month: april issue no:2017(20) maadhyamgiftededucation.co.in/assets/files/students/20. april...

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MONTH: APRIL ISSUE NO:2017(20)

GREAT MATHEMATICIANS

Bhudhayan (Around 800 BC)

Nationality: India Famous For: Budhayana Sulbasutr is noted for containing several early Mathematical results including an approximation of the square root of 2 and the statement of a version of later known as Pythagoras theorem.

Euclid (365 – 275 BC)Nationality: GreekFamous For: Known as “father of geometry”. The earliest known maths book, titled ‘Elements’ was written by Euclid. It serves as a textbook to teach geometry and mathematics. His mathematical system is known as “Euclidean geometry.”

Thales (624 – 546 BC)Nationality: GreekFamous For: “father of science” & Thales’ theorem. Thales used principles of mathematics, specifically geometry, to solve everyday problems. He is considered as the “first true mathematician”.

Pythagoras (570 – 495 BC)Nationality: GreekFamous For: Pythagorean theorem.

Pythagoras is best known in mathematics for the Pythagorean Theorem.

Aryabhata (476 – 550 AD)Nationality: IndianFamous For: Writing Āryabhaṭīya and the Arya-siddhanta.Contribution include his work on providing an approximate value to pi. He likewise touched on the concepts of sine, cosine, and the place-value system.

Omar Khayyam (1048 – 1131 AD)Nationality: PersianFamous For: Most algebraic principles have been drawn from his books, Treatise on Demonstration of Problems of Algebra . In the area of geometry, Khayyam worked on the “theory of proportions.”

Rene Descartes (1596 – 1650 AD)Nationality: FrenchFamous For: Cartesian coordinate system. The “Cartesian coordinate system” in mathematics is named after Rene Descartes. He is seen as the father of analytical geometry in addition to explaining “infinitesimal calculus and analysis.”

John Napier (1550-1617) Nationality: BritainFamous For: Invention of Natural Logarithms, Popularized the use of the Decimal Point and Napier's Bones tool for Lattice Multiplication.

Srinivasa Ramanujan (1887-1920)Nationality: IndiaFamous For: Landau - Ramanujan constant. He helped in expanding mathematical theory, particularly in continued fractions, infinite series, mathematical analysis, and number theory. He conducted mathematical research in isolation.


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The word “Mathematics” comes from the Greek word ‘Mathemata’, meaning ‘things that arelearned’.

The origins of mathematics are lost in antiquity but we know that it was used 4,000years ago by ancient people, such as the Babylonians and Egyptians, to work out thecalendar, so that they could know in advance when to sow their crops, or when the riverNile was going to flood, or to solve quadratic equations. They even knew about thetheorem now wrongly attributed to Pythagoras.

Numbers are almost as old as the human civilization itself. The ancient civilizations inIndia, China, and elsewhere had developed their own systems of denoting numbers. TheIndians and Egyptians used the base 10 to count numbers. e.g:– they used numbers 1 to10 and then used groups of 10 to count larger numbers. The Mayans in South Americaused the base 20, while the ancient Syrians used base 2 to count numbers.Historically, irrational numbers like √2, √3 were known to the ancient mathematicianswell before the negative numbers.

Origin of Numbers


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Saharan desert ants may have built in “pedometers” thatcount steps and allow the ants to measure exact distance.Ants with stilts glue to their legs travel too far and pass theirnest entrance, suggesting that sterile length is important fordistance determination.Ants, navigates in their habitat by path integration. Theycontinuously integrate directions as determined by theircelestial compass and distances traveled.

Ant Odometer

Ishango Bone (18,000 B.C.)

The Ishango baboon bone (found in Ishango, near the

headwaters of the Nile River), with its sequence of notches,

was first thought to be a simple tally stick used by a Stone

Age African. These bones suggest a simple understanding of

doubling or halving. The full mystery of Ishango bone can’t be

solved until other similar bones are discovered.

Dice (3000 B.C.)

Dice was originally made from the ankle bones of animals and

the oldest known dice was found in the southeastern Iran.

Dice was among the earliest means for producing random

numbers. And now a days it is used for finding probability also.

In ancient civilizations, people used dice to predict the future,

believing that the Gods influenced dice outcomes.

Magic Square (2200 B.C.)

Magic squares originated in China and were first mentioned ina manuscript from the time of Emperor Yu. A magic squareconsists of N2 boxes, called Cells, filled with integers that areall different. The sum of the numbers in the horizontal rows,vertical columns and diagonals are equal. Indian mathematicianShrinivas Ramanujan’s magic square is a well-known example.


