Mathematics(History,Formula etc.) and brief description on S.Ramanujan.

A brief history of Mathematics
Before the Ancient Greeks:
• Egyptians and Babylonians (c. 2000 BC):
• Knowledge comes from “papyri”
• Rhind Papyrus

Babylonian Math
• Main source: Plimpton 322
• Sexagesimal (base-sixty) originated with ancient
Sumerians (2000s BC), transmitted to
Babylonians … still used —for measuring
time, angles, and geographic coordinates

Greek Mathematicians
• Thales (624-548)
• Pythagoras of Samos (ca. 580 - 500 BC)
• Zeno: paradoxes of the infinite
• 410- 355 BC- Eudoxus of Cnidus (theory
of proportion)
• Appolonius (262-190): conics/astronomy
• Archimedes (c. 287-212 BC)

Ptolemy (AD 83–c.168), Roman Egypt
• Almagest: comprehensive treatise on
geocentric astronomy
• Link from Greek to Islamic to European
science

Al-Khwārizmī (780-850), Persia
• Algebra, (c. 820): first
book on the systematic
solution of linear and
quadratic equations.
• He is considered as the
father of algebra:
• Algorithm: westernized
version of his name

Leonardo of Pisa (c. 1170 – c.
1250) aka Fibonacci
• Brought Hindu-Arabic
numeral system to Europe
through the publication of
his Book of Calculation, the
Liber Abaci.
• Fibonacci
numbers, constructed as
an example in the Liber
Abaci.

Cardano, 1501 —1576)
illegitimate child of Fazio Cardano, a friend of
Leonardo da Vinci.
He published the solutions to the cubic and quartic
equations in his 1545 book Ars Magna.
The solution to one particular case of the cubic, x3 +
ax = b (in modern notation), was communicated to
him by Niccolò Fontana Tartaglia (who later claimed
that Cardano had sworn not to reveal it, and engaged
Cardano in a decade-long fight), and the quartic was
solved by Cardano's student Lodovico Ferrari.

John Napier (1550 –1617)
• Popularized use of the (Stevin’s)
decimal point.
• Logarithms: opposite of powers
• made calculations by hand much
easier and quicker, opened the way
to many later scientific advances.
• “MirificiLogarithmorumCanonisDesc
riptio,” contained 57 pages of
explanatory matter and 90 of tables,
• facilitated advances in astronomy
and physics

Galileo Galilei (1564-1642)
• “Father of Modern Science”
• Proposed a falling body in a vacuum
would fall with uniform acceleration
• Was found "vehemently suspect of
heresy", in supporting Copernican
heliocentric theory … and that one
may hold and defend an opinion as
probable after it has been declared
contrary to Holy Scripture.

René Descartes (1596 –1650)
• Developed “Cartesian
geometry” : uses algebra to
describe geometry.
• Invented the notation using
superscripts to show the
powers or exponents, for
example the 2 used in x2 to
indicate squaring.

Blaise Pascal (1623 –1662)
• important contributions to the
construction of mechanical
calculators, the study of
fluids, clarified concepts of
pressure and.
• wrote in defense of the scientific
method.
• Helped create two new areas of
mathematical research:
projective geometry (at 16) and
probability theory

Pierre de Fermat
(1601–1665)
• If n>2, then
a^n + b^n = c^n has no
solutions in non-zero
integers a, b, and c.

Sir Isaac Newton (1643 – 1727)
• conservation of momentum
• built the first "practical" reflecting
telescope
• developed a theory of color based on
observation that a prism decomposes
white light into a visible spectrum.
• In mathematics:
• development of the calculus.
• demonstrated the generalised binomial
theorem, developed the so-called
"Newton's method" for approximating
the zeroes of a function....

Euler (1707 –1783)
• important discoveries in
calculus…graph theory.
• introduced much of modern
mathematical terminology and
notation, particularly for
mathematical analysis,
• renowned for his work in
mechanics, optics, and
astronomy.

David Hilbert (1862 –1943)

• Invented or developed a
broad range of
fundamental ideas, in
invariant theory, the
axiomatization of
geometry, and with the
notion of Hilbert space

Claude Shannon (1916 –2001)]
• famous for having founded
“information theory” in 1948.
• digital computer and digital
circuit design theory in 1937
• demonstratedthat electrical
application of Boolean algebra
could construct and resolve any
logical, numerical relationship.
• It has been claimed that this was
the most important master's

Theano
Hypatia
Caroline Herschel

Sophie Germain
Emilie du Chatelet

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Theano was the wife of Pythagoras. She
and her two daughters carried on the
Pythagorean School after the death of
Pythagoras.
She wrote treatises on mathematics,
physics, medicine, and child psychology.
Her most important work was the principle
of the “Golden Mean.”

