## Introduction

The introduction of Aryabhatta to the world happened through his remarkable work in the field of mathematics and astronomy. Aryabhata is one of the most renowned Indian Mathematicians, in fact, one of the firsts. Born in the Gupta era that is during the rule of the Gupta Dynasty in 475 CE in Kusumapura, Pataliputra, he was known for his extraordinary knowledge in the astronomical field. He has written many treaties in both mathematics and astronomy. He was also the author of many mathematical books which to date is considered holy and reverend immensely. Many of his works were lost, but some are still available for modern scholars and hold great credibility. And his inventions, discoveries and contributions have brought pride to our country. It has also inspired many budding scientists to follow his path and make discoveries.

### Who is Aryabhatta?

To understand who is Aryabhata it is important to dig a little deeper beyond the Aryabhata Scientist and learn more by finding Aryabhata Information about his inventions and discoveries. There is not enough information about his personal life rather all are curious to know what did Aryabhatta invent? And therefore Aryabhatta Inventions and Aryabhatta Discoveries is still a topic of interest, as there is a new generation curious to find about this Mathematical genius.

Basic Information

Birth- 476 CE

Birth Place- Kusumapura, capital Patalipitra in the Gupta Era.

Present Day- birthplace is known to be Bihar, Patna, India.

Works- His Most Notable work is Aryabhatiya and Arya Siddhanta.

Death- 550 CE

### Aryabhatta Biography

Aryabhata Information

The birthplace and year of Aryabhata are still estimated based on his works and influences. In one of his widely popular works Aryabhatiya, it was mentioned, he was 23 years old when we were 3600 years into Kaliyug, which dates back to 499 CE and thus estimating his birth year to be 476 CE. Not to be misunderstood the text Aryabhatiya was published 3600 years into Kaliyug, it was much later when his works of discoveries and text were found. He always considered Kusumapura, Pataliputra his native place which is present-day Patna, Bihar. His actual birthplace and the family he was born into is still unknown.

Abu Rayhan al-Biruni who is also known as Al-Biruni, a famous Islamic Mathematician who studied the works of Aryabhata stated that Aryabhata must be called Aryabhata 1 or Aryabhata the Elder. This statement was given claiming there were two scientists named Aryabhata who lived during the same period. This created commotion and confusion and did not help in understanding Aryabhata’s life rather created much more confusion. The confusion was cleared much later in the year 1926 by B Datta when he said the works Al-Biruni confused to be of two scientists, is only of one, and that is Aryabhata.

Pataliputra which was the capital of Kusumapura in the Gupta Empire was a major learning hub and was the centre of a communication network. Because of which the works around the world reached the place easily that helped Aryabhata to make major mathematical and astronomical advancements. It was believed that he was the head of his school Kulpa in Kusumapura. And later to pursue his interest in astronomy also went to study at Nalanda University located in Pataliputra, the speculations of him being the head of his university also remained intact.

### Aryabhata’s Works and Legacy

The legacy of Aryabhata is truly unmatched, and no one can replicate his major achievements at a world-class level that is relevant to this day ever since. His visionary approach was noteworthy. Let’s take a look at Aryabhatta Inventions and Aryabhatta Discoveries.

### Aryabhatta Inventions And Aryabhatta Discoveries

The major works of his that have not been lost are Aryabhatiya and Arya-Siddhanta. In both his works he explored Mathematics and astronomy the correlation. And he also explained how mathematical equations could help find out the workings of the world via astronomy.

Aryabhatiya:- This book is also called Arya-status-ash which is directly translated as Aryabhata’s 108 because in the text there are 108 verses. It is written in the form of a sutra that is a collection of aphorisms which is a concise way of writing a statement or a scientific principle.

These verses are his works that are a way to remember the complex calculations in a simple format, in the form of 13 introductory verses. These are divided into 4 chapters or padas, the 1st Chapter is Gitikapada that has 13 verses. It deals with cosmology. The planetary revolutions, in a maha yuga, is mentioned to be up to 4.32 million years.

The 2nd Pada or chapter is the Ganitapada, Ganita in Sanskrit means calculations. It has 33 verses, all dedicated to mathematics. Explaining, mensuration, simple, quadratic, and indeterminate equations and arithmetic and geometric equations.

