Aryabhatta

Aryabhata, an ancient Indian mathematician and astronomer, made significant contributions to the fields of mathematics and astronomy. His innovative work included the invention of the decimal system and the use of zero as a placeholder, as well as precise calculations for the value of pi and the determination of planetary motion. Aryabhata's insights laid the foundation for India's rich tradition in mathematics and astronomy, shaping the development of calendars, space exploration, and scientific research. His legacy endures through awards, institutions, and scientific discoveries named in his honour, reflecting his lasting impact on Indian culture and scientific inquiry.

The origins of Indian mathematics can be traced as far back as the Indus Valley Civilization (around 3000–1500 BCE). In ancient India mathematically principles arose to facilitate daily life like construction, trade, astronomy etc. However our ancient civilization was quite advanced. During the Classical period (400 BCE–1600 CE) Maurya, Gupta, and Chola empires were patrons of mathematical knowledge that expanded significantly, covering a wide range of topics including arithmetic, algebra, geometry, and trigonometry. Indian mathematicians are credited with discovery of ‘zero’ numeral and also decimal place-value system.

"Sulba Sutras" were written during this time by Baudhayana, Apastamba, and Katyayana where advanced geometric knowledge, including the Pythagorean theorem and techniques for constructing various geometric shapes is given. Brahmagupta (598–668 CE) in his work "Brahmasphutasiddhanta" discussed algebra, including solutions to quadratic equations and the rules for arithmetic operations with zero and negative numbers.

Aryabhata (476–550 CE) wrote "Aryabhatiya" and presented groundbreaking theories in astronomy and mathematics. Aryabhata's contributions include an accurate approximation of the value of pi, methods for calculating the areas of triangles and circles, and a heliocentric model of the solar system. He was born in 476 CE at Kusumapura, located in present-day Patna, Bihar.

Education and Career: Aryabhata pursued his advanced studies in Kusumapura, a centre known for its scholarly pursuits. It is speculated that he might have received education at Nalanda University, given its proximity and reputation as a hub of learning. Some accounts even suggest that Aryabhata held a prominent position at Nalanda University and established an observatory at the Sun Temple in Taregana, Bihar.

Aryabhatiya is the primary source of Aryabhata's work, though it wasn't titled by Aryabhata himself. His disciple, Bhaskara I, referred to it as Ashmakatantra, while it's also known as Arya-shatas-aShTa due to its 108 verses. The text is written concisely, typical of sutra literature, with each line aiding memory for complex systems.
The Aryabhatiya comprises four chapters or pādas:

1. Gitikapada: Discusses large units of time and presents a cosmology different from earlier texts. It also includes a table of sines and details planetary revolutions.
2. Ganitapada: Covers topics like mensuration, arithmetic, geometric progressions, equations, and shadows.
3. Kalakriyapada: Focuses on units of time, planetary positions, intercalary months, and the seven-day week.
4. Golapada: Explores geometric and trigonometric aspects of the celestial sphere, ecliptic features, and the cause of day and night.

Khagol-shastr: The astronomical segment of Aryabhatiya, known as Khagol-shastra, focuses on celestial observations and calculations. Aryabhata's deep understanding of astronomy shines through in this portion of his work.

• Relativity of Motion: Aryabhata's Aryabhatiya is notable for its description of the relativity of motion. He expressed this concept through an analogy, stating that just as a person in a moving boat sees stationary objects on the shore as moving backward, so do people on Earth perceive stationary stars as moving towards the west.

Arya Siddhanta: Another significant contribution by Aryabhata is the Arya Siddhanta, a text dedicated to astronomical calculations. This treatise includes detailed descriptions of various astronomical instruments utilised during Aryabhata's era, such as the gnomon, shadow instrument, angle-measuring devices, cylindrical stick, umbrella-shaped device, and water clocks.

In the first chapter of the Aryabhatiya, Aryabhata discusses astronomical constants and presents a sine table, laying the groundwork for subsequent calculations. He delves into various mathematical aspects necessary for astronomical computations, demonstrating his meticulous attention to detail.

Earth's Rotation: Aryabhata's most notable astronomical contribution lies in his assertion of the earth's rotation on its axis. Contrary to prevailing beliefs of his time, Aryabhata boldly proclaimed that the earth rotates regularly, causing the apparent movement of the stars—a notion echoed in modern astronomy. His insight into the earth's rotation revolutionised celestial understanding and paved the way for further astronomical advancements.

