Aryabhata, a prominent Indian mathematician and astronomer, is well known around the world for his work and legacy in these fields. One of the first mathematicians in India, Aryabhata, was born in the Gupta era during the reign of the Gupta Dynasty in Kusumapura, Pataliputra in 475 CE. Aryabhata is noted for his unparalleled knowledge in the domains of astronomy and mathematics, having written treaties in both.
Many of Aryabhata’s works have been lost to time’s tidal wave, but some are still available, and modern scholars hold them reverently because of their tremendous credibility. Therefore, we must be aware of Aryabhata’s notable discoveries, which have given India so much pride.
Who is Aryabhata?
If you want to comprehend who Aryabhata is, then you have to dig a little deeper and know more about his legacies and inventions. But, before you know about his discoveries, you have to know about his life or as much information as can be found about his life.
- Though his birthplace is unknown, he considered his native place to be Kusumapura, Patuliputra.
- Patuliputra was the hub of educational advancement and communication networks, which helped Aryabhata make his astronomical and mathematical discoveries. Historians claim that he was also the head of the school Kulpa in Kusumapura. He went to study at Nalanda University, and rumor has it that he was also the head of that university.
Aryabhata’s Notable Inventions
Aryabhata had remarkable achievements that are relevant to this day as he had the most excellent visionary approach. Though most of his works are lost in time, his most significant works are Arya-Siddhanta and Aryabhatiya. In both texts, Aryabhata explores astronomy and mathematics and the correlation between the two. He also discussed how the equations of mathematics could help figure out the world’s workings via astronomy.
Aryabhatiya
His magnum opus, Ariyabhatiya,contains 121 verses where he explains astronomical treatises.
- The text’s mathematical portion has 33 verses that give you 66 rules. The text is divided into four chapters ⏤ Ganitapada (33 verses), Golapada (50 verses), Gitikapada (13 verses), and Kalakriyapada (25 verses).
- Among numerous things, Aryabhatiya covers the nature of the solar system, the systematic system of the planet’s position in space, and the reasons for the eclipses of the moon and the sun.
- Aryabhata has earned the title of “Father of Algebra” as he had an extensive understanding and explanation of the planetary system using the Sanskrutik mode of calculation that was widespread in Vedic times. The mathematical portion includes algebra, arithmetic, spherical trigonometry, and plane trigonometry.
- Aryabhatiya covers sums of power series, continued fractions, the table of sines, and quadratic equations. It’s an enormously influential text, and it introduces many concepts fundamental to contemporary mathematics and astronomy.
The Concept of Zero
- In Aryabhatiya, he introduced a “system of numerals” using Indian alphabets to designate numbers. His number system ensured that one would represent numbers up to 1018 with an alphabetical notation. It is considered that Aryabhata was familiar with the concept of zero and the place value system.
- However, the symbol zero is found nowhere in Aryabhata’s works. French mathematician Georges Ifrah argued that the knowledge and existence of zero were indirectly mentioned in Aryabhata’s place-value system as a placeholder for the powers of 10 with null coefficients.
Calculation of Pi
Aryabhata calculated the value of Pi up to two decimal places, or 3.14. Then, in the second part of the Aryabhatiyam, he explained that to add four to a hundred, multiply it by eight. Then, add 62,000 again. As the rule concludes, one can find the circumference of a circle with a diameter of 20,000. This way gives you the value of Pi, 62832/20000=3.1416. Aryabhata’s value of Pi is a close approximation of the contemporary value and the most accurate one amongst the ancients.
The First Known Person to Resolve Diophantine Equations
A Diophantine equation consists of more than one unknown integer. For example, ax∓by=c where the given integers are a, b, and c while the unknown integers are x and y. Aryabhata was the earliest known man to find a solution to this equation of the form by = ax + c and by = ax – c. Aryabhata promptly discovered a popular but new method called the “Kuttaka method” for this purpose. Kuttaka means “to pulverize,” and the method was based on a recursive algorithm which included writing the actual factors in smaller numbers. The equation was considered challenging to solve at that time, and the Kuttaka method quickly became very popular. The Kuttaka method is still the standard method to find solutions to such equations.
Solar System
Aryabhata came to the conclusion that the earth rotates on its axis daily. Therefore, the movement of the star is achieved by the movement of the earth. In the first chapter of his text, Aryabhatiya, he explains the number of rotations of the earth in a yuga. He made these claims when people still believed that the sky was moving. To describe his phenomenon of a concept, he proposed a geometrical model where two epicycles indicated the moon and the sun. According to the geographical model, the two epicycles governed the planets, where the smaller one was slow and the larger one was fast. He also claimed that the moon and other planets shine due to the reflected sunlight.
Contributions to Algebra and Trigonometry
He provided simple solutions to complicated mathematical problems like summing the first n integers, the square of the integers, and their cubes. In addition, he also correctly calculated the areas of a circle and a triangle, which you can find in his writings in Ganitapadam. He also provides a table of sines in trigonometry. He calculated the approximate values at 90°/24 = 3° 45′ intervals. Aryabhata utilized the formula for sin(n + 1)x – sin nx in terms of sin nx and sin (n – 1)x. He also introduced versine into trigonometry.
His work is still relevant in the present scientific world because it was he who brought India to the attention of the world in the fields of mathematics and astronomy. For example, Aryabhata’s calendar calculations have resulted in the Hindu calendar “Panchagram.” The calendar was also used to create the Islamic calendar “Jalali.” The modified version of the calendar is still in use in Iran and Afghanistan. Visit BYJU’S FutureSchool blog to learn more.
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