Bhaskara II was an influential 12th century Indian mathematician born in 1114 AD in Bijapur, India. He wrote several important mathematical texts, including Lilavati which covered arithmetic and algebra. Some of Bhaskara's key contributions included solving indeterminate equations, introducing the concept of 0/0 having infinite solutions, and a cyclic method for solving algebraic equations that was later rediscovered by European mathematicians. He made advances in areas such as calculus, algebra, and number theory. Bhaskara II represents the peak of mathematical knowledge in 12th century India.
This a PPT about "BHASKARACHARYA" a great indian mathematician ,who wrote a 4 books about brief mathematics back in 1150 AD
Presentation done by
P. Pushpanvitha
8th standard
This presentation is about the Indian Mathematician Bhaskara II.
Prepared for B.Ed. Sem. II students of Mathematics pedagogy, of university of Lucknow.
This a PPT about "BHASKARACHARYA" a great indian mathematician ,who wrote a 4 books about brief mathematics back in 1150 AD
Presentation done by
P. Pushpanvitha
8th standard
This presentation is about the Indian Mathematician Bhaskara II.
Prepared for B.Ed. Sem. II students of Mathematics pedagogy, of university of Lucknow.
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Bhaskar 2 and Field Medal
1.
2.
• Bhaskara II is a famous mathematician of ancient
India. He was born in 1114 A.D. in the city of
Bijapur, Karnataka state, India. Peoples also know
him as Bhaskaracharya, which means “Bhaskara the
Teacher”.
• Bhaskara II became head of the astronomical
observatory at Ujjain, which was the leading
mathematical centre in India at that time He wrote
six books and but a seventh work, which is claimed
to be by him, is thought by many historian to be a
late forgery.
LIFE SKETCH OF
BHASKARA II
3. • The three most important books he published were Lilavati
(The Beautiful), which is about mathematics; Bijaganita (Seed
Counting), which is about algebra; and an astronomical work,
Karanakutuhala (The Calculation of Astronomical Wonders).
Lilavati is the first known published work that uses the decimal
position system.
• His father name was Mahesvara. By profession he was an
astrologer, who taught him mathematics, which he later passed
on to his son Loksamudra. In many ways, Bhaskaracharya
represents the peak of mathematical knowledge in the 12th
century.
4.
• 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 quadratic, cubic and quartic indeterminate
equations.
• 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 seventeenth 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.
• His method for finding the solutions of the problem x2 − ny2 = 1 (so called
"Pell's equation") is of considerable interest and importance.
Bhaskaracharya's significant
contribution to mathematics
5. • Siddhānta Shiromani (Sanskrit for "Crown of treatises") is the
major treatise of Indian mathematician Bhāskarāchārya. He wrote
Siddhanta Sherman in 1150 AD when he was 36 years old. The work
is composed in Sanskrit Language in 1450 verses
• Lilavati The name of the book comes from his daughter Līlāvatī. It
is the first volume of Siddhānta Shiromani. The book contains thirteen
chapters, 278 verses, mainly arithmetic and mensuration.
• Bijaganita It is the second volume of Siddhānta Shiromani. It is
divided into six parts, contains 213 verses and is devoted to algebra.
• Ganitadhyaya and Goladhyaya Ganitadhyaya and Goladhyaya of
Siddhanta Shiromani are devoted to astronomy.).
MAJOR CONTRIBUTION-
SIDDANTA SHIROMANI
6.
Lilavati is the first part of Bhaskaracharya's work
Siddhantashiromani which he wrote at the age of 36.
• Lilavati mainly deals with what we call as `Arithmetic' in today's
mathematical parlance.
• It consists of 279 verses written in Sanskrit in poetic form (terse
verses).
• There are certain verses which deal with Mensuration
(measurement of various geometrical objects), Volume of
pyramid, cylinders, heaps of grains etc., wood cutting, shadows,
trigonometric relations
• Bhaskaracharya wrote this work by selecting good parts from
Sridharacharya's Trishatika and Mahaviracharya's
Ganitasarasamgraha and adding material of his own.
LILAVATHI
7.
• Lilavati has an interesting story associated with how it got its
name.
• Bhaskaracharya created a horoscope for his daughter Lilavati,
stating exactly when she needed to get married.
• He placed a cup with a small hole in it in a tub of water, and
the time at which the cup sank was the optimum time Lilavati
was to get married. Unfortunately, a pearl fell into the cup,
blocking the hole and keeping it from sinking.
• Lilavati was then doomed never to wed, and her father
Bhaskara wrote her a manual on mathematics in order to
console her, and named it Lilavati.
• This appears to be a myth associated with this classical work.
THE NAME ‘Lilavati’
8.
Out of a group of swans, 7/2 times the square root of
the number are playing on the shore of a tank. The
two remaining ones are swimming in the water.
What is the total number of swans?
SOLUTION : let the total no. of swans = x2 No. of
swans playing on the shore of a tank. =7/2x No. of
swans swimming in the water =2
Total no. of swans = No. of swans playing on the
shore of a tank + No. of swans swimming in the
water.
