AryabhatTa

Bijeesh A B - VI C -

Aryabhata was the great Hindu Mathematician. He lived from 475 AD to 550 AD. He wrote on arithmetic including undo this heading arithmetic and geometric progressions, quadratic equations, and indeterminate equations. His work often called Aryabhatiya consists of a collection of astronomical tables and the Aryastasata which include the Ganita, a note on arithmetic, the Kalakriya on time and its measure and the Gola on the sphere. Aryabhata was one of those ancient scholars of India who could stand with pride among the greatest scholars even of the modern age.

Puzzle

   1)There is a number which is very peculiar. This number is 3times the sum of its digits. Can you find the number?

 2) Write the biggest number that can be written with four one’s?

3) Can you write 1789 in roman numbers?

 4) What is the sum of first 70 odd numbers?

5) Find the value of:

                                   CCLXV+CXVI+XIII+VI=?

Beginning of algebra

 It is said that algebra as a branch of mathematics began about 1550 BC, that means more than 3500 years ago, when people in Egypt started using symbols to denote unknown numbers .Around 300 BC, use of letters to denote unknown and forming expressions from them was quite common in India. Many great Indian mathematicians Aryabhata, Brahmagupta, Mahavira and Bhaskara II and others, contributed a lot to the study of Algebra.

Branches of mathematics

The branches of mathematics in which we study about numbers is called arithmetic. The branch in which we learn about figures in two and three dimensions and their properties is called geometry. The branch in which we use letters along with numbers to write rules and formulas in general is called algebra.    

Answers for the puzzleS

1Ans) 27

            2+7=9

            9x3=27

2Ans) 285311670611

3Ans) MDCCLXXXIX

4Ans) 4,900 (70x70)

5Ans) CD  
  
                        CLXV              265

                      C XVI               166

                                 XIII                 13                        

                  VI            +       6    
  

           Ans          CD               400  

                                                          

Mathematicians with Extraordinary Powers of Memory

We look here at a few mathematicians who have shown extraordinary powers of memory

John Wallis (Born: 23 Nov 1616 in Ashford, Kent, England Died: 28 Oct 1703 in Oxford, England) whose calculating powers are described:

[Wallis] occupied himself in finding (mentally) the integral part of the square root of 3 10⁴⁰; and several hours afterwards wrote down the result from memory. This fact having attracted notice, two months later he was challenged to extract the square root of a number of 53 digits; this he performed mentally, and a month later he dictated the answer that he had not meantime committed to writing.

Von Neumann (Born: 28 Dec 1903 in Budapest, Hungary - Died: 8 Feb 1957 in Washington D.C., USA) whose feats of memory are described by Herman Goldstine:

As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English.  

On one occasion I tested his ability by asking him to tell me how the 'Tale of Two Cities' started. Whereupon, without pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes.

Von Neumann's ability to do mental arithmetic is the source of a large number of stories which no doubt have grown the more impressive with the telling. It is hard to decide between fact and fiction. However, it is clear that multiplying two eight digit numbers in his head was a task that he could accomplish with little effort. Again it would appear that von Neumann's 'almost perfect' memory played a large part in his ability to calculate.

Only one mathematician has ever described in detail how he was able to perform incredible feats of memory and calculating. This is A C Aitken, (Born: 1 April 1895 in Dunedin, New Zealand Died: 3 Nov 1967 in Edinburgh, Scotland) .

He could instantly give the product of two numbers each of four digits but hesitated if both numbers exceeded 10,000. 

Among questions asked him at this time were to raise 8 to the 16th power; in a few seconds he gave the answer 281,474,976,710,656 which is correct. ... he worked less quickly when asked to raise numbers of two digits like 37 or 59 to high powers....

 Asked for the factors of 247,483 he replied 941 and 263; asked for the factors of 171,395 he gave 5, 7, 59 and 83, asked for the factors of 36,083 he said there were none. 

He, however, found it difficult to answer questions about numbers higher than 1,000,000.

Another mathematician George Parker Bidder

was born in 1806 at Moreton Hampstead in Devonshire, England. He was not one to lose his skills when educated and wrote an Number Base Systems.