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Plimpton 322 (It is named after a New York publisher George

Plimpton who, in 1922, bought the tablet for $10 from a

dealer and then donated it to a Columbian University) refers

to a mysterious Babylonian clay tablet featuring numbers in a

cuneiform script. The tables specify the Pythagorean triples-

i.e. whole numbers that specify the Pythagorean Theorem

Plimpton 322 (1800 B.C.)

Rhind Papyrus (1650 B.C.)

The rhind papyrus is the most important source of information

concerning ancient Egyptian mathematics. This scroll, about a

foot of 30 cm high and 18 feet (5.5 m) long was found in a

tomb in Thebes on the east bank of the river Nile. It includes

mathematical problems involving fractions, A.P., algebra,

geometry and accounting.

Pythagoras Triangle and Theorem (800 BC)

Pythagorean triangles were probably known even earlier as

“Babylonians”. Although Pythagoras is often credited with the

formulation of the Pythagorean Theorem in about 580 B.C. but

evidence suggest that theorem was developed by Indian

mathematician Baudhayan in about 800 B.C. in his book

Baudhayana Sulba Sutra. It states that the square of

hypotenuse length is equal to the sum of the square of other

two lengths in a right angle triangle.

What are Fibonacci Numbers ?

Fibonacci Numbers are an interesting idea. The numbers in the sequence can be made byadding the previous two numbers. The Fibonacci Numbers occurs in nature, in populationgrowth in rabbits and also the development of the spiral in a snail’s shell.

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Platonic Solids (350 B.C.)

Plato described the five Platonic solids in Timaeus in around 350 B.C. A Platonic solid

is a convex multifaceted 3-D object whose faces are all identical polygons, with sides

of equal length and angles of equal degrees. A Platonic solid also has the same number

of faces meeting at every vertex. The ancient Greeks recognized and proved that

only five Platonic solids can be constructed: the tetrahedron, cube, octahedron,

dodecahedron, and icosahedron.


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Euclid’s Elements (300 B.C.)

Element of Greek mathematician Euclid is a mathematical and

geometric treatise consisting of 13 books attributed to the

ancient Greek mathematicians Euclid in Alexandria. It is a

collection of definitions, postulates, propositions and

mathematical proofs of propositions. Books cover Euclidean

Geometry and the ancient Greek version of elementary

number theory.

Pi, symbolized by the Greek letter π, is the "ratio of a

circle's circumference to its diameter and is approximately

equal to 3.14159. Perhaps ancient peoples observed that for

every revolution of a cartwheel, a cart moves forward about

three times the diameter of the wheel-an early recognition

that the circumference is about three times the diameter.

An ancient Babylonian tablet states that the ratio of the

circumference of a circle to the perimeter of an inscribed

hexagon is 1 to 0.96, implying a value of pi of 3.125.

π (250 BC)

Greek mathematician Archimedes (c. 250 B.C.) was the first to give us amathematically rigorous range for -a value between 223/71 and 22/7. The Welshmathematician William Jones (1675-1749) introduced the symbol π in 1706, mostlikely after the Greek word for periphery, which start, with the letter “π”.

TetrahedronFour sided

HexahedronSix sided

IcosahedronTwenty sided

DodecahedronTwelve sided

OctahedronEight sided


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Discovery of Zero (650 AD)

Undoubtedly taken for granted today, the number (or lack thereof)known as “zero” was not always a part of the human mathematicalmindset. Since zero is more of a concept than an actual number, thedevelopment of ‘true zero’ took quite some time to enter into humanconsciousness.Zero was known to Indians well before others an ancient Indianastronomer named ARYABHATTA has discovered zero for hiscomplex astronomical calculation.The first recorded zero is attributed to the Babylonians in the 3rdcentury B.C. – A long period followed when no one else used a zeroplace holder. From India it moved to China and then to the Islamiccountries zero finally reached Western countries (Europe) in 12thcentury.

Thabit Amicable Number (850 AD)

Amicable numbers aretwo different numbers sorelated that the sum ofthe proper divisor ofeach of number is equalto the other number. Forexample:- (220,284)

Check these numbers are amicable or not ?(1184, 1210), (2620, 2924), (5020,5564), (6362,6368)

The proper divisor of220 is 1,2,4,5,10,11,20,22,44,55,110 andthe sum of thesenumbers is 284.The proper divisor of284 is 1, 2,4,71 & 144and the sum of thesenumbers is 220.

Golden Ratio (1509 AD)

In 1509, an Italian mathematician Luca Pacioli, publishedthe Divina proportione, a treatise on a number that isnow widely known as the Golden Ratio. We can easilyunderstand the proportion by dividing a line into 2segments so that the ratio of the whole segment to thelonger parts is the same as the ratio of the longer part(b) to the shorter part (a) or (a+b)/b = b/a = 1.61803…

Loxodrome (1537 AD)

The Loxodrome was invented by Portuguese

mathematician and geographer Pedro Nunes. For the

purpose of terrestrial navigation, the loxodromic spiral

goes through the north south meridians of the earth at a

constant angle. The loxodrome coil is like a gigantic snake

around the earth and spirals around the poles without

reaching them.

