Maths ppt by x d

“You know how many
sciences had origin in
India. Mathematics began
there. You are even
counting 1,2,3,etc to zero
after Sanskrit figures and
you all know that algebra
also originated in India.”
-Vivekananda

India had a glorious past in every walks of
knowledge.
However, the Indian contribution to the field of
mathematics are not so well known.
Mathematics took its birth in India before 200
BC,ie the Shulba period.
The sulba sutras were developed during Indus
valley civilization.
There were seven famous Sulbakars
(mathematicians of indus valley civilization)
among which Baudhyana was the most famous.

 The earliest known mathematics in india
dates back from 3000to 2600 bc in the Indus
Civilization of North India and Pakistan.
 Mathematicians in this era used decimal
system,ratios, angles, pie(π) and used a base
8 numeral system.
 Made early contributions to the study of zero
as a number, negative numbers, arithmetic,
algebra in addition to trigonometry.
 The works were composed in sanskrit
language
 Most of methamatical concepts were
transmitted to Middle East, China and
Europe.

 Samhitas stands for „compilation of
knowledge‟ or collection of „mantras or
hymns‟
 The religious texts of vedic period provide
evidence of use of large numbers
 By the time of yajurvedasamhita, numbers as
high as 10¹² were included in the texts.
 The Shatpatha Brahamana (ca. 7th century
BC) contains rules for ritual geometric
constructions.

 Sulba Sutras literally means „aphorism of the
chords;.
 Most mathematical problems considered in
the Sulba Sutras spring from a „single
theorogical requirement‟, that of
constructing fire altars(or shape) which have
different shapes but occupy same area.
 Budhayana composed budhayana sulba sutra,
best known sulba sutras.

 BUDHAYANA( 800 BC)
 YAJNAVALKYA
 MANAVA
 PANINI(4TH CENTURY BC)
 ARYABHATTA (476-550 CE)
 VARAHAMIHIRA(505-587)
 SHRIDHARA
 BHASKARA
 LILAVATI

 Author of the earliest Sulba Sutra that contains
important mathematical results like value of pi and
stating a version of what is now called puthagorean
theorem.
 He found answers to the questions like „circling the
square‟
 He also discovered value of √2 which is as follows:-
√2≈1+1/3+1/3 . 4 - 1/3 . 4. 34=577/408≈1.414216

 He is well known for chandahsutra, the
earliest known sanskrit treatise on prosody
 As little is known about him, he variously
known either as the younger brother of
panini(4th century bc) or as patanjali, the
author of mahabhashya( 2nd century bc)
 His work contains basic ideas of Fibonacci
numbers.
 Pingala was also aware of combinatorial
identity:

 He was sanskrit grammarian born in Gandhara,in
the modern day of Khyber Pakhtunkhwa, Pakistan.
 He is pecularly known for his 3,959 rules of Sanskrit
Morphology, syntax and semantics in grammar
known as ashtadhyayi
 He is was the first to come up with the idea of
using letters of the alphabets to represent
numbers.

 One of the most remarkable and celebrated
Ancient Indian Mathematician.
 Made avaluable contribution through his
“Aryabhatiya”.
 His contributions are:-
Approximation of pi which is an irrational
number
Place value system
Invention of Zero
Area of triangle
Trigonometry

 Bhaskara's arithmetic text Leelavati covers the
topics of definitions, arithmetical terms, interest
computation, arithmetical and geometrical
progressions, plane geometry, solid geometry,
the shadow of the gnomon, methods to
solve indeterminate equations,
and combinations.
 He was the first person to find derivatives and
calculus.
 He was the discoverer of spherical trigonometry.
 His book Bijaganita was the to recognize two
square roots for a positive number(positive and
negative square roots)

 He is considered to be one of the nine jewels (Navaratnas) of
the court of legendary ruler Yashodharman Vikramaditya of
Malwa.
 Pancha-Sidhhantika, Brihat-Samhita, Brihat Jataka are his
notable works
 He was the first to mention in his works that ayanamsa or
shifting of the equinox is 50.3 seconds.
 Varahamihira's mathematical work included the discovery of
the trigonometric formulas
 Varahamihira improved the accuracy of the sine tables of
Aryabhata I.
 He was among the first mathematicians to discover a version
of what is now known as the Pascal's triangle. He used it to
calculate the binomial coefficients.

