BHASKARA II
1114 - 1185
Kiran Kandel,
Aerospace 1st year, CU.
Life sketch of Bhaskara II

Mathematician and astronomer of
medieval India .

Born in 1114 at Bijapur, Karnataka.

He became the head of
Astronomical Observatory at Ujjain

His father Mahesvara, was also a
mathematician and an
astronomer.
Education

Bhaskara II himself wrote about his education,
‘I have studied eight books of grammar, six texts of medicine, six
books on logic, five books of mathematics, four vedas, five books on
Bharat Shastras and two Mimansas.’

Called himself as a poet and Vedanti.
Siddhanta Siromani

Lilavati
•
1st volume of Bhaskara’s
Siddhanta Shiromani, named
after his daughter.
•
Covers the topics of definitions,
arithmetical terms, arithmetical
and geometrical progressions,
plane geometry, methods to
solve indeterminate equations
and combinations.

Bijaganita
•
2nd volume of Siddhanta
Shiromani
•
The first text to recognize
that a positive number has
square roots.
•
Devoted to algebra.

Grahaganita
•
3rd volume which consist of
Ganitadhyaya and Goladhyaya.
•
He considered instantaneous
speeds of the motion of planet.
•
Devoted to astronomy and
sphere.
•
He gave the value of the Earth’s
circumference as 4967 ‘yojane’
(1 yojane=8km), which means
39736 km, and claimed the
diameter of earth as 1581 yojane
i.e. 12648 km. The modern values
are 40212 km and 12800 km
respectively.
Contributions in mathematics

Proof of the Pythagoras theorem

Solutions of the indeterminate quadratic equation, ax^2 + b = y^2.

Integer solutions of linear and quadratic indeterminate equations (kuttaka method)
for e.g. 100X + 90=63Y.

A cyclic Chakravala method for solving indeterminate equations of the second
order (61X^2 + 1 = Y^2).

Bhaskara gave the first general method for finding the solutions of the problem x^2 –
ny^2 = 1

He has also given the terms for numbers in multiple of 10.

The value of pie was found 3.14166.
‘A particle of tuition conveys science to a
comprehensive mind: and having reached it,
expands of its own impulse. As oil poured on water,
as a secret entrusted to the vile, as alms bestowed
upon the worthy, however little so does science
infused into a wise mind spread by intrinsic force.’
- Bhaskara II
Thank you