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Hypatia was the daughter of Theon, who
was considered one of the most educated
men in Alexandria, Egypt.

Hypatia was known more for the work she
did in mathematics than in astronomy,
primarily for her work on the ideas of
conic sections introduced by Apollonius.

Hypatia

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Her first experience in mathematics was
her catalogue of nebulae.

She calculated the positions of her
brother's and her own discoveries and
amassed them into a publication.

One interesting fact is that Caroline never
learned her multiplication tables.

Caroline Herschel

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She is best known for her work in number
theory.

Her work in the theory of elasticity is also
very important to mathematics.

Sophie Germain

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Among her greatest achievements were
her “Institutions du physique” and the
translation of Newton's “Principia”, which
was published after her death along with a
“Preface historique” by Voltaire.

Emilie du Châtelet was one of many
women whose contributions have helped
shape the course of mathematics

Emilie du Chatelet

Index
•Aryabhatta
•Bhaskaracharya
•Shakuntala Devi
•Narayana Pandit

Aryabhatta
Aryabhatta came to this world on the 476
A.D at Patliputra in Magadha which is
known as the modern Patna in Bihar. Some
people were saying that he was born in the
South of India mostly Kerala. But it cannot
be disproved that he was not born in
Patlipura and then travelled to Magadha
where he was educated and established a
coaching centre. his first name is “Arya”
which is a south indian name and “Bhatt” or
“Bhatta” a normal north indian name which
could be seen among the trader people in
India.

Aryabhatta was aware that the earth rotates on its axis. The earth rotates round
the sun and the moon moves round the earth. He discovered the 9 planets position
and related them to their rotation round the sun. Aryabhatta said the light received
from planets and the moon is gotten from sun. He also made mention on the eclipse
of the sun, moon, day and night, earth contours and the 365 days of the year as the
exact length of the year. Aryabhatta also revealed that the earth circumference is
24835 miles when compared to the modern day calculation which is 24900 miles.
Aryabhatta have unusually great intelligence and well skilled in the sense that all
his theories has became wonders to some mathematicians of the present age. The
Greeks and the Arabs developed some of his works to suit their present demands.
Aryabhatta was the first inventor of the earth sphericity and also discovered that
earth rotates round the sun. He was the one that created the formula (a + b)2 = a2
+ b2 + 2ab

Bhaskaracharya
• Bhaskaracharya otherwise known as Bhaskara is probably the most
well known mathematician of ancient Indian today. Bhaskara was
born in 1114 A.D. according to a statement he recorded in one of his
own works. He was from Bijjada Bida near the Sahyadri mountains.
Bijjada Bida is thought to be present day Bijapur in Mysore state.
Bhaskara wrote his famous Siddhanta Siroman in the year 1150 A.D.
It is divided into four parts; Lilavati (arithmetic), Bijaganita
(algebra), Goladhyaya (celestial globe), and Grahaganita (mathematics
of the planets). Much of Bhaskara's work in the Lilavati and
Bijaganita was derived from earlier mathematicians; hence it is not
surprising that Bhaskara is best in dealing with indeterminate analysis.
In connection with the Pell equation, x^2=1+61y^2, nearly solved by
Brahmagupta, Bhaskara gave a method (Chakravala process) for
solving the equation.
• O girl! 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 playing
with amorous fight, in the water. What is the total number of swans?
• Teaching and learning mathematics was in Bhaskara's blood. He learnt
mathematics from his father, a mathematician, and he himself passed
his knowledge to his son Loksamudra. To return to the timeline click
here: timeline.

• Bhaskaracharya was the head of the observatory at
Ujjain. There are two famous works of his on
Mathematical Astronomy - Siddhanta-Siromani and
Karana-Kutuhala. Besides his work on
Algebra, Lilavati Bija Ganita too is famous. The law
of Gravitation, in clear tems, had been propounded by
Bhaskaracharya 500 years before it was rediscovered
by Newton. Centuries before him there had been
another mathematician Bhaskaracharya also in
Bharat ( India ).
• The subjects of his six works include
arithmetic, algebra, trigonometry, calculus, geometry, a
stronomy. There is a seventh book attributed to him
which is thought to be a forgery. Bhaskaracharya
discovered the concept of differentials, and
contributed a greater understanding of number systems
and advanced methods of equation solving. He was
able to accurately calculate the sidreal year, or the time
it takes for the earth to orbit the sun. There is but a
scant difference in his figure of 365.2588 days and the
modern figure of 365.2596 days.