PUZZLES
9. X2=7/2X+2
2 X2 = 7X+4
2 X2-7X-4 = 0
2 X2-8X+X-4 = 0
(2X+1) (X-4) =0
X-4 = 0
X = 4
Total no. of swans = X2 = 16
• Bhaskaracharya gives a very interesting puzzle from the epic
Mahabharata where Arjuna uses a certain number of arrows
(say x) to destroy the horses of Karna, a certain number to
destroy his chariot, flag, bow and to cut o his head. The
solution of the puzzle is the root of a quadratic equation.
10. 1/4th of a herd of camels were seen in a forest . Twice the
square root of the herd had gone to the mountain remaining
15 were seen at the bank of river. find the no. of camels.
SOLUTION: let the total no. of camels= x2
No. of camels gone to the mountain = 2x
No. of camels seen in a forest = 1/4 x2
No. of remaining camels = 15
Total no. of camels = No. of camels gone to the mountain + No.
of camels seen in a forest + No. of remaining camels
12.
First to declare a/0=infinite.
First to declare a+ infinite=infinite.
Gave idea about the value of 0/0-
Sequence :5*1,5*1/2,5*1/3,5*1/4,5*1/5……..
1 1/2 1/3 1/4 1/5
it approaches 0/0 as numerator, denominator both going
to zero.
But every term is 5 so limit is 5 and 0/0=5
Replace 5 by any no. and you get that as a limit – so 0/0 can
be anything.
ACCOMPLISHMENTS
13.
Bhaskara II dies in 1185 at the age of 71.
Several of Bhaskara’s findings were not explored heavily after
his death and ended up being “discovered” later by European
mathematicians.
The cyclic method to solve algebraic equations, 6 centuries later
Galois,Euler and Langrange rediscoverd this and called it
“inverse cyclic”.
Differential calculus-
. Rediscoverd as “differential coefficient”.
. “Rolle’s Theorem”.
.Newton and Leibnitz receive credit .
BHASKARA REPRESENTS THE PEAK OF MATHEMATICAL
KNOWLEDGE IN 12th CENTURY.
AFTER BHASKARA II
14.
15. The medal was designed by
Canadian sculptor
R. Tait McKenzie.
On the obverse is Archimedes
and a quote attributed to him
which reads in Latin: "Transire
suum pectus mundoque potiri"
("Rise above oneself and grasp
the world"). The date is written
in Roman numerals and
contains an error
("MCNXXXIII" rather than
"MCMXXXIII"). In capital
Greek letters the word
ΑΡXIMHΔΟΥΣ, or "of
Archimedes".
16. On the reverse is the inscription (in
Latin):
CONGREGATI
EX TOTO ORBE
MATHEMATICI
OB SCRIPTA INSIGNIA
TRIBUERE
Translation: "Mathematicians
gathered from the entire world have
awarded for outstanding writings."
In the background, there is the
representation of Archimedes' tomb, with
the carving illustrating his theorem On
the Sphere and Cylinder, behind a
branch. (This is the mathematical result
of which Archimedes was reportedly
most proud: Given a sphere and a
circumscribed cylinder of the same height
and diameter, the ratio between their
volumes is equal to ⅔.)
17. Awarded for Outstanding contributions in mathematics
attributed to young scientists
Country Varies
Presented by International Mathematical Union (IMU)
Reward(s) CA$15,000
First awarded 1936; 83 years ago
Last awarded 2018
18. The Fields Medal is regarded as one of the highest honors
a mathematician can receive, and has been described as the
mathematician's "Nobel Prize" , although there are several key
differences, including frequency of award, number of awards,
and age limits.
After the Abel Prize , The field medal is considered as the second
most prestigious international award in mathematics.
The name of the award is in
honour of Canadian
mathematician
John Charles Fields.
19. The medal was first awarded in 1936 to Finnish
mathematician Lars Ahlfors and American mathematician
Jesse Douglas, and it has been awarded every four years
since 1950.
Lars Ahlfors
20. In 2014, the Iranian mathematician
Maryam Mirzakhani
became the first woman Fields
Medalist.
21. FIRST INDIAN: Manjul Bhargava was awarded
the Fields Medal in 2014. According to the International
Mathematical Union citation, he was awarded the prize
"for developing powerful new methods in the geometry of
numbers, which he applied to count rings of small rank
and to bound the average rank of elliptic curves".
22. 2018
Rio de Janeiro,
Brazil
Caucher Birkar
"for his proof of the boundedness of Fano varieties and for
contributions to the minimal model program".
2018
Rio de Janeiro,
Brazil
Alessio Figalli
"for his contributions to the theory of optimal transport,
and its application to partial differential equations, metric
geometry, and probability"
2018
Rio de Janeiro,
Brazil
Peter Scholze
"for transforming arithmetic algebraic geometry over
p-adic fields through his introduction of perfectoid spaces,
with application to Galois representations and for the
development of new cohomology theories."
2018
Rio de Janeiro,
Brazil
Akshay
Venkatesh
"for his synthesis of analytic number theory, homogeneous
dynamics, topology, and representation theory, which has
resolved long-standing problems in areas such as the
equidistribution of arithmetic objects."
YEAR ICM
LOCATION
MEDALIST CITATION
23. The most recent group of Fields Medalists received their
awards on 1 August 2018 at the opening ceremony of the
IMU International Congress, held in Rio de Janeiro,
Brazil. The medal belonging to one of the four joint
winners, Caucher Birkar, was stolen shortly after the
event. The ICM presented Birkar with a replacement
medal a few days later.
In all sixty people have been awarded the
field medals.
