Bhaskara was an Indian mathematician and astronomer from the 12th century who made significant contributions in mathematics. He was born in Bijjada Biddha in present-day Karnataka and became the head of an astronomical observatory in Ujjain, a leading center of mathematics in ancient India. Some of his major contributions included introducing the Hindu-Arabic decimal number system, discovering principles of calculus and applying them to astronomy, proving the Pythagorean theorem, and providing solutions to quadratic, cubic and quartic equations. He wrote several important texts including Siddhanta Shiromani covering topics like arithmetic, algebra, astronomy and advanced mathematics.

1. PADEGOGY OF MATHEMATICS
Done by :- Ritesh Anand
Section :- C
Roll no.:- 221904
Topic:-contribution of Bhaskar in mathematics.
ASSIGNED BY
Mahendra mithrama

2. Introduction
Baskara is also known as Bhaskara or Bhaskarcharya, this
later name mean “Baskara the teacher”
 He was born near Bijjada Biddha [ in present day called district Karnataka state]
His father Mahesvara was the person who taught him
about astronomy as he was Ujjain the leading mathematical
center of ancient India.
Bhaskara followed in his father’s footsteps and became a mathematician,
astronomer and astrologer himself. He went on to become the head of an
astronomical observatory at Ujjain, the leading mathematical centre of ancient
India. The centre was a famous school of mathematical astronomy

3. Major contribution Area of Bhashkar in Mathematics
 Hindu Arabic Decimal System
 First degree of intermediate Equation
 Trigonometric formula.
 First discover gravity 500 years before Sir Issac Newton
 Calculations
 Arithematic
 Write mathematics in poetic language
 Cardinal number
 Proof of the Pythagorean theorem
 Discovered the principles of differential calculus and its application
 Quadratic equation
 In calculus
 Solutions of Diophantine Equations of the second order

4. Hindu Arabic Decimal System
o He was most likely the first to use a circle for the Zero for the Hindu
Arabic Decimal System
o He is considered to be follower of aryabhatta and one of the most
renowned scholars of the Aryabhatta’s astronical school
Proof of the Pythagorean theorem
He made many significant contributions to mathematics throughout his career.
He is credited to have given 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.
Quadratic equation
In Lilavati, solutions of quadric , cubic and quartic indeterminate equation are explained.
Solutions of indeterminate quadratic equations (of the type ax + b = y).

5. He is credited to have discovered spherical trigonometry,a branch of spherical geometry
which is of great importance for calculations in astronomy, geodesy and navigation.
Trigonometric formula
Algebra
work ‘Bijaganita’ ("Algebra") was a work in 12 chapters. This book covered topics
like positive and negative numbers, zero, surds, determining unknown quantities,
and elaborated the method of ‘Kuttaka’ for solving indeterminate equations and
Diophantine equations. He also filled many of the gaps in his predecessor Brahmagupta’s work.
Calculations
His work on calculus was groundbreaking and much ahead of his times.
He not only discovered the principles of differential calculus and its application
to astronomical problems and computations, but also determined solutions
of linear and quadratic indeterminate equations (Kuttaka). The works in calculus
performed by the Renaissance European mathematicians of the 17th century I
s comparable to the rules he had discovered way back in the 12th century.

6. He wrote Siddantha siromani in 1500 A.D when he was 36 years old.
It contains 1450 verses.
It is divided into 4 parts
Lilavathi
Beejaganitha ("Algebra")
Ganithadaya
GolaDyaya
In fact each part can be considered as separate Book.
The number of verses in each part are as follows
 Lilavati has 278 verses
 Beejaganita has 213 verses,
 Ganitadhyaya has 451
 Goladhyaya has 501 verses

7. Lilavati
The first part ‘Lilavati’ consists of 13 chapters, mainly definitions, arithmetical terms,
interest computation, arithmetical and geometrical progressions, plane geometry,
and solid geometry among others. It also has a number of methods of computing numbers
such as multiplications, squares, and progressions.
Beejaganitha ("Algebra")
His work ‘Bijaganita’ ("Algebra") was a work in 12 chapters.
This book covered topics like positive and negative numbers, zero, surds,
determining unknown quantities, and elaborated the method of ‘Kuttaka’
for solving indeterminate equations and Diophantine equations. He also filled many
of the gaps in his predecessor Brahmagupta’s work.

8. The sections ‘Ganitadhyaya’ and ‘Goladhyaya’ of
‘Siddhanta Shiromani’ are devoted to astronomy. He
used an astronomical model developed by
Brahmagupta to accurately define many astronomical
quantities, including the length of the sidereal year.
These sections covered topics such as mean
longitudes of the planets, true longitudes of the
planets, solar and lunar eclipses, cosmography and
geography, etc.
Ganithadaya and GolaDyaya

9. Baskara Tells
“I have studied 8 books of Grammer 6 text of medicine, 6 books logic
5 books on bharat shastras, and 2 mimansas
Conclusion