Solar and Lunar Eclipses: Aryabhata provided scientific explanations for solar and lunar eclipses, dispelling myths surrounding their causes. He attributed eclipses to the interplay of shadows cast by and falling on the earth, elucidating their mechanics in meticulous detail. Aryabhata's explanations, grounded in observation and mathematical reasoning, offered a rational understanding of celestial phenomena.

Measurement of Time: Aryabhata meticulously calculated the sidereal rotation and the duration of the sidereal year, contributing to the accurate measurement of time in astronomical contexts. His precise calculations, expressed in modern units of time, underscored his proficiency in mathematical astronomy.

Innovative Instruments: In addition to his theoretical contributions, Aryabhata developed innovative instruments like the chakra yantra and the gola yantra, facilitating astronomical observations and computations. These instruments, coupled with Aryabhata's theoretical insights, enhanced the precision and accuracy of astronomical measurements.

Decimal System: Aryabhata is credited with inventing the decimal system and introducing zero as a placeholder, revolutionising numerical notation. He meticulously described the first 10 decimal places and provided algorithms for computing square and cubic roots using this system.

Value of Pi: In his mathematical endeavours, Aryabhata calculated the value of pi (π) with remarkable precision, using the approximation 62,832/20,000, which is approximately equal to 3.1416. This approximation closely aligns with the modern value of pi and stands as one of the most accurate among ancient mathematicians. Aryabhata's work also hinted at his understanding of the irrational nature of pi.

Calculation of Areas: Aryabhata demonstrated proficiency in calculating the areas of geometric shapes, including triangles and circles. For instance, he provided a method for determining the area of a triangle by multiplying the result of a perpendicular with half the side length, as stated in his work Ganitapadam.

Table of Sines: Using the Pythagorean theorem as a foundation, Aryabhata devised one of the two methods for constructing a table of sines. This innovation facilitated trigonometric calculations and furthered the understanding of angular relationships in geometry and astronomy.

Additional Contributions: Beyond these accomplishments, Aryabhata's mathematical legacy includes advancements in mathematical series, quadratic equations, compound interest calculations, proportions, and solutions to various linear equations. His breadth of contributions encompassed diverse areas of arithmetic and algebra, laying the groundwork for subsequent developments in mathematics.

• Calendrical Calculations: The calendrical calculations introduced by Aryabhata and his followers remain integral to the preparation of the Panchangam, the Hindu calendar, in India. These calculations serve practical purposes and continue to be utilised in daily life.
• Aryabhatta Award: The Astronautical Society of India instituted the Aryabhatta Award, an annual recognition bestowed upon individuals who have made notable lifetime contributions to astronautics and aerospace technology in India. This award celebrates excellence in these fields and honours Aryabhata's legacy.
• India's First Satellite and Lunar Crater: India's first satellite, Aryabhata, and the lunar crater Aryabhata were named in honour of this great Indian scientist. These tributes underscore Aryabhata's pioneering role in advancing India's space exploration endeavours.
• Aryabhatta Research Institute: The Aryabhatta Research Institute of Observational Sciences (ARIES) serves as a centre for research and training in astrophysics, astronomy, and atmospheric sciences. Located near Nainital in Uttarakhand, ARIES continues Aryabhata's legacy of scientific inquiry and exploration.
• Bacillus Aryabhattai: In 2009, scientists at the Indian Space Research Organisation (ISRO) discovered a bacterial species named Bacillus Aryabhattai.

Aryabhata, an Indian astronomer and mathematician of the Gupta dynasty, made significant contributions to the classical period of Indian mathematics and astronomy. His seminal works, Aryabhattiya and Arya-Siddhanta, have had a profound influence on the Indian astronomical tradition and were translated into various languages, spreading his ideas to neighbouring cultures.

Aryabhata's methods and results were instrumental in the development of astronomical calculation techniques, particularly in the Islamic world during the Golden Age. His work, translated into Arabic, influenced renowned scholars like Al-Khwarizmi and Al-Biruni, shaping their understanding of celestial mechanics. Aryabhata's trigonometric tables and astronomical calculations were widely adopted, including in the computation of Arabic astronomical tables (zijes). The impact of his contributions extended to Europe, where his methods formed the basis of the Tables of Toledo, serving as the most accurate ephemeris in Europe for centuries. Aryabhata's enduring legacy underscores his pivotal role in advancing both Indian and global understanding of mathematics and astronomy.