Indian contributions to the world

My family attends a Sunday school here in Us, where the elders try to keep the youth (and adults) updated about the Indian Culture. My daughters often ask me what the Indians have contributed to the world. So I decided to list some major contributions here. All links below are connected to Wikipedia.

I will continue adding to these as the time goes on. I invite you all to send me details on other similar contributions. Feel free to add more to this here.


ARYABHATTA: (476 AD) MASTER ASTRONOMER AND MATHEMATICIAN

Aryabhatta was born in 476 AD in Kusumpur, Bihar.

He is the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. When he was 23 years old, he wrote his most famous work -- the Aryabhatiya (499), which was a text on astronomy and an unparalleled treatise on mathematics.

Aryabhatt's intellectual brilliance remapped the boundaries of mathematics and astronomy. He also wrote the Arya-Siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary Varahamihira, as well as through later mathematicians and commentators including Brahmagupta and Bhaskara I. This work appears to be based on the older Surya Siddhanta, and uses the midnight-day-reckoning, as opposed to sunrise in Aryabhatiya. This also contained a description of several astronomical instruments, the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semi-circle and circle shaped (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device called chhatra-yantra, and water clocks of at least two types, bow-shaped and cylindrical.

A third text that may have survived in Arabic translation is the Al-ntf or Al-nanf, which claims to be a translation of Aryabhata, but the Sanskrit name of this work is not known. Probably dating from the ninth century, it is mentioned by the Persian scholar and chronicler of India, Abū Rayhān al-Bīrūnī.

Major contributions of Aryabhatta include:

• Process of calculating the motion of planets


• Process of calculating the time of eclipses.


• Aryabhatta was the first to proclaim that the earth is round and that it rotates on its axis, orbits the sun and is suspended in space - 1000 years before Copernicus published his heliocentric theory.
• Calculating Pi to four decimal places: 3.1416. Centuries later, in 825 AD, the Arab mathematician, Mohammed Ibna Musa credited the value of Pi to the Indians, "This value has been given by the Hindus."
• Found the sine table in trigonometry.
• His most spectacular contribution was the concept of zero without which modern computer technology would have been non-existent. Aryabhatt was a colossus in the field of mathematics.
  

BHASKARACHARYA II (1114 AD): GENIUS IN ALGEBRA

Bhaskara was born in the obscure village near Bijjada Bida (in present day Bijapur district, Karnataka state, India.

He later became the head of the astronomical observatory at Ujjain. Bhaskaracharya's work in Algebra, Arithmetic and Geometry catapulted him to fame and immortality.

His renowned mathematical works called "Lilavati" and "Bijaganita" are considered to be unparalleled and a memorial to his profound intelligence. Its translation in several languages of the world bears testimony to its eminence. In his treatise "Siddhant Shiromani" he wrote about planetary positions, eclipses, cosmic science, mathematical techniques and astronomical equipment.

In the "Surya Siddhant" he makes a note on the force of gravity: "Objects fall on earth due to a force of attraction by the earth. Therefore, the earth, planets, constellations, moon, and sun are held in orbit due to
this attraction." Bhaskaracharya was thus the first to discover gravity, 500 years before Sir Isaac Newton.

He was the champion among mathematicians of ancient and medieval India. His works fired the imagination of Persian and European scholars, who through research on his works earned fame and popularity.

Some of Bhaskara's contributions to mathematics include the following:

• A proof of the Pythagorean theorem by calculating the same area in two different ways and then canceling out terms to get a² + b² = c2.
• In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations.
• Solutions of indeterminate quadratic equations (of the type ax² + b = y²).
• Integer solutions of linear and quadratic indeterminate equations (Kuttaka). The rules he gives are (in effect) the same as those given by the renaissance European mathematicians of the 17th century
• A cyclic, Chakra-vala (Chakra means cyclic or circular) method for solving indeterminate equations of the form ax² + bx + c = y. The solution to this equation was traditionally attributed to William Brouncker in 1657, though his method was more difficult than the chakravala method.
• His method for finding the solutions of the problem x² − ny² = 1 (so-called "Pell's equation") is of considerable interest and importance.
• Solutions of Diophantine equations of the second order, such as 61x² + 1 = y². This very equation was posed as a problem in 1657 by the French mathematician Pierre de Fermat, but its solution was unknown in Europe until the time of Euler in the 18^th century.
• Solved quadratic equations with more than one unknown, and found negative and irrational solutions.
• Preliminary concept of mathematical analysis.
• Preliminary concept of infinitesimal calculus, along with notable contributions towards integral calculus.
• He conceived differential calculus, after discovering the derivative and differential coefficient.
• Stated Rolle's theorem, a special case of one of the most important theorems in analysis, the mean value theorem. Traces of the general mean value theorem are also found in his works.
• Calculated the derivatives of trigonometric functions and formulas.
• In Siddhanta Shiromani , Bhaskara developed spherical trigonometry along with a number of other trigonometrical results.