Logarithm (1614 AD)

Logarithms were invented independently by John Napier,

a Scotsman, and by Joost Burgi, a Swiss. Napier's

logarithms were published in 1614; Burgi's logarithms

were published in 1620. The objective of both men was

to simplify mathematical calculations. This approach

originally arose out of a desire to simplify multiplication

and division to the level of addition and subtraction.

Slide Rule (1621 AD)

William Oughtred and others developed the slide rule in the 1600s.The slide rule is a mechanical analog computer which is based on thework of logarithms. Before electronic calculators were developed,slide rule was the tool used most often in science and engineeringfor multiplication and division, and also for "scientific" functionssuch as roots, logarithms and trigonometry, but does not generallyperform addition or subtraction.

Fermat’s Last theorem (1637 AD)

Fermat’s last theorem was actually a conjecture and remained

unproved for over 300 years. It was finally proven in 1994

by Andrew Wiles. It was always called a “theorem”, due to Fermat’s

uncanny ability to propose true conjectures. Originally the

statement was discovered by Fermat’s son Clement-Samuel among

margin notes that Fermat had made in his copy of

Diophantus’ Arithmetica. an + bn =cn has no non-zero

solutions for n>2, (a,b,c,n∈N)

“I have discovered a truly remarkable proof which this margin is too small to contain” - Fermat


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Imaginary numbers (i)

Do You Know that ‘i’ is an amazing number which is the onlyimaginary number. However, when you square it, it becomes real. Ofcourse, it wasn’t instantly created. It took several centuries toconvince mathematicians to accept this new number.Girolamo Cardano(1545) in his book Ars Magna, solved the equationx(10-x)=40, finding the answer to be 5 plus or minus √-15.Later, in 1637, Rene Descartes came up with the standard form forcomplex numbers, which is “a+bi” a + bi

Do You Know ? This kind of protractor makes use of two outer arms that may rotate with respect to a fixed central arm. The two rotating arms may be clamped so that they can be set at fixed angles.

Pascal’s triangle (1654)

One of the most famous integer patterns in the history of

mathematics is Pascal’s triangle. Blaise Pascal was the first to

write a treatise about this progression in 1654.

The first seven rows of Pascal’s triangle are depicted at upper

right. Each number in the triangle is the sum of above two of

it. Fractal figure of it is shown in figure.

L'Hopital's Analysis of the Infinitely Small (1696)

L'Hôpital's rule uses derivatives to help evaluate limits

involving indeterminate forms. If we have an indeterminate

form 0/0 or ∞/∞ all we need to do is differentiate the

numerator & denominator and then take the limit.

Goldbach Conjecture (1742)

Every integer greater than 2 can be written as the sum of

three prime numbers, such as 21 = 11 + 7 + 3. (A prime number

is a number larger than 1, such as 5 or 13, that is divisible only

by itself or 1)


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Least Squares (1795)

Least squares is a mathematical procedure for finding the

"best-fitting" curve for a given set of data points by minimizing

the sum of the squares of the offsets of the points from the

curve.

In 1795, German mathematician and scientist Carl Friedrich

Gauss, at the age of 18, began to develop least-squares analysis.

Three-Armed Protractor (1801)

In the seventeenth century, protractors began to be used as

stand-alone instruments by sailors for ocean maps. In 1801, Joseph

Huddart, an English naval captain invented the three-armed

protractor for plotting the position of a boat on navigation maps.

OR

Since the time of Euclid (c. 325-270 B.C.), the so-calledparallel postulate seemed to reasonably describe how ourthree-dimensional world works.According to this postulate, given a straight line and apoint not on that line, only one straight line through thepoint exists that never intersects the original line.This can be visualized by imagining a bowling ball sinkinginto a rubber sheet. If you were to place a marble intothe depression formed by the stretched rubber sheet,and give the marble a sideways push, it would orbit thebowling ball for a while, like a planet orbiting the sun.

Non-Euclidean Geometry (1829)


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Four-Color Theorem (1852)

Mapmakers have believed for centuries that just fourcolors were sufficient for coloring any map drawn on aplane, so that no two distinct regions sharing a commonedge are of same color, although two regions can share acommon vertex and have the same color.In 1852, mathematician and botanist Francis Guthrie wasthe first to conjecture that four colors must besufficient when he attempted to color a map of countiesof UK.