He was a jain Mathematician
His celebrated work was Ganithasarangraha.
He showed ability in quadratic equations,
indeterminate equations.

 He was an Indian mathematician, Sanskrit pundit
and philosopher.
 He was known for two treatises: Trisatika (sometimes
called the Patiganitasara) and the Patiganita.
 The book discusses counting of numbers, measures,
natural number, multiplication, division, zero, squares,
cubes, fraction, rule of three, interest-calculation,
joint business or partnership and mensuration.
 He was one of the first to give a formula for
solving quadratic equations.

 Proof of the Sridhar Acharya Formula,
 let us consider,
 Multipling both sides by 4a,
 Substracting 4ac from both sides,
 Then adding b² to both sides,
 We know that,
 Using it in the equation,
 Taking square roots,
 Hence, dividing by get
 In this way, he found the proof of 2 roots.

A Glimpse of the History of Mathematics (5)
Mathematics Education
‘Mathematics
is
a European invention’
Even simple arithmetical operations were not known
or could not be performed in the European number
system before the introduction of the Hindu-Arabic
decimal system some 1000 years ago.
How ridiculous is their claim of making very
complicated computations during those days when
they had only the primitive type of number symbols or
numerals only ? (Refer to the Greek, Roman and other
numerals of the 1st century A.D.)

Eurocentric chronology of mathematics history.
Modified Eurocentric chronology of mathematics history.
‘Mathematics
is
a European invention’

The Ancient World (1)
Babylonian Mathematics
The Babylonian civilization replaced that of the
Sumerians from around 2000 BC. So, Babylonian
Mathematics, inherited from the Sumerians, cannot be
older than that of Sumerian mathematics. Counting in
Sumerian civilization was based on a sexagesimal
system, that is to say base 60. It was a positional
system one of the greatest achievement in the
development of the number system Babylonians used
only two symbols to produce their base 60 positional
system.

Number names, number symbols, arithmetical
computations, traditional decimal notation go back
to the origin of Chinese writing.
The number system which was used to express this
numerical information was based on the decimal
system and was both additive and multiplicative in
nature.
Chinese Mathematics

About 3000 BC the Egyptians developed their
hieroglyphic writing (picture writing) to write
numerals This was a base 10 system without
a zero symbol. It was not a place value
system. The numerals are formed by putting
together the basic symbols .
The Egyptian number systems were not well
suited for arithmetical calculations.
Egyptian Mathematics

In the first millennium BC, the Greeks had no single
national standard numerals.
The first Greek number system is an acrophonic system.
The word 'Acrophonic' means that the symbols for the
numerals come from the first letter of the number name.
The system was based on the additive principle.
A second ancient Greek number system is the
alphabetical system. It is sometimes called the
'learned' system. As the name 'alphabetical'
suggests, the numerals are based on giving values
to the letters of the alphabet .
Greek Mathematics

The evidence of the first use of mathematics in
the Indian subcontinent was found in the Indus
valley and dates back to at least 3000 BC.
Excavations at Mohenjodaro and Harrapa, and
the surrounding area of the Indus River, have
uncovered much evidence of the use of basic
mathematics. The maths used by this early
Harrapan civilization was very much for
practical means, and was primarily concerned
with weights, measuring scales and a
surprisingly advanced 'brick technology',
(which utilized ratios). The ratio for brick
dimensions 4:2:1 is even today considered
optimal for effective bonding
Hindu Mathematics
(?)