Women in mathematics

Hypatia of Alexandriya( ca. 400 AD )

Emilie du Chatelet(1706-1749)

Maria Gaetana Agnesi(1718-1799)

Sophie Germain(1776-1831)

Ada Lovelace (1815-1852)

Sofia Kovalevskava(1850-1891)

Alicia Boole Stott(1860-1940)

Rozsa Peter(1905-1977)

Mary Cartwright(1900-1998)

Olga Taussky Todd(1906-1995)

Julia Robinson(1919-1985)

Olga Ladyzhenskava(1922-2004)

Olga Oleinik(1925-2001)

MATHEMATICAL KNOWLEDGE OF INDIA

Kamna Venugopal

VIII.A

The layman’s knowledge of Indian mathematics stays only on two Indian contributions to mathematics. Many also claim that these ‘two achievements’ that is the discovery of zero and the discovery of Pythagoras theorem are great. The most unfortunate reality is that we have not sustained our claims by submitting proofs for even these two. If we search through the ancient Indian Sanskrit literature, hundreds and thousands of modern scientific information bits, on mathematics written during the Vedic period and afterwards can be seen. Not merely zero and Pythagoras theorem. Bringing all of them to a light is a Herculean task. Demonstrating with few examples on a variety of subject areas need not be very difficult. But the important and crucial requirement to claim Indian contributions is that one has to search almost all important texts.

Shakuntala Devi

 

P.MEGHANA DAS

VIII-A

Shakuntala Devi is an Indian calculating prodigy. Shakuntala was born on November 4, 1939 in Bangalore, India was well known Human Computer - [Indian legend]. 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. In 2006 she released a new book called In the Wonderland of Numbers with Orient Paperbacks which talks about a girl Neha and her fascination for numbers. Shakuntala Devi is a calculating prodigy who was born on November 4, 1939 in Bangalore, India .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. Shakuntala Devi was born in Bangalore, India to an orthodox priestly Brahmin family. At the age of three she manifested an extraordinary love for numbers and by the time she was five years old, Shakuntala became an expert in complex mental Arithmetic. With a divine skill in numbers from the age of three, she has been stunning the whole world with her uncanny skill in computing the most intricate problems mentally, even quicker than the highly sophisticated computers in the world.

Many more........ these words....wouldn't die.....

"As long as algebra is taught in school, there will be prayer in school."

-Cokie Roberts

"Do not worry about your problems with mathematics, I assure you mine are far greater."

- Albert Einstein

"God does arithmetic."

-Karl Friedrich Gauss

"God does not care about our mathematical difficulties. He integrates empirically."

-Albert Einstein

"God made the natural numbers, all the rest is the work of man."

-Leopold Kronecker

"He who can properly define and divide is to be considered a god."

-Plato

"How dare we speak of the laws of chance? Is not chance the antithesis of all law?"

-Bertrand Russell

"I admit that mathematical science is a good thing. But excessive devotion to it is a bad thing."

-Aldous Huxley

"I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate."

-David Mumford

"I don't believe in mathematics."

-Albert Einstein

"I have no faith in political arithmetic."

-Adam Smith

"If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy."

-Alfréd Rényi

"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy."

-G. H. Hardy

"In mathematics you don't understand things. You just get used to them."

-John Von Neumann

"It is easy to lie with statistics. It is hard to tell the truth without it."

-Andrejs Dunkels

"Life is good for only two things, discovering mathematics and teaching mathematics."

-Siméon Poisson

"Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning."

-John Locke

"Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another."

-Bernard Le Bouyer de Fontenelle

"Mathematics consists of proving the most obvious thing in the least obvious way."

-George Polya

"Mathematics is a game played according to certain simple rules with meaningless marks on paper."

-David Hilbert

"[Mathematics] is an independent world created out of pure intelligence."

-William Wordsworth

"Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state."

-Plato

"Mathematics is not yet capable of coping with the naïveté of the mathematician himself."

-Abraham Kaplan

"Mathematics is the art of giving the same name to different things."

-Jules Henri Poincaré

"Mathematics is the only instructional material that can be presented in an entirely undogmatic way."

-Max Dehn

"Mathematics is the science of what is clear by itself."

-Carl Jacobi

"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

-Bertrand Russell, referring to the axiomatic method, where certain properties of an (otherwise unknown) structure are assumed and consequences thereof are then logically derived

"Mathematics seems to endow one with something like a new sense."

-Charles Darwin

"Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform."

-Bertrand Russell

"Measure what is measurable, and make measurable what is not so."

-Galileo Galilei

"Medicine makes people ill, mathematics make them sad and theology makes them sinful."

-Martin Luther

"No human investigation can be called real science if it cannot be demonstrated mathematically."

-Leonardo da Vinci

"Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important...The knowledge doesn't make life any sweeter or happier, does it?"

-Helen Keller

"One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them."

-Heinrich Rudolf Hertz