Aryabhata was a famous Indian mathematician and astronomer born in 476 CE in Bihar, India. He authored seminal works on mathematics and astronomy, including the Āryabhaṭ īya and Arya-siddhanta. Some of his key contributions included being the first to propose that the Earth rotates on its axis and revolves around the sun. He also introduced sine, cosine, versine and inverse sine in trigonometry and compiled sine and cosine tables. His work had a significant influence on the development of mathematics and astronomy in India and other parts of the world. Several institutions and discoveries are named after him in recognition of his pioneering contributions.

1. GREAT MATHEMATICIAN

2. Aryabhata (476–550 CE) was the first in the line of great mathematician-astronomers
from the classical age of Indian mathematics and Indian astronomy. His most famous
works are the Āryabhaṭ īya (499 CE, when he was 23 years old) and the Arya-siddhanta.
Aryabhata mentions in the Aryabhatiya that it was composed 3,630 years into the Kali
Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was
born in 476
Aryabhata was born in Taregna (literally, song of the stars), which is a small town in
Bihar, India, about 30 km (19 mi) from Patna (then known as Pataliputra), the capital city
of Bihar State.
It is fairly certain that, at some point, he went to Kusumapura for advanced studies
and that he lived there for some time. Both Hindu and Buddhist tradition, as well as
Bhāskara I (CE 629), identify Kusumapura as Pāṭ aliputra, modern Patna. A verse
mentions that Aryabhata was the head of an institution (kulapati) 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.[1]Aryabhata is also reputed to have set up an observatory at the Sun
temple in Taregana, Bihar.

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4. Great Works >>
• Aryabhata's work was of great influence in the Indian astronomical tradition and
influenced several neighbouring cultures through translations. The Arabic translation
during the Islamic Golden Age (c. 820 CE), was particularly influenced. Some of his results
are cited by Al-Khwarizmi and in the 10th century Al-Biruni stated that Aryabhata's
followers believed that the Earth rotated on its axis.
• His definitions of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram
jya) influenced the birth of trigonometry. He was also the first to specify sine and versine
(1 − cos x) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.
• Aryabhata's astronomical calculation methods were also very influential. Along with the
trigonometric tables, they came to be widely used in the Islamic world and used to
compute many Arabic astronomical tables (zijes). In particular, the astronomical tables in
the work of the Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin
as the Tables of Toledo (12th c.) and remained the most accurate ephemeris used in
Europe for centuries.
• Calendric calculations devised by Aryabhata and his followers have been in continuous
use in India for the practical purposes of fixing the Panchangam (the Hindu calendar). In
the Islamic world, they formed the basis of the Jalali calendar introduced in 1073 CE by a
group of astronomers including Omar Khayyam,[33] versions of which (modified in 1925)
are the national calendars in use in Iran and Afghanistan today. The dates of the Jalali
calendar are based on actual solar transit, as in Aryabhata and earlier Siddhanta
calendars. calender.

5. • He gave the formula (a + b)2 = a2 + b2 + 2ab.
• He taught the method of solving the following problems:

6. • Indeterminate equations
• A problem of great interest to Indian mathematicians since ancient
times has been to find integer solutions to equations that have the
form ax + by = c, a topic that has come to be known as diophantine
equations. This is an example from Bhāskara's commentary on
Aryabhatiya:
– Find the number which gives 5 as the remainder when divided by 8, 4 as the
remainder when divided by 9, and 1 as the remainder when divided by 7
• That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value
for N is 85. In general, diophantine equations, such as this, can be
notoriously difficult. They were discussed extensively in ancient Vedic
text Sulba Sutras, whose more ancient parts might date to 800 BCE.
Aryabhata's method of solving such problems is called the kuṭṭ aka
(कु ट क ) method. Kuttaka means "pulverizing" or "breaking into small
pieces", and the method involves a recursive algorithm for writing the
original factors in smaller numbers. Today this algorithm, elaborated
by Bhaskara in 621 CE, is the standard method for solving first-order
diophantine equations and is often referred to as the Aryabhata
algorithm. The diophantine equations are of interest in cryptology, and
the RSA Conference, 2006, focused on the kuttaka method and earlier
work in the Sulbasutras.

7. India's firs t s atellite and the lunar crater A ryabhata
are named in his honour. A n Ins titute for conducting
res earch in as tronomy, as trophys ics and atmos pheric
s ciences is the A ryabhatta Res earch Ins titute of
Obs ervational S ciences (A RIOS ) near Nainital, India. The
inter-s c hool A ryabhata Maths C ompetition is als o named
after him,as is Bacillus aryabhata, a s pecies of bacteria
dis covered by IS RO s cientis ts in 2009.

8. Nivedita Tomar
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MATHEMATICS