 Not only the fundamental concepts of Ganit
(Mathematics) such as those of counting numbers,
zero and infinity but also various arithmetical and
algebraic operations are being claimed to have
been present in the Hindu Granth Vedah some
6000 years ago a time when there was nothing
like Hindusthan, Hindu, Hindi and the Devanagari
script verson of Vedah. This is a total lie. If there
is anything that is worth mentioning, they are the
ones found in the excavation of Mohenjadaro and
Harrapa which did not belong to what is known
today as India. (Refer to the Brahmi numerals of
the first century A.D.)
‘Mathematics
is
a Hindu creation’

Nepalese Mathematics (1)
The Ancient World
(6)
Record written in Bramhi and Nepal Bhasa (Bhujimol)
scripts and in the brick found while reconstructing
the Dhando Stupa at Chabahil (Kathmandu) 2003
testifies that counting numbers were used in Nepal
as early as 3rd century B.C.
The Lichhavian numerals used in the beginning of the
last millennium is both additive and multiplicative. It
was decimal in nature. There exists a complete
analogy between the Lichhavian number system and
the 14th Century B.C. Chinese system both in form
and technique of writing numbers using numerals.

Renaissance Mathematics(2)
Once the European community based their
study, research and application on the Hindu-
Arabic Number System, their contributions to
the theory and application of mathematics
grew tremendously during the latter part of
the seventeenth century.
During the same period, worldwide usage of
the Hindu-Arabic number system proved to be
a boon for both mathematics and the whole of
human society.
Progress towards the calculus continued with
Fermat, who, together with Pascal, began the
mathematical study of probability. However
the calculus was to be the topic of most
significance to evolve in the 17th Century

18th – 19th Centuries (3)

The 1800s—societal emphasis Mathematics teaching
mainly meant arithmetic and basic geometry--skills
needed for daily life. Specialized content might be learned
on the job or in special academies. There was little formal
teacher education until late in the century.
 Children in U.K. were once again enjoined to go to school,
but could leave the educational system once they could
read, write and had an elementary knowledge of
Arithmetic. It was now generally accepted that some level
of understanding of Mathematics was absolutely
necessary for modern life, and there were few schools
who did not give Mathematics a place in a student's
timetable of classes.

 By 1823, while Augustus De Morgan was at Cambridge,
the analytical methods and notation of differential
calculus made their way into the course
 The 19th Century saw rapid progress. Fourier's work on
heat was of fundamental importance. In geometry
Plücker produced fundamental work on analytic
geometry and Steiner in synthetic geometry.

 Progress towards the calculus continued with Fermat, who, together
with Pascal, began the mathematical study of probability. However the
calculus was to be the topic of most Non-euclidean geometry
developed by Lobachevsky and Bolyai led to characterisation of
geometry by Riemann. Gauss, thought by some to be the greatest
mathematician of all time, studied quadratic reciprocity and integer
congruences. His work in differential geometry was to revolutionise
the topic. He also contributed in a major way to astronomy and
magnetism.
 The 19th Century saw the work of Galois on equations and his insight
into the path that mathematics would follow in studying fundamental
operations. Galois' introduction of the group concept was to herald in
a new direction for mathematical research which has continued
through the 20th Century.
 Cauchy, building on the work of Lagrange on functions, began rigorous
analysis and began the study of the theory of functions of a complex
variable. This work would continue through Weierstrass and Riemann.

 Algebraic geometry was carried forward by Cayley
whose work on matrices and linear algebra
complemented that by Hamilton and Grassmann.
Cantor invent set theory almost single handedly while
his analysis of the concept of number added to the
major work of Dedekind and Weierstrass on irrational
numbers
 Lie's work on differential equations led to the study of
topological groups and differential topology. Maxwell
was to revolutionise the application of analysis to
mathematical physics. Statistical mechanics was
developed by Maxwell, Boltzmann and Gibbs. It led to
ergodic theory.
 The study of electrostatics and potential theory. By
Fredholm led to Hilbert and the development of
functional analysis.