Venn Diagram (1880)

In 1880, John Venn (1834–1923) introduced the conceptof Venn diagram.A Venn diagram is a diagrammatic representation of allpossible logical relations between a finite collection ofdifferent sets. The first to use the term "Venndiagram" was Clarence Irving Lewis in 1918, in his book"A Survey of Symbolic Logic".

Venn diagrams are very similar to Euler Diagrams, which were invented by Leonhard

Euler (1708–1783) in the 18th century.

Fifteen Puzzle (1874)

A sliding tile puzzle invented by Sam Loyd that becameworldwide obsession. Fifteen little tiles ,numbered 1 to15,were placed in 4×4 frame in serial order except for tile 14& 15, which were swapped around and the lower right handsquare was left empty. The objective of puzzle was to get allthe tiles in correct order; the only allowed moves were slidingcounters into the empty square.

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ISRO launches 104 satellites in one go, creates historyPolar Satellite Launch Vehicle (PSLV) of ISROcreated launch history by placing a record 104spacecraft in their desired orbits. No spaceagency has launched such a large number ofsatellites in a single flight so far. (While ISRO’sPSLV launched 20 satellites last year, Russia’sDnepr launcher holds the record for lifting 37satellites to orbit in June 2014.) It carried a mainremote-sensing satellite in the Cartosat-2 seriesand two small spacecraft, all for ISRO, and 101small foreign commercial satellites.http://www.thehindu.com/news/national/ISRO-launches-104-satellites-in-one-go-creates-history/article17305373.ece

Scientists develop new WiFi system thatcan provide ‘100 times faster’ internetScientists have developed a system where wirelessdata comes from a few central ‘light antennas’,which are able to very precisely direct the rays oflight supplied by an optical fibre. The antennascontain a pair of gratings that radiate light rays ofdifferent wavelengths at different angles (‘passivediffraction gratings’). Changing the lightwavelengths also changes the direction of the ray oflight. Since a safe infrared wavelength is used thatdoes not reach the vulnerable retina in your eye,this technique is harmless.http://www.hindustantimes.com/tech/netherlands-scientists-develop-new-wifi-system-that-can-provide-100-times-faster-internet/story-HoGEtK1ZG9ojAZZjMro1KK.html

National Science Day iscelebrated in India on 28February each year tomark the discovery ofthe Raman effect byIndian physicist SirChandrasekhara VenkataRaman on 28 February1928

North East West South

National Science Day

ADDING TO YOUR KNOWLEDGE


“Success can come to you by courageous devotion to the task lying in front of you”

Raman effect: Raman Effect (1928): Achange in the wavelength of light occurswhen a light beam is deflected bymolecules.

Hypatia who was

born in 351 AD was

the first women

recognized as a

mathematician and

scientist since the

recording of

history.

HYPATIA

Hypatia has been given the credit for

the astrolate which was used to

measure star positions that were

relative to the Earth

References : "The Math Book: From Pythagoras to the 57th dimensions, 250 milestones in the history of mathematics, Clifford A. Pickover"

“The Universal Book Of Mathematics: From Abracadabra to Zeno’s Paradoxes , David Darling”

“The Mathematics of Sonya Kovalevskaya”, Roger Cooke, Springer; 1984

http://www.thehindu.com/news/national/ISRO-launches-104-satellites-in-one-go-creates-history/article17305373.ece

http://www.hindustantimes.com/tech/netherlands-scientists-develop-new-wifi-system-that-can-provide-100-times-faster-internet/story-HoGEtK1ZG9ojAZZjMro1KK.html

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RESPONSE SHEET

1) Which of the events in History of Mathematics fascinated you most and why so ?

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________________________________________________________2) If Zero had never been invented then what would today’s mathematics be like ?

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________________________________________________________3) Fermat’s theorem states that the Diophantine equation an + bn = cn has no non-zerosolutions for n > 2, (a, b, c, n∈N). Upto what extent you agree with statement.Give explanation.

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Research Work

a) Find out new sets of Thabit Amicable Number (discovered in the year 850AD) at your own.

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b) Try to design your own three armed protector (developed in 1801). Then tell us that

how its different from protector you are using ?

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YOUR FEEDBACK

My Name: _______________________________________________

I am in class: __________________

From School: ______________________________________________

Topics well explained in this issue:

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Topics need more explanation in this issue:

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Suggest next Theme:

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Any other:

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PROJECT TEAM

Dr. Jyoti Sharma , Prof. Pankaj Tyagi , Prof. Shobha Bagai , Prof. Bibhu Biswal

Email id: [email protected]

RESEARCH TEAM

Shilpi Bariar, Sreelatha S. Naraynan, Anurag Saini, Davinder Kaur, Shantanu Joshi


mailto:[email protected]

month: april issue no:2017(20) maadhyamgiftededucation.co.in/assets/files/students/20. april...

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