Shakuntala Devi
• Shakuntala Devi is a calculating prodigy who was born on
November 4, 1939 in Bangalore, India. Her father worked in a
"Brahmin circus" as a trapeze and tightrope performer, and
later as a lion tamer and a human cannonball. Her calculating
gifts first demonstrated themselves while she was doing card
tricks with her father when she was three. They report she
"beat" them by memorization of cards rather than by sleight of
hand. By age six she demonstrated her calculation and
memorization abilities at the University of Mysore. At the age of
eight she had success at Annamalai University by doing the same.
Unlike many other calculating prodigies, for example Truman
Henry Safford, her abilities did not wane in adulthood. In 1977
she extracted the 23rd root of a 201-digit number mentally. On
June 18, 1980 she demonstrated the multiplication of two 13-
digit numbers 7,686,369,774,870 x 2,465,099,745,779 picked at
random by the Computer Department of Imperial
College, London. She answered the question in 28 seconds.
However, this time is more likely the time for dictating the
answer (a 26-digit number) than the time for the mental
calculation (the time of 28 seconds was quoted on her own
website). Her correct answer was
18,947,668,177,995,426,462,773,730.

• This event is mentioned on page 26 of the 1995
Guinness Book of Records ISBN 0-553-56942-2.
In 1977, she published the first study of
homosexuality in India.According to Subhash
Chandra's review of Ana Garcia-Arroyo's book
The Construction of Queer Culture in India:
Pioneers and Landmarks,For Garcia-Arroyo the
beginning of the debate on homosexuality in the
twentieth century is made with Shakuntala
Devi's book The World of Homosexuals
published in 1977. [...] Shakuntala Devi's (the
famous mathematician) book appeared. This book
went almost unnoticed, and did not contribute to
queer discourse or movement. [...] The reason for
this book not making its mark was
becauseShakuntala Devi was famous for her
mathematical wizardry and nothing of
substantial import in the field of homosexuality
was expected from her.

Narayana Pandit
• Narayana was the son of Nrsimha (sometimes written
Narasimha). We know that he wrote his most famous
work Ganita Kaumudi on arithmetic in 1356 but little else is
known of him. His mathematical writings show that he was
strongly influenced by Bhaskara II and he wrote a
commentary on the Lilavati of Bhaskara
IIcalled Karmapradipika. Some historians dispute that
Narayana is the author of this commentary which they
attribute to Madhava.
• In the Ganita Kaumudi Narayana considers the
mathematical operation on numbers. Like many other Indian
writers of arithmetics before him he considered an algorithm
for multiplying numbers and he then looked at the special
case of squaring numbers. One of the unusual features of
Narayana's work Karmapradipika is that he gave seven
methods of squaring numbers which are not found in the

• Narayana also gave a rule to calculate
approximate values of a square root. He did
this by using an indeterminate equation of the
second order, Nx2 + 1 = y2, whereN is the
number whose square root is to be calculated.
If x and y are a pair of roots of this equation
with x < y then √N is approximately equal
to y/x. To illustrate this method Narayana
takes N = 10. He then finds the solutions x =
6, y = 19 which give the approximation 19/6
= 3.1666666666666666667, which is correct
to 2 decimal places. Narayana then gives the
solutions x = 228, y = 721 which give the
approximation 721/228 =
3.1622807017543859649, correct to four
places. Finally Narayana gives the pair of
solutions x = 8658, y = 227379 which give
the approximation 227379/8658 =
3.1622776622776622777, correct to eight
decimal places. Note for comparison that √10
is, correct to 20
places, 3.1622776601683793320

Young Srinivasa
• Born in 1887

• Grew up in South India

• Recited formulas for fun

• Had no formal education or training

• Received a scholarship to Kumbakonam Town High
School

After his college
attempts…
• Married Srimathi Janaki
• For awhile, they were
supported by a wealthy man
named Ramanchandra Rao
• Srinivasa sent some of his
work to two famous English
mathematicans

Godfrey Hardy: Cambridge
University
• Saw srinivasa’s work and was
impressed by how he did the problems
• Offered him a scholarship at Trinity
College
• At first he had to refuse but later
accepted the offer
• When he returned to India, his
condition worsened
• He died in 1920

His Work
• His work helps
Physicists
• He was able to
approximate Pi

RAMANUJAN’S
MAGIC SQUARE
22 12 18 87 Do you know
88 17 9 25
THE BIRTH
DATE OF
10 24 89 16
Srinivasa
19 86 23 11 Ramanujan?

RAMANUJAN’S MAGIC
SQUARE

It is 22nd Dec
22 12 18 87 1887.

88 17 9 25
Yes. It is
10 24 89 16 22.12.1887
19 86 23 11
BE A PROUD INDIAN

Mathematics(History,Formula etc.) and brief description on S.Ramanujan.

Mathematics(History,Formula etc.) and brief description on S.Ramanujan.

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