Some Numerals of the World (1)
The number system employed throughout the greater
part of the world today was probably developed in India,
but because it was the Arabs who transmitted this
system to the West the numerals it uses have come to be
called Arabic ( Hindu-Arabic) .

I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1000
Roman Numerals:
Brahmi Numerals:

Until 771, the Egyptian, Greek, and other
cultures used their own numerals in a
manner similar to that of the Romans.
Thus the number 323 was expressed like
this:
Egyptian : 999 nn III ,
Greek : HHH ÆÆ III ,
Roman : CCC XX III

 Modern Hindu- Arabic
 Early Hindu-Arabic
 Arabic Letters
 Early Arabic
 Modern Arabic
 Early Devanagari
 Later Devanagari

! @ # $ % ^ & * (
1 2 3 4 5 6 7 8 9
SomeNumeralsused
inIndia
SomeNumeralsused
inNepal

Ancient Chinese Lichchavian

An Inscribed Statue of the Year 207 From Maligaon, Kathmandu
Translation of Castro
and Garbini
'Of the great king
Jayavarma, on the fourth
day of the seventh (?)
fortnight of summer, in the
year 207'.
According to Rajbanshi
the year is 107
Rajbanshi Castro/Gabini
Samvat Samvat
107 207
100 200
7 7
4 4

Some Conflicting Interpretations of Inscribed Numerals of
Ancient Nepal
FabricationofNepal’sHistory

In 18th century mathematics is already
a modern science
Mathematics begins to develop very
fast because of introducing it to
schools
Therefore everyone have a chance to
learn the basic learnings of
mathematics

Thanks to that, large number of new
mathematicians appear on stage
There are many new ideas, solutions to
old mathematical problems,researches
which lead to creating new fields of
mathematics.
Old fields of mathematics are also
expanding.

THE MODERN ERA OF MATHEMATICS IN
INDIA
During his short lifetime,
Ramanujan independently
compiled nearly 3900
results (mostly identities
and equations), and his
work continues to inspire
a vast amount of further
research till date.
Ramanujan

Harish
Harish Chandra formulated a
fundamental theory of representations
of Lie groups and Lie algebras. He even
extended the concept of a
characteristic representation of finite -
dimensional of semi simple Lie groups
to infinite-dimensional representations
of a case and formulated a Weyl’s
character formula analogue. Some of
his other contributions are the specific
determination of the Plancherel
measure for semisimple groups, the
evaluation of the representations of
dicrete series, based on the results of
Eisenstein series and in the concept of
auto orphic forms, his “philosophy of
cusp forms” ,

Manjul
Bhargav
Well
Known for
his
contribution
to
NUMBER
THEORY

In Dallas she competed with a computer to see who give the cube root of 188138517
faster, she won. At university of USA she was asked to give the 23rd root of the
number
9167486769200391580986609275853801624831066801443086224071265164279346
5704086709659327920576748080679002278301635492485238033574531693511190
35965775473400756818688305620821016129132845564895780158806771.
She answered in 50 seconds. The answer is 546372891. It took a UNIVAC 1108
computer, full one minute (10 seconds more) to confirm that she was right after it was
fed with 13000 instructions.
Now she is known to be Human Computer .
SHAKUNTALA DEVI
• She was born in 1939
• In 1980, she gave the product of two, thirteen digit
numbers within 28 seconds, many countries have invited
her to demonstrate her extraordinary talent.

 He was a Swiss mathematician.
 Johann Bernoulli made the biggest
influence on Leonhard.
 1727 he went to St Petersburg where he
worked in the mathematics department
and became in 1731 the head of this
department.
 1741 went in Berlin and worked in Berlin
Academy for 25 years and after that he
returned in St Ptersburg where he spent
the rest of his life..

