Aryabhatta - It's Contribution to mathematics and Astronomy
Aryabhatta was the first mathematician astronomer from the classical age of India when mathematics and astronomy were still in their nascent stages of development around the globe.
His works have been extensively used by the Greeks and others in the Middle East.
Aryabhata became famous as a mathematician and astronomer. In his only surviving work, Aryabhatiya, he covered a wide range of topics, such as extracting square roots, solving quadratic equations and predicting eclipses
Aryabhatta (or Aryabhata) (476 – 550 CE) was an Indian mathematician and astronomer who is regarded as a towering figure in both these fields.
Some of his works have been lost through the ages but his influence may be seen in the works of succeeding Indian mathematicians who frequently refer to his works.
Among other things, Aryabhata calculated the closest approximate value of pi till that time; was the first known person to solve Diophantine equations; was the first to explain that the moon and planets shine due to reflected sunlight, and made major contributions to the fields of Trigonometry and Algebra.
Aryabhatta was one of the greatest mathematicians in history and a pioneer in the classical age of Indian mathematics and astronomy.
Early life
Based on his works and influences, speculation surrounds Aryabhata’s birthplace and year. His famous book, ‘Aryabhatiya’, stated he was 23 years old, 3600 years into Kaliyug, dating back to 499 CE, which suggests his birth year as 476 CE. While ‘Aryabhatiya’ came out 3600 years into Kaliyug, the acknowledgment of Aryabhata’s contributions to the text surfaced significantly later.
Abu Rayhan al-Biruni, an esteemed Islamic mathematician who studied Aryabhata’s writings, suggested referring to Aryabhata as Aryabhata 1 or Aryabhata the Elder. He speculated that two scientists named Aryabhata existed simultaneously, causing confusion and turmoil. However, in 1926, B Datta resolved this discrepancy, clarifying that the works Al-Biruni attributed to two different scientists were actually by a single individual, Aryabhata.
Pataliputra, the capital of Kusumapura in the Gupta Empire, was a prominent learning institution and the heart of a communication network.
Hence, works from all over the world readily transport to the location, allowing Aryabhata to make significant mathematical and astronomical advances. He was to be the principal of his Kusumapura school, Kulpa. Later, to continue his passion for astronomy, he proceeded to study at Nalanda University in Pataliputra, and rumors about him becoming the head of his university persisted.
Aryabhatiya is the Most Famous Treatise by Aryabhata
Although Aryabhatta wrote several treatises, Aryabhatiya is his only known surviving work and it is widely regarded as his definitive work.
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 Aryabhatiya covers arithmetic, algebra, plane trigonometry and spherical trigonometry.
It also contains continued fractions, quadratic equations, sums of power series and a table of sines.
Aryabhatiya was a hugely influential text and it presents many ideas that are foundational to modern astronomy and mathematics.
Aryabhata’s inventions and discoveries
‘Aryabhatiya’ and ‘Arya-Siddhanta’ are two of the most important works by Aryabhata. In each of his publications, he investigated mathematics, astronomy, and correlation. He also discussed how mathematical equations can help you learn about the workings of the planet through astronomy.
1. Aryabhatiya
Aryabhatiya or Arya-status-ash, which translates directly as ‘Aryabhata’s 108’ since the text has 108 verses. The writings are in the form of a sutra, which is a collection of aphorisms, short statements, or scientific principles.
These poems are his works in the form of 13 introduction verses that are a means of recalling difficult computations in a simple manner. The division is into four chapters or ‘Padas’, the first of which is ‘Gitikapada’, which has 13 verses. It is about cosmology. In a ‘maha yuga’, the planetary revolutions are said to last up to 4.32 million years.
The ‘Ganitapada’ is the second ‘Pada’ or chapter. ‘Ganita’ signifies computations in Sanskrit. It comprises 33 poems, all of which are about mathematics. mensuration, simple, quadratic, and indeterminate equations, as well as arithmetic and geometric equations
The third ‘Pada’ is the ‘Kalakriya Pada’, which consists of 25 verses that tally the days, weeks, and months using different units of time. And the fourth chapter, ‘Golapada’, has 50 verses. Aryabhata goes into the causes of days and nights, the rise of zodiac signs, eclipses, the celestial equator, nodes, and the structure of the globe in this chapter.
