MATHEMATICS IN

INDIA(ANCIENT, MEDIEVEL AND

MODERN PERIODS) AND ITS applications

“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

MATHEMATICS IN INDIA 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. His works were mainly based on geometry and include enunciation of today’s Pythagoras theorem and obtaining square root of 2 correctly upto 5 decimals.

MATHEMATICS DURING

ANCIENT INDIA

EARLIEST KNOWN MATHEMATICS 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.

VEDIC PERIOD- SAMHITAS AND BRAHMANS 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.

VEDIC PERIOD- SULBA SUTRAS 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.

MATHEMATICIANS DURING ANCIENT OR CLASSICAL PERIOD .

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

BUDHAYANA(800 BCE)

BUDHAYANA(800 BCE) 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

PINGALA(300-200BCE)

PINGALA(300-200BCE) 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:

PANINI(4TH CENTURY BC)

PANINI(4TH CENTURY BC)

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.

ARYABHATTA(476-550 CE)

ARYABHATTA(476-550 CE)

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(1114-1185)

BHASKARA(1114-1185) 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)

VARAHAMIHIRA(505-587 CE)

VARAHAMIHIRA(505-587 CE)  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.

mahavira

SHRIDHAR ACHARYA(870- 930)

SHRIDHAR ACHARYA(870- 930)

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 SRIDHARYA’S FORMULA

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.

MATHEMATICS DURING MEDIEVAL INDIA AND

ITS CONTEMPORA

RY WORLD

A STORY OF COMPLETE FABRICATION(2)

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 Education A Glimpse of the History of Mathematics (6)

‘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.

Mathematics Education A Glimpse of the History of Mathematics (7)

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.

The Ancient World (2)

Mathematics Education A Glimpse of the History of Mathematics (8)

Chinese Mathematics

The Ancient World (3)

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.

Mathematics Education A Glimpse of the History of Mathematics (9)

Egyptian Mathematics

The Ancient World (4)

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 .

Mathematics Education A Glimpse of the History of Mathematics (10)

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

The Ancient World (5)

Mathematics Education A Glimpse of the History of Mathematics (11)

Hindu Mathematics

(?)

A NEW WAVE OF FABRICATION

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 Education A Glimpse of the History of Mathematics (12)

‘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.

Mathematics Education A Glimpse of the History of Mathematics (13)

Mathematics Education A Glimpse of the History of Mathematics (20)

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

Mathematics Education A Glimpse of the History of Mathematics (23)

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.

Mathematics Education A Glimpse of the History of Mathematics (24)

18th – 19th Centuries (4)

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.

Mathematics Education A Glimpse of the History of Mathematics (25)

18th – 19th Centuries (5)

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.

Mathematics Education A Glimpse of the History of Mathematics (26)

18th – 19th Centuries (6)

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.

Mathematics Education A Glimpse of the History of Mathematics (27)

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) .

Mathematics Education A Glimpse of the History of Mathematics (28)

Some Numerals of the World (2)

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

Roman Numerals:

Brahmi Numerals:

Mathematics Education A Glimpse of the History of Mathematics (29)

Some Numerals of the World (3)

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

Mathematics Education A Glimpse of the History of Mathematics (30)

Some Numerals of the World (4)

Modern Hindu- Arabic

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

Mathematics Education A Glimpse of the History of Mathematics (31)

Some Numerals of the World (5)! @ # $ % ^ &

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Mathematics Education A Glimpse of the History of Mathematics (32)

Some Numerals of the World (6)

Ancient Chinese Lichchavian

Mathematics Education A Glimpse of the History of Mathematics (33)

Some Numerals of the World (7)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 Samvat107 207

100 200

7 7 4 4

Mathematics Education A Glimpse of the History of Mathematics (34)

Some Numerals of the World (8)Some Conflicting Interpretations of Inscribed Numerals of

Ancient Nepal

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Mathematics In the

Modern World

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

MODERN DAY 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 EFFECT OF MODERN MATHEMATICIANS

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 Chandra

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 9167486769200391580986609275853801624831066801443086224071265164279346570408670965932792057674808067900227830163549248523803357453169351119035965775473400756818688305620821016129132845564895780158806771.

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.

SOME FAMOUS MATHEMATICIANS OF MODERN TIME

LEONHARD EULER

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..

LEONHARD PAUL EULER (1707-1783)

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

ACHIEVEMENTS AND DISCOVERIES

SIR ISAAC NEWTON

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.

ISAAC NEWTON (1642-1727)

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.

ACHIEVEMENTS AND DISCOVERIES

CARL GAUSS

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.

CARL GAUSS (1777 - 1855)

 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.

ACHIEVEMENTS AND DISCOVERIES

JOHN VON NEUMANN

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. 

JOHN VON NEUMANN (1903-1957)

 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.

ACHIEVEMENTS AND DISCOVERIES

ALAN TURING 

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 (1912 - 1954)

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.

ACHIEVEMENTS AND DISCOVERIES

BENOIT MANDELBROT

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 (1924-2010)

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.

ACHIEVEMENTS AND DISCOVERIES

APPLICATIONS OF MATHEMATICAL CONCEPTS

•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

MATHEMATICS AND MATHEMATICIANS HAVE REALLY MADE OUR LIFE POSSIBLE TODAY. HERE ARE SOME EXAMPLES IN WHICH COMMON CONCEPTS OF MATHEMATICS ARE USED IN OUR DAILY LIFE.

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.

MATHS EXIST IN EVERY SECONF OF OUR LIFE. SO WE SHOULD RESPECT MATHS AND MATHEMATICIANS WHO MAKE OUR LIFE MUCH MORE EASIER THAN BEFORE AND ALSO SAVES LIFES OF OUR DEAR ONES. WE ARE SURE MATHS WILL PROGRESS EVEN AT MUCH GREATER RATES AND WILL TAKE US TO NEW HEIGHTS IN THIS UNIVERSE.

Linear algebra, graph theory, SVD

Google:

Error correcting codes: Galois theory

Internet: Network theory

Security: Fermat, RSA

Mathematicians really have made the modern world possibleMathematicians really have made the modern world possible

Medical imaging: Radon Transform

Communications: FFT, Shannon

Medical Statistics: Nightingale

MATHS IN NATURE

HEXAGON IN NATUREA 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.

UNDERSTANDING PERCENTAGE

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.

DECIMAL CALCULATOR

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).

SYMMETRY IN TOWER

MATHS HELPING OUR LIVES

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.

MATHS IN ENGINEERING 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.

GEOMETRY IN CIVILThis 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.

PARALLELOGRAMS

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.

CUBES AND CONESThis 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.

SPHERE AND CUBE

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.

PYRAMIDSThis 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.

RECTANGLES AND CIRCLES

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 IN CAD 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

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.

MATHS IN MEDICINEMedical 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).

MATHS IN BIOLOGY 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

MATHS IN MUSIC 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.

ROTATIONAL SYMMETRY IN GLOBE

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 IN FORENSIC

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“……… Henri Poincaré

EFFORTS BY:-STUDENTS OF X-D,DAV INTERNATIONAL SCHOOL, AMRITSARBATCH-2013

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