 Euler worked in almost all areas of mathematics:
geometry, calculus, trigonometry, algebra,applied
mathematics, graph theory and number theory, as well
as , lunar theory, optics and other areas of physics.
 Concept of a function as we use today was introduced
by him;he was the first mathematician to write f(x) to
denote function
 He also introduced the modern notation for the
trigonometric functions, the letter e for the base of the
natural logarithm (now also known as Euler‟s number),
the Greek letter Σ for summations and the letter i to
denote the imaginary unit

 There aren't many subjects that Newton
didn't have a huge impact in — he was one of
the inventors of calculus, built the first
reflecting telescope and helped establish the
field of classical mechanics with his seminal
work, "Philosophiæ Naturalis Principia
Mathematica."
 He was the first to decompose white light
into its component colors and gave us the
three laws of motion, now known as Newton's
laws.

 We would live in a very different world had Sir Isaac
Newton not been born.
 Other scientists would probably have worked out
most of his ideas eventually, but there is no telling
how long it would have taken and how far behind
we might have fallen from our current technological
trajectory.

 Isaac Newton is a hard act to follow, but if anyone
can pull it off, it's Carl Gauss.
 If Newton is considered the greatest scientist of all
time, Gauss could easily be called the greatest
mathematician ever.
 Carl Friedrich Gauss was born to a poor family in
Germany in 1777 and quickly showed himself to be
a brilliant mathematician.
 You can find his influence throughout algebra,
statistics, geometry, optics, astronomy and many
other subjects that underlie our modern world.

 He published "Arithmetical Investigations," a
foundational textbook that laid out the tenets of
number theory (the study of whole numbers).
 Without number theory, you could kiss computers
goodbye.
 Computers operate, on a the most basic level, using
just two digits — 1 and 0, and many of the
advancements that we've made in using computers
to solve problems are solved using number theory.

 John von Neumann was born in Budapest a few
years after the start of the 20th century, a well-
timed birth for all of us, for he went on to design
the architecture underlying nearly every single
computer built on the planet today.
 Von Neumann received his Ph.D in mathematics
at the age of 22 while also earning a degree in
chemical engineering to appease his father, who
was keen on his son having a good marketable
skill.
 In 1930, he went to work at Princeton University
with Albert Einstein at the Institute of Advanced
Study.

 Right now, whatever device or computer that you are
reading this on, be it phone or computer, is cycling
through a series of basic steps billions of times over
each second; steps that allow it to do things like
render Internet articles and play videos and music,
steps that were first thought up by John von
Neumann.
 Before his death in 1957, von Neumann made
important discoveries in set theory, geometry,
quantum mechanics, game theory, statistics,
computer science and was a vital member of the
Manhattan Project.

 Alan Turing a British mathematician who has
been call the father of computer science.
 During World War II, Turing bent his brain to the
problem of breaking Nazi crypto-code and was
the one to finally unravel messages protected by
the infamous Enigma machine.
 Alan Turing's career and life ended tragically
when he was arrested and prosecuted for being
gay.
 He was found guilty and sentenced to undergo
hormone treatment to reduce his libido, losing
his security clearance as well. On June, 8, 1954,
Alan Turing was found dead of apparent
suicide by his cleaning lady.


 Alan Turing was instrumental in the development of
the modern day computer.
 His design for a so-called "Turing machine" remains
central to how computers operate today.
 The "Turing test" is an exercise in artificial
intelligence that tests how well an AI program
operates; a program passes the
 Turing test if it can have a text chat conversation
with a human and fool that person into thinking
that it too is a person.

 Mandelbrot was born in Poland in 1924 and
had to flee to France with his family in 1936
to avoid Nazi persecution.
 After studying in Paris, he moved to the U.S.
where he found a home as an IBM Fellow.
 Working at IBM meant that he had access to
cutting-edge technology, which allowed him
to apply the number-crunching abilities of
electrical computer to his projects and
problems.
 Benoit Mandelbrot died of pancreatic cancer
in 2010.

