Mathematics(History,Formula etc.) and brief description on S.Ramanujan.
A brief history of MathematicsBefore 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 ofLeonardo da Vinci.He published the solutions to the cubic and quarticequations in his 1545 book Ars Magna.The solution to one particular case of the cubic, x3 +ax = b (in modern notation), was communicated tohim by Niccolò Fontana Tartaglia (who later claimedthat Cardano had sworn not to reveal it, and engagedCardano in a decade-long fight), and the quartic wassolved by Cardanos 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, thena^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 "Newtons 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 masters
Theano Hypatia Caroline HerschelSophie Germain Emilie du Chatelet
HomeTheano was the wife of Pythagoras. Sheand her two daughters carried on thePythagorean School after the death ofPythagoras.She wrote treatises on mathematics,physics, medicine, and child psychology.Her most important work was the principleof the “Golden Mean.”
HomeHypatia was the daughter of Theon, whowas considered one of the most educatedmen in Alexandria, Egypt.Hypatia was known more for the work shedid in mathematics than in astronomy,primarily for her work on the ideas ofconic sections introduced by Apollonius. Hypatia
HomeHer first experience in mathematics washer catalogue of nebulae.She calculated the positions of herbrothers and her own discoveries andamassed them into a publication.One interesting fact is that Caroline neverlearned her multiplication tables. Caroline Herschel
HomeShe is best known for her work in numbertheory.Her work in the theory of elasticity is alsovery important to mathematics. Sophie Germain
HomeAmong her greatest achievements wereher “Institutions du physique” and thetranslation of Newtons “Principia”, whichwas published after her death along with a“Preface historique” by Voltaire.Emilie du Châtelet was one of manywomen whose contributions have helpedshape the course of mathematics Emilie du Chatelet
AryabhattaAryabhatta came to this world on the 476 A.D at Patliputra in Magadha which is known as the modern Patna in Bihar. Somepeople were saying that he was born in theSouth of India mostly Kerala. But it cannot be disproved that he was not born inPatlipura 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 roundthe sun and the moon moves round the earth. He discovered the 9 planets positionand related them to their rotation round the sun. Aryabhatta said the light receivedfrom planets and the moon is gotten from sun. He also made mention on the eclipseof the sun, moon, day and night, earth contours and the 365 days of the year as theexact length of the year. Aryabhatta also revealed that the earth circumference is24835 miles when compared to the modern day calculation which is 24900 miles.Aryabhatta have unusually great intelligence and well skilled in the sense that allhis theories has became wonders to some mathematicians of the present age. TheGreeks 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 thatearth 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 Bhaskaras 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 Bhaskaras 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 Chandras review of Ana Garcia-Arroyos 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 Devis book The World of Homosexuals published in 1977. [...] Shakuntala Devis (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 Narayanas 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 helpsPhysicists• He was able toapproximate Pi
RAMANUJAN’S MAGIC SQUARE22 12 18 87 Do you know88 17 9 25 THE BIRTH DATE OF10 24 89 16 Srinivasa19 86 23 11 Ramanujan?
RAMANUJAN’S MAGIC SQUARE It is 22nd Dec22 12 18 87 1887.88 17 9 25 Yes. It is10 24 89 16 22.12.188719 86 23 11 BE A PROUD INDIAN