2. Mathematical Discoveries
‘Aryabhatiya’ extensively describes Indian Mathematical Literature, investigating the Vedic method of solving mathematical problems, a technique that has endured to the present day. Algebra, arithmetic, plane trigonometry, and spherical trigonometry were all covered in detail. He adhered to the ‘Sanskrutik’ tradition or method of computation that was prominent throughout the Vedic period.
Aryabhata earned the title ‘Father Of Algebra’ due to his remarkable comprehension and explanation of planetary systems using algebra. Aryabhata successfully calculated pi’s value to two decimal places, 3.14. He also employed null coefficients and was well aware of the use of zero in such a situation. He used the Sanskritic tradition, primarily denoted by letters and alphabets, in contrast to Brahmi numbers.
3. Astronomy Discoveries
Aryabhata accurately claimed that the Earth rotates on its axis around the sun daily, causing the apparent movement of stars due to the planet’s rotation. This view contrasted the prevalent belief at the time of a rotating sky. He quantitatively defined heliocentrism as the axial rotation of planets around the sun.
His astronomical findings are broadly classified into four categories. These include a description of the solar system’s motion, eclipses, sidereal periods, and heliocentrism.
4. The motion of the solar system
Aryabhata proposed that the world revolves on its axis once a day. And the relative movement of the stars is caused by the earth’s motion. He specifies the number of earth rotations in a yuga in the opening chapter of his work, Aryabhatiyam.
Aryabhata developed a geometrical model of the solar system to explain this occurrence, wherein the moon and sun moved on epicycles – circles moving atop one another. In this model, he guided the motion of the planets using two epicycles. The little one moved slowly, but the larger one moved swiftly.
Aryabhata arranged the planets in terms of distance from Earth as follows: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms (group of stars). He estimated the planets’ periods and locations using the relative velocity of the points.
In the case of Venus and Mercury, they traveled around the Earth at the same rate as the Sun. However, Jupiter, Saturn, and Mars, stars or points, traveled around the Earth at a set velocity, reflecting each planet’s journey through a zodiac.
5. Eclipses
With scientific experiments, Aryabhata explained lunar and solar eclipses. He said that the planets and moonshine were created by reflected sunlight. He described eclipses as shadows falling on the Earth.
A lunar eclipse occurs when Earth blocks sunlight from reaching the moon, casting a shadow on its surface. Later, he explained the breadth and size of the Earth’s shadow before calculating the size of the eclipsed portion during an eclipse. The experiments of Aryabhata created the groundwork for Indian astronomers to refine the computations.
6. Sidereal Periods.
Using current time units, Aryabhata computed the sidereal rotation (the rotation of the Earth in relation to the stars) to be 23 hours, 56 minutes, and 4.1 seconds. The present time is written as 23:56:4.091.
7. Heliocentrism
Aryabhata proposed an astronomical concept in which the Earth spins on its axis. His model also provided adjustments for estimations of the mean speeds of the planets in relation to the Sun. His calculations were based on the heliocentric concept, which states that the planets and Earth rotate around the Sun, which is at the centre of the universe.
Aryabhata described the geocentric model of the solar system, which scientifically explained solar and lunar eclipses. He also calculated the year to be 365 days 6 hours, 12 minutes, and 30 seconds, which is just 3 minutes and 20 seconds longer than today’s figures.
8. Relation with Nalanda University
Aryabhata mentions in his book Aryabhatiya that he had been honoured in Kusumapura. Both Buddhist and Hindu traditions along with the reports of Bhaskara I, who provided commentary on Aryabhatiya, identify Kusumapura as Pataliputra, the capital city of Magadha. Since the University of Nalanda was situated in Pataliputra during that period and also because Aryabhata was mentioned as Kulapa (Head of Institution) in a verse, it has been speculated that he might have been the head of Nalanda University too.
9. Translations
The works of Aryabhata were translated into Arabic language from its original Sanskrit version. It also influenced the works of Persian polymath Al-Khwarizmi and Arab Astronomer Al-Zarqali. For instance, after Aryabhatiya was translated into Arabic around 820 CE, the approximation of Pi was mentioned in Al-Khwarizmi’s book on algebra.
10. Legacy and Honours
In 1975, The Indian Government launched its first satellite named Aryabhata to honour this great astronomer.
The image of the Aryabhata satellite is featured on the reverse of an Indian 2-rupee note.
A species of bacteria discovered by ISRO scientists in the Earth’s stratosphere was named Bacillus Aryabhata after him.
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