 Benoit Mandelbrot landed on this list thanks to his
discovery of fractal geometry.
 Fractals, often-fantastical and complex shapes built
on simple, self-replicable formulas, are fundamental
to computer graphics and animation.
 Without fractals, it's safe to say that we would be
decades behind where we are now in the field of
computer-generated images.
 Fractal formulas are also used to design cellphone
antennas and computer chips, which takes
advantage of the fractal's natural ability to minimize
wasted space.

•The modern world would not exist without
maths
•With maths you can tell the future and save
lives
•Maths lies at the heart of art and music
•Maths is a subject full of mystery, surprise
and magic

In Mohenjodaro a system of
calculation akin to the decimal
system was in use.
Trigonometry deals with
triangles, particularly with
right triangles in which
one angle is 90 degrees,
and with periodic
functions.

Linear algebra, graph theory, SVDGoogle:
Error correcting codes: Galois theory
Internet: Network theory
Security: Fermat, RSA
Mathematicians really have made the modern world possible
Medical imaging: Radon Transform
Communications: FFT, Shannon
Medical Statistics: Nightingale

A honeycomb is an array of hexagonal (six-
sided) cells, made of wax produced by
worker bees. Hexagons fit together to fill all
the available space, giving a strong structure
with no gaps. Squares would also fill the
space, but would not give a rigid structure.
Triangles would fill the space and be rigid,
but it would be difficult to get honey out of
their corners.

 Using money is a good way of understanding
percentages. As there are 100 pence in £1,
one hundredth of £1 is therefore 1 pence,
meaning that 1 per cent of £1 is 1 pence. From
this we can calculate that 50 per cent of £1 is
50 pence. This photograph shows three British
currency notes: a £5 note, a £10 note and a
£20 note. If 50 pence is 50 per cent of £1,
then £5 is 50 per cent of £10, and so £10 is 50
per cent of £20.

 A pocket calculator is one way in which
decimals are used in everyday life. The
value of each digit shown is determined by
its place in the entire row of numbers on
the screen. In this photograph, the 7 is
worth 700 (seven hundreds), the 8 is worth
80 (eight tens) and the 6 is worth 6 (six
ones).

 An article in the Sunday Times in June
2004 revealed the fact that you can't even
assume that buying larger bags of exactly
the same pasta would work out cheaper.
It said that in many of the supermarkets
buying in bulk, for example picking up a
six-pack of beer rather than six single
cans, was in fact more expensive.
 The newspaper found that the difference
can be as much as 30%. The supermarket
chains may be exploiting the assumption
people have that buying in bulk is
cheaper, but if you work it out quickly in
your head you'll never be caught out.

 If it is rainy and cold outside, you
will be happy to stay at home a
while longer and have a nice hot
cup of tea. But someone has built
the house you are in, made sure it
keeps the cold out and the warmth
in, and provided you with running
water for the tea. This someone is
most likely an engineer. Engineers
are responsible for just about
everything we take for granted in
the world around us, from tall
buildings, tunnels and football
stadiums, to access to clean
drinking water. They also design
and build vehicles, aircraft, boats
and ships. What's more, engineers
help to develop things which are
important for the future, such as
generating energy from the sun,
wind or waves. Maths is involved in
everything an engineer does,
whether it is working out how much
concrete is needed to build a
bridge, or determining the amount
of solar energy necessary to power
a car.

This a pictures with some
basic geometric
structures. This is a
modern reconstruction of
the English Wigwam. As
you can there the door
way is a rectangle, and
the wooden panels on the
side of the house are
made up of planes and
lines. Except for really
planes can go on forever.
The panels are also
shaped in the shape of
squares. The house itself
is half a cylinder.

This is a modern day
skyscraper at MIT.
The openings and
windows are all made
up of parallelograms.
Much of them are
rectangles and
squares. This is a
parallelogram kind of
building.

This is the Hancock Tower,
in Chicago. With this
image, we can show you
more 3D shapes. As you
can see the tower is
formed by a large cube.
The windows are
parallelogram. The
other structure is made
up of a cone. There is a
point at the top where
all the sides meet, and
There is a base for it
also which makes it a
cone.

