TWO FAMOUS MATHEMATICIANS

1. TWO FAMOUS
MATHAMATICIANS

2. Aryabhata
Āryabhaa
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

3. Major
works
Āryabhaīya, 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 Āryabhaīya (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 Pāaliputra, 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]

4. 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]

5. 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.

6. 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.