Sunday, March 15, 2009

Interesting facts of mathematicians!

Following are some interesting events in the early lives of few of the most famous and genius mathematicians of the world. I am always in awe whenever I read about them and their lives. I do not want to devote the post to their biographies, rather a collection of the most interesting reads! I have randomly picked the great ones. Randomness is another fact of life that I keep pondering about and find it so difficult to accept its existence in life!

SRINIVASA RAMANUJAM
He had always intrigued me and thus, want to start with him. I am yet to lay my hands on the book The Man Who Knew Infinity: A Life of the Genius Ramanujan

Birth: Born on 22 December 1887 in Erode, Tamil Nadu, India, at the place of residence of his maternal grandparents. His father, K. Srinivasa Iyengar worked as a clerk in a sari shop and hailed from the district of Thanjavur.

One day at school, the teacher was explaining division and said that "if you divide any number by itself, you get 1.''

The teacher in a small high school in southern India turned round to see a tiny hand trying to reach the ceiling. Oh by the gods, him again! That Aiyangar boy with his horribly difficult and quite irrelevant questions. Like last week, when he wanted to know how long it would take for a steam train to reach Alpha Centauri. As if he would be able to afford the fare if he knew. Well, he couldn't let him exercise his hands too much.

``Yes Ramanujan?''

The small boy with shining eyes stood up. He spoke slowly, with the calm confidence of one who did not need to be told he was the best in the class.

``Is zero divided by zero also equal to one?''

Unfortunately for all those other teachers who've been asked this question at least twenty times in their lives, the response to the question is unknown. But the life of the boy, Srinivasa Ramanujan Aiyangar, certainly isn't.

By age 11, he had exhausted the mathematical knowledge of two college students, who were lodgers at his home. He was later lent a book on advanced trigonometry written by S.L. Loney. He completely mastered this book by the age of 13 and he discovered sophisticated theorems on his own. By 14 he was achieving merit certificates and academic awards.

Awesome, is it not?

PYTHAGORAS
I could not really get specific early life incidents but have added some noteworthy facts.

Birth: Born around 565 B.C. on the Greek island Samos off the Coast of Asia-Minor, his father Mnesarchos was a wealthy merchant and an engraver. His mother Pythais was a native of Samos.

Pherekydes, a philosopher and a fiction writer, was the teacher of Pythagoras. Pythagoras too was a mathematician as his mentor. He (Pherekydes), put forward the doctrine of transmigration of souls and cycle of birth liberation of human being from this life cycle which was proffessed by his student, Pythagoras. This theory is analogous to the doctrine of poorva janma (Past Life), punar janma (Re-birth) and moksha (Salvation), of the Hindu philosophy.

How the famous Pythagoras Theorem was propounded?
In the earlier days, Egypt was considered more advanced than Greece. The journey to Egypt was recognized as broadening the horizon of knowledge and wisdom. Ancient Egyptians knew the technique of preparing bricks and constructed buildings using them. From this, they acquired knowledge of shape, size and volume of solids. Thus, they developed some geometry for measurement and decimal number system for calculations. Pythagoras would have learnt all these theories during his travels to Egypt. The Egyptians knew that a triangle having sides of length three, four, and five units was a right-angled triangle. They also knew some elementary trigonometry. Pythagoras worked on right-angled triangles and propounded his theory; ‘The Pythagoras Theorem.’ The Pythagoras theorem states – The square of the hypotenuse is equal to the sum of the squares of the other two sides of the right-angled triangle.

FIBONACCI

Born: Fibonacci, or more correctly Leonardo da Pisa or Leonardo Pisano, was born in Pisa in 1175 AD. He was the son of a Pisan merchant.

Leonardo Pisan was known as Fibonacci, which is short for filius Bonacci meaning "the son of Bonaccio". His father's name was Guglielmo Bonaccio. Fi'-Bonacci is like the English names of Robin-son and John-son.

Well, one may say, what is in a name? But, I was too amused to know how he got his name and thus, thought of sharing my amusement.

His famous contributions being the decimal number system and the famous being the Fibonacci series.

He learnt about the decimal system from Arabs who in turn had learnt from the Hindus. He introduced this number system into Europe - the positional system we use today - based on ten digits with its decimal point and a symbol for zero:
1 2 3 4 5 6 7 8 9 0

His wrote a book on how to do arithmetic in the decimal system, called Liber abbaci (meaning Book of the Abacus or Book of Calculating)

Fibonacci Series
In Fibonacci's Liber Abaci book, chapter 12, he introduces the following problem:

How Many Pairs of Rabbits Are Created by One Pair in One Year?

A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear also.


Then he showed the solution to the above stated problem from where the series got derived.

beginning 1 first 2 second 3 third 5 fourth 8 fifth 13 ..... end 377

Fibonacci says his book Liber Abaci (the first edition was dated 1202) that he had studied the "nine Indian figures" and their arithmetic as used in various countries around the Mediterranean and wrote about them to make their use more commonly understood in his native Italy. So he probably merely included the "rabbit problem" from one of his contacts and did not invent either the problem or the series of numbers which now bear his name.

D E Knuth adds the following in his monumental work The Art of Computer Programming: Volume 