This is another building at
MIT. this building is made
up of cubes, squares and a
sphere. The cube is the
main building and the
squares are the windows.
The doorways are
rectangle, like always. On
this building There is a
structure on the room
that is made up of a
sphere.

This is the Pyramids, in
Indianapolis. The
pyramids are made up
of pyramids, of course,
and squares. There are
also many 3D geometric
shapes in these
pyramids. The building
itself is made up of a
pyramid, the windows a
made up of tinted
squares, and the
borders of the outside
walls and windows are
made up of 3D
geometric shapes.

This is a Chevrolet SSR Roadster
Pickup. This car is built with
geometry. The wheels and lights
are circles, the doors are
rectangular prisms, the main
area for a person to drive and
sit in it a half a sphere with the
sides chopped off which makes
it 1/4 of a sphere. If a person
would look very closely the
person would see a lot more
shapes in the car. Too many to
list.

 Geometry is a part of
mathematics concerned with
questions of size, shape, and
relative position of figures
and with properties of space.
Geometry is one of the oldest
sciences
Computer-aided design,
computer-aided geometric
design. Representing shapes
in computers, and using these
descriptions to create
images, to instruct people or
machines to build the shapes,
etc. (e.g. the hood of a car,
the overlay of parts in a
building construction, even
parts of computer
animation).

Computer graphics is
based on geometry -
how images are
transformed when
viewed in various ways.
Robotics. Robotic vision,
planning how to grasp a
shape with a robot arm,
or how to move a large
shape without
collission.

Structural engineering.
What shapes are rigid
or flexible, how they
respond to forces and
stresses. Statics
(resolution of forces)
is essentially
geometry. This goes
over into all levels of
design, form, and
function of many
things.

Medical imaging - how to
reconstruct the shape of a tumor
from CAT scans, and other medical
measurements. Lots of new
geometry and other math was
(and still is being) developed for
this.
Protein modeling. Much of the
function of a protein is
determined by its shape and how
the pieces move. Mad Cow Disease
is caused by the introduction of a
'shape' into the brain (a shape
carried by a protein). Many drugs
are designed to change the shape
or motions of a protein -
something that we are just now
working to model, even
approximately, in computers,
using geometry and related areas
(combinatorics, topology).

 Physics, chemistry, biology,
 Symmetry is a central concept
of many studies in science - and
also the central concept of
modern studies of geometry.
Students struggle in university
science if they are not able to
detect symmetries of an object
(molecule in stereo chemistry,
systems of laws in physics, ... ).
the study of transformations and
related symmetries has been,
since 1870s the defining
characteristic of geometric
studies

 Music theorists often use mathematics to
understand musical structure and
communicate new ways of hearing music.
This has led to musical applications of set
theory, abstract algebra, and number
theory. Music scholars have also used
mathematics to understand musical
scales, and some composers have
incorporated the Golden ratio and
Fibonacci numbers into their work.

A globe is a good example of rotational
symmetry in a three-dimensional object. The
globe keeps its shape as it is turned on its
stand around an imaginary line between the
north and south poles. The globe shown here
dates from the late 15th or early 16th
century and is one of the earliest three-
dimensional representations of the surface of
the Earth. It can be found in the Historical
Academy in Madrid.

 MATHS IS APLLIED TO CLARIFY THE BLURRED
IMAGE TO CLEAR IMAGE.
 THIS IS DONE BY USING DIFFERENTIAL AND
INTEGRAL CALCULUS.

THE FUTURE OF MATHEMATICS
TATA INSTITUTE OF
FUNDAMENTAL
REASRCH
INDIAN INSTITUTE OF
TECHNOLOGY
"The true method of forecasting the future of mathematics
lies in the study of its history and its present state“………

 Gaurav Sroa
 Viresh Singh
 Lohitash Punj
 Tanish Aggarwal
 Abhinav Mahajan
 Himanshu Kumar
 Harshil Mahajan

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