The 3rd Pada is the Kalakriya Pada consisting of 25 verses, where using varying units of time the count of days, weeks and months. And the 4th Chapter is Golapada that consists of 50 verses. In this chapter, Aryabhata delves into the causes of days and nights, rising of zodiac signs, eclipse, celestial equator, node and the shape of the earth.

Mathematical Discoveries:- In Aryabhatiya Indian Mathematical Literature was extensively mentioned. The Vedic way to solve mathematical problems was explored and unsurprisingly this has also survived to modern times. The details of algebra, arithmetic, plane trigonometry, spherical trigonometry were discussed. He followed the Sanskrutik tradition or method of calculations that were prevalent in the Vedic Times. The title of ‘Father Of Algebra’ was given to Aryabhata, due to his notable understanding and explanation of planetary systems using it. Aryabhata correctly concluded the valueof pi up to 2 decimal places, 3.14. He also used null coefficients and very rightly was aware of the use of zero in such a place. He used Sanskritic tradition that was mainly denoted by letters and alphabets, unlike the Brahmi numerals.

Astronomy Discoveries:- Aryabhatta rightly insisted that the earth rotates daily on its axis around the sun and the movement of stars appeared to be because of the relative motion caused due to the rotation of the earth. This was in contrast to the then very popular belief that it was the sky that rotates. Rightly with calculated evidence, it was explained heliocentrism is the rotation of planets around the sun, axially.

His astronomical discoveries are majorly divided into four sections. These include an explanation of the motion of the solar system, eclipses, sidereal periods and heliocentrism.

### The motion of the solar system

Aryabhatta suggested that the earth rotates on its axis daily. And the relative movement of the stars is caused by the motion of the earth.

In this first chapter of his book Aryabhatiya, he mentions the number of earth rotations in a yuga.

To explain this phenomenon, he proposed a geometrical model of the solar system in which the moon and sun were carried by epicycles which means a circle moving on another circle. According to this model, the motion of the planets was governed by two epicycles. The smaller one was slow and the larger one was fast.

In terms of the distance from the earth, the order of the planets was- the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn and the asterisms (group of stars). The periods and positions of the planets were calculated on the relative motion of the points.

In the case of Venus and Mercury, they moved with the same mean speed as the Sun around the Earth. However, Jupiter, Saturn and Mars, stars or points moved around the Earth at a specific velocity representing the motion of each planet through a zodiac.

Eclipses

Aryabhata explained lunar and solar eclipses with scientific experiments. He stated that the planets and the Moonshine due to the reflected sunlight. He explained the eclipses in terms of shadows falling on the Earth.

A lunar eclipse occurs when the Earth’s shadow is blocked by the Moon. Later, he discussed the extent and size of the Earth’s shadow and then computed the size of the eclipsed part during an eclipse. Aryabhatta experiments laid the foundation for Indian astronomers to improve the calculations.

Sidereal Periods

Considering the modern units of time, Aryabhatta calculated the sidereal rotation ( the rotation of the Earth concerning the stars) as 23 hours, 56 minutes and 4.1 seconds. The modern value of time was written as 23:56:4.091.

Heliocentrism

Aryabhatta gave an astronomical model which stated that the Earth rotates on its axis. His model also gave corrections for the calculations of mean speeds of the planets concerning the Sun. His calculations were based on the heliocentric model in which the planets and the Earth revolve around the Sun at the centre of the universe.

The geocentric model of the solar system was described by Aryabhata, scientifically explaining the solar and lunar eclipses. He also estimated the length of the year to be 365 days 6 hours 12 minutes 30 seconds which only deviates from today’s calculations by 3 minutes 20 seconds.

### Death of Aryabhata Scientist

Aryabhata died a successful mathematician, astronomer and scientist at the age of 74. The place and time of death are still unknown. It was believed he spent most of his life in Kusumapura, Pataliputra.

### Aryabhata's Legacy

Indian astronomical traditions and other cultures were highly influenced by Aryabhata's work. His works, experiments and calculations were translated into several languages to help other astronomers. During the Islamic Golden Age, the Arabian translation was specifically influential. Some of his results were cited by great Arabian mathematicians such as Al-Biruni and Al-Khawarizmi who believed that the Earth rotates on its axis.

Aryabhata's definitions for cosine, sine, inverse sine, verse sine gave birth to Trigonometry. He was one of the first mathematicians to determine sine and versine (1-cosx) tables from 0 to 90 degrees in the interval of 3.75 degrees to an accuracy of 4 decimal places.

The modern names of Trigonometric functions, sine and cosine are derived from the Sanskrit words “jya” and “Kojya” which were introduced by him.

His astronomical calculation techniques were also very popular among different astronomers. They were widely used to form Arabic astronomical tables “zijes”.

Along with this, his calendrical calculations have been used in India to form the Hindu calendar “Panchgram”. This calendar formed the basis of the Islamic calendar “Jalali'' which was introduced by a group of Islamic astronomers in 1073 CE. The modified versions of this calendar are still in use in Afghanistan and Iran.

To honour Aryabhata for his works, the Bihar Government has established Aryabhatta Knowledge University to promote astronomical knowledge among interested students. As well as the first Indian satellite was also named after him.

### Conclusion

The contributions of a scientist since Aryabhata has never been the same. He truly made the world notice India, in terms of holding scientific knowledge and value that made a difference to the world. He challenged and contradicted many beliefs that were going on at the time and through calculations provided pieces of evidence for it to be true. And after all these years, his work does not flinch from meticulous accuracy. There are very few scientists who achieved in their lifetime an extraordinary duty of work and Aryabhata was one of them. India recognizes his contributions. His work was widely popular and appreciated in the Islamic world especially his astronomical discoveries which were translated into Arabic in the 8th Century. The first Indian Satellite to be sent to space was named after him as a tribute. He was the first in the classical age of India that excelled as a mathematician and an astronomer. At the time, without any advanced technology available, being able to estimate and approximate his discoveries is truly remarkable. We must take pride in his works as Indians.

1. Did Aryabhata Invent Zero?

A French mathematician Georges Ifrah who closely followed the works of Aryabhata argued that Aryabhata has implicitly used zero in place of null coefficients but since he followed Sanskrit tradition that only contained letters and alphabets he mentioned alphabets and a dot in place of zero. So he was very much aware of a number like zero that can exist as a unit or in the tens place and mostly used in a decimal place. Aryabhata’s discovery of zero provided a direction to astronomers and mathematicians to improve their calculations and get precise results.

2. What Aryabhata Discovered?

Aryabhata’s major discoveries in the works not lost were the value of pi, that is 3.14, the heliocentrism of the solar system wherein he estimated the axial rotation of planets around the sun. And mostly used Indian languages in his mathematical equations. He was also known for discovering the trigonometric functions, sine and cosine. These are the modern words that are taken from the Sanskrit origin “jya” and “kojya”. Most of his works are lost but of what remains all have stood the test of time and still hold to this day.

3. What is Aryabhata Famous For?

Aryabhata is famous for being a mathematician, astronomer and scientist in the classical age. His works most have not been found, but whatever texts were discovered, has shown remarkable and accurate calculations. He had an in-depth knowledge of algebra, trigonometry, solving square roots, extracting quadratic equations, geometric and arithmetic progressions, the workings of the solar system and proved so through mathematical evidence. He is known to be the ‘Father of Algebra.” The most famous work of Aryabhata is his book that had 108 verses dedicated to mathematics, calculations of planetary motions, rising zodiac signs, length of a week and many astronomical discoveries.

4. What is Arya-Siddhanta?

Arya-Siddhanta is the lost work of Aryabhata on astronomical computations. It is known through the writings of his contemporary, Varahmihira, and later commentators and mathematicians including Bhaskara 1 and Brahmagupta. This thesis appears to be based on ShauryaSiddhantaand uses midday-night calculations, in opposition to sunrise in Aryabhatiya. This thesis also contains information on various astronomical instruments such as the gnomon, angle measuring devices, shadow instruments, semicircular and circular, cylindrical stick yasti-yantra, Chhota-yantra, an umbrella-shaped device, two types of water clocks, bow-shaped and cylindrical.

5. What was the contribution of Aryabhatta In Trigonometry?

Aryabhatta Designed a book called Aryabhatiya. This book has a section named Ganitpadain in which he has provided the area of the triangle for trigonometric calculations. He stated that the area of a triangle is the product of half of the side with its perpendicular.

In this book, he has also discussed trigonometric functions such as sine and cosine. He named sine Ardha-jya which means half-chord. However, sine was referred to as jobs when the Arabic translators translated his thesis. Later, the word jiba was translated into the Latin word sinus which means “bay” or “cove”. Thereupon, this was translated into English and termed as “sine”.