TWO FAMOUS MATHAMATICIANS

Aryabhata

Āryabha�a

Born 476 CE

prob. Ashmaka

Died 550 CE

Era Gupta era

Region India

Main

interests Mathematics, Astronomy

Notable

ideas Explanation of Lunar eclipse andSolar eclipse, Rotation

of earth on its axis, Reflection of light by

moon, Sinusoidal functions,Solution of single variable

quadratic equation, Value of π correct to 4 decimal

places, Circumference of Earth to 99.8% accuracy,

Calculation of the length of Sidereal year

Major

works Āryabha�īya, Arya-siddhanta

Aryabhata was the first in the line of great mathematician-astronomersfrom the classical age of Indian mathematics and Indian astronomy. His works include the Āryabha�īya (499 CE, when he was 23 years old)[5] and the Arya-siddhanta.

The works of Aryabhata dealt with mainly mathematics and astronomy.

Biography

Name

While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names

having the "bhatta" suffix, his name is properly spelled Aryabhata: every astronomical text spells

his name thus,[6] including Brahmagupta's references to him "in more than a hundred places by

name".[7]Furthermore, in most instances "Aryabhatta" does not fit the metre either.[6]

Time and place of birth

Aryabhata mentions in the Aryabhatiya that it was composed 3,600 years into the Kali Yuga,

when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476.[4]

Aryabhata provides no information about his place of birth. The only information comes

from Bhāskara I, who describes Aryabhata as āśmakīya, "one belonging to the aśmaka country."

During the Buddha's time, a branch of the Aśmaka people settled in the region between

the Narmada and Godavari rivers in central India; Aryabhata is believed to have been born

there.[6][8]

Education

It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived

there for some time.[11] Both Hindu and Buddhist tradition, as well as Bhāskara I (CE 629), identify

Kusumapura as Pā�aliputra, modern Patna.[6] A verse mentions that Aryabhata was the head of

an institution (kulapa) at Kusumapura, and, because the university of Nalanda was in Pataliputra

at the time and had an astronomical observatory, it is speculated that Aryabhata might have

been the head of the Nalanda university as well.[6] Aryabhata is also reputed to have set up an

observatory at the Sun temple in Taregana, Bihar.[12]

Works

Aryabhata is the author of several treatises on mathematics and astronomy, some of which are

lost.

His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively

referred to in the Indian mathematical literature and has survived to modern times. 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.

The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of

Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators,

includingBrahmagupta 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. It also

contained a description of several astronomical instruments: the gnomon (shanku-yantra), a

shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular and circular

(dhanur-yantra /chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device called

the chhatra-yantra, and water clocks of at least two types, bow-shaped and cylindrical.[8]

A third text, which may have survived in the Arabic translation, is Al ntf or Al-nanf. It claims that it

is a translation by Aryabhata, but the Sanskrit name of this work is not known.

Probably dating from the 9th century, it is mentioned by the Persian scholar and chronicler of

India, Abū Rayhān al-Bīrūnī.[8]

Pythagoras

Born Approximately 569 BC, Samos Greece

Died Approximately 500 - 475 BC, Metapontum Italy

Pythagoras is often referred to as the first pure mathematician. He was born on the island of

Samos, Greece in 569 BC. Various writings place his death between 500 BC and 475 BC in Metapontum, Lucania, Italy. His father, Mnesarchus, was a gem merchant. His mother's name was Pythais. Pythagoras had two or three brothers.

Some historians say that Pythagoras was married to a woman named Theano and had a daughter Damo, and a son named Telauges, who succeeded Pythagoras as a teacher and possibly taught Empedocles. Others say that Theano was one of his students, not his wife, and say that Pythagoras never married and had no children.

Pythagoras was well educated, and he played the lyre throughout his lifetime, knew poetry and recited Homer. He was interested in mathematics, philosophy, astronomy and music, and was greatly influenced by Pherekydes (philosophy), Thales (mathematics and astronomy) and Anaximander (philosophy, geometry).

Pythagoras left Samos for Egypt in about 535 B.C. to study with the priests in the temples. Many of the practices of the society he created later in Italy can be traced to the beliefs of Egyptian priests, such as the codes of secrecy, striving for purity, and refusal to eat beans or to wear animal skins as clothing.

Ten years later, when Persia invaded Egypt, Pythagoras was taken prisoner and sent to Babylon (in what is now Iraq), where he met the Magoi, priests who taught him sacred rites. Iamblichus (250-330 AD), a Syrian philosopher, wrote about Pythagoras, "He also reached the acme of perfection in arithmetic and music and the other mathematical sciences taught by the Babylonians..."

In 520 BC, Pythagoras, now a free man, left Babylon and returned to Samos, and sometime later began a school called The Semicircle. His methods of teaching were not popular with the leaders of Samos, and their desire for him to become involved in politics did not appeal to him, so he left.

Pythagoras settled in Crotona, a Greek colony in southern Italy, about 518 BC, and founded a philosophical and religious school where his many followers lived and worked. The Pythagoreans lived by rules of behavior, including when they spoke, what they wore and what they ate. Pythagoras was the Master of the society, and the followers, both men and women, who also lived there, were known as mathematikoi. They had no personal possessions and were vegetarians. Another group of followers who lived apart from the school were allowed to have personal possessions and were not expected to be vegetarians. They all worked communally on discoveries and theories. Pythagoras believed:

All things are numbers. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. The physical world can understood through mathematics.

The soul resides in the brain, and is immortal. It moves from one being to another, sometimes from a human into an animal, through a series of reincarnations called transmigration until it becomes pure. Pythagoras believed that both mathematics and music could purify.

Numbers have personalities, characteristics, strengths and weaknesses.

The world depends upon the interaction of opposites, such as male and female, lightness and darkness, warm and cold, dry and moist, light and heavy, fast and slow.

Certain symbols have a mystical significance.

All members of the society should observe strict loyalty and secrecy.