Aryabhatta was an Indian mathematician and astronomer from the 5th century who made several contributions to mathematics including trigonometry, algebra, and a more accurate approximation of pi. His work was influential in the development of mathematics and astronomy in India and later in the Islamic world and Europe. Bhaskara II was a 12th century mathematician who wrote the first work using the decimal number system and made contributions to calculus, algebra, and spherical trigonometry. He is considered one of the greatest mathematicians of ancient India. Both Aryabhatta and Bhaskara II's work had a significant and lasting impact on the fields of mathematics and astronomy both in India and globally.

1. INDIAN
MATHEMATICIAN
AND THEIR
CONTRIBUTIONS

2. The Father of Indian Mathematics
‘Aryabhatta’

3. Kusumapura, India), astronomer and the earliest
Indian mathematician whose work and history are
available to modern scholars He flourished in
Kusumapura—near Patalipurta (Patna), then the
capital of the Gupta dynasty—where he composed
at least two works, Aryabhatiya (c. 499) and the
now lost Aryabhatasiddhanta.
Aryabhatasiddhanta circulated mainly in the
northwest of India and, through the Sāsānian
dynasty (224–651) of Iran, had a profound
influence on the development of Islamic
astronomy. Its contents are preserved to some
extent in the works of Varahamihira (flourished c.
550), Bhaskara I (flourished c. 629), Brahmagupta
(598–c. 665), and others. It is one of the earliest
astronomical works to assign the start of each day
to midnight.

4. Aryabhatta made several contributions to
Mathematics inventions and theories. Due to his
significant contribution and achievement in
mathematics, he is also called The King of Indian
Mathematics. Some of the important discoveries
he made in the mathematics field are:
Aryabhata became famous as a mathematician
and astronomer. In his only surviving work,
Aryabhatiya, he covered a wide range of topics,
such as extracting square roots, solving quadratic
equations,
The place value system and zero Trigonometry,
Algebra , Aryabhata discovered an approximation
of pi 62832/20000 = 3.1416 , Indeterminate
equations

5. Aryabhatta died in 550 CE in Patliputra only. The
contributions made by Aryabhatta are still used
in today’s times. Go through Aryabhatta’s work
that is still practised.
Aryabhata’s astronomical calculating methods are
used in the Islamic world to calculate dates for
calendars.Trigonometric tables are used to
compute numerous Arabic astronomy tables.
Aryabhatta’s definitions of cosine, sine, versine
and inverse sine impacted the development of
trigonometry mathematics. Moreover, he was also
the first to give sine and versine (1 cos x) tables
in 3.75° intervals from 0° to 90°, with 4 decimal
places of precision.
The contemporary terms ‘sine’ and ‘cosine’ are
mistranslations of Aryabhata’s phrases jy and
koji.

6. The well-known mathematician of ancient India,
Aryabhatta, has received several honours from the
government of India like:
To honour such great Indian mathematicians, the
Bihar Government created Aryabhatta Knowledge
University (AKU) in Patna to develop and manage
educational infrastructure linked to leadership,
medical, technical, and associated professional
education. Bihar State University Act of 2008
governs the AKU university. Moreover, the
government of India names India’s first satellite
(Aryabhata and the lunar crater Aryabhata) after
Aryabhatta to embrace his contribution to
astronomy and mathematics.The Aryabhata
satellite appears on the backside of the Indian
two-rupee note.

7. Aryabhatta’s contributions to mathematics
and astronomy were phenomenal and
influential. The discoveries and inventions
made by the Aryabhatta turned out to be
helpful in the science and mathematics
fields. Aryabhatta’s contributions to
mathematics like trigonometry, pi, place
value system, etc. solve significant problems
and are still practised and taught in schools
and colleges. His contribution to astronomy
brought major changes in the scientific
sector, which led scientists and astronauts to
achieve new milestones in astronomy.

8. About ‘Bhaskara II ’

9. the Learned, (born 1114, Biddur, India—died c.
1185, probably Ujjain), the leading mathematician
of the 12th century, who wrote the first work with
full and systematic use of the decimal number
system.
Bhāskara II was the lineal successor of the noted
Indian mathematician Brahmagupta (598–c. 665)
as head of an astronomical observatory at Ujjain,
the leading mathematical centre of ancient India.
The II has been attached to his name to distinguish
him from the 7th-century astronomer of the same
name. In Bhāskara II’s mathematical works
(written in verse like nearly all Indian
mathematical classics), particularly Līlāvatī (“The
Beautiful”) and Bījagaṇita (“Seed Counting”), he
not only used the decimal system but also
compiled problems from Brahmagupta and others.

10. Contribution of Bhaskara II to Mathematics
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 quadric , cubic and quartic indeterminate equation are
explained.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
Chakravala 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.The first general method for finding the solutions of the
problem x2 − ny2 = 1 (so-called “Pell’s equation “)was given by Bhaskara II.
Solutions of Diophantine Equations of the second order, such as 61x2 + 1 =
y2.

11. equations with more than one unknown, and found
negative and irrational i solutions.Preliminary
concept of mathematical analysis.Preliminary
concept of infinitesimal Calculus, along with
notable contributions towards integral calculus
.Conceived differential calculus, after discovering
the derivative and differential coefficient.Stated
Roll’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
formula.In Siddhanta Shiromani, Bhaskara
developed spherical trigonometry along with a
number of other trigonometric results.He
concluded that dividing by zero would produce an
infinity.

12. all time. His work on mathematics and astronomy
has had a lasting impact on the field of science
and serves as an inspiration to future generations
of mathematicians and
scientists.Bhaskaracharya's contributions to
mathematics and astronomy were not limited to
his own time or region. His ideas and methods
were later transmitted to the Arab world and
Europe, where they had a profound influence on
the development of calculus and other branches
of mathematics.In India, Bhaskaracharya's work
continued to be studied and refined by later
generations of mathematicians and astronomers.
His ideas on calculus, algebra, and astronomy laid
the foundation for the development of a rich
tradition of mathematics in India, which
continued to thrive for centuries.

13. In the end, Bhaskaracharya's legacy is a
testament to the power of human curiosity
and the enduring value of knowledge. His
contributions to mathematics and astronomy
have stood the test of time, and his ideas
continue to inspire new generations of
mathematicians and scientists around the
world. The story of Bhaskaracharya is a
reminder that even in the most difficult
circumstances, the human mind has the
power to create and discover, and that the
pursuit of knowledge is a never-ending
journey.

15. BY
CDT.RISHAV RAJ
ROLL NO – 6815
HOUSE – PANDYA
CLASS – IX ‘A’
SUB.TEACHER - MRS.NV