, Aryabhata uses the sign, Versine = 1 – Cosine, and the opposite sign. Although there is some work related to this in Surya Siddhanta, Aryabhata’s work matches its full description. He is thought to have known the formulas for twin and half angles for the sign function. One of the important trigonometric relationships used by Aryabhata is to express sin (n + 1) x by sin x and sin (n-1) x. Aryabhata created a sign table, which specified the value of the sign and the Versailles up to 90 degrees with a difference of 3 degrees 45 minutes. With this formula he can easily recursively create this sign table. The formula is-

sin (n + 1) x – sin nx = sin nx – sin (n – 1) x – (1/225 ) sin nx

The sign table made by Aryabhata is mentioned here. It can be said that Aryabhata used Rsinθ instead of direct sinθ in his sign table. Here R denotes the radius of a particular circle. Aryabhata used the value of this radius as 3438 , probably because Aryabhata took the length of a circle as a unit in a circle of single radius for a minute angle. The complete circumference of a circle has an angle at its center (360 × 60) = 21600 minutes. As such, the circumference of the circle is 21600 units and the radius of that circle will be 21600/2 π, using the value found as Aryabhatta 6 = 3.1416 , the value of the radius is about 3438 .

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The sign table made by Aryabhata

Algebra :


Aryabhata devised a general method of solving equations with multiple unknown numbers (commonly known as the Diophantine equation). It was called “Kuttak”. An example is used in the work of the first sculptor when explaining the method of kuttak – “Find the number which is divided by 8 divided by 5, 9 divided by 4 and 7 divided by 1 remaining.” Later in India, the Kuttak method was used as the ideal method to solve such problems. Aryabhata’s work mentions the formula for the sum of the squares and cubes of the terms with the power of the first n natural numbers.

Pie value :



In the second chapter of Aryabhatti’s book, Aryabhatta writes: “Adding one hundred to four and multiplying it by eight and adding sixty-two thousand to it gives the circumference of a circle of twenty thousand units in diameter.” As such, Aryabhata determined the value of pi ((4 + 100) × 8 +62000) / 20000 = 62832/20000 = 3.1416 , which is by far the most accurate of any mathematician’s time.

Aryabhata’s contribution to astronomy :


In the Golpad part of the Aryabhatiya book, Aryabhata mentions through example that the earth revolves around its own axis. He also calculated the axial motion of the earth. According to him, the circumference of the earth was 39.968 km, which is more accurate than any measurement taken up to that time (only 0.2% incorrect). The shape of the orbits of the planets in the solar system was elliptical in his commentary, he made an accurate measurement of the duration of one year, specifying the exact cause of solar and lunar eclipses and determining its time.

Aryabhata has explained the real reasons for solar and lunar eclipses. He also devised a method for determining the duration of solar eclipses and lunar eclipses. Aryabhata said that the light of the moon is actually the result of the reflection of the light of the sun.

Click on Wikipedia to see more details about the biography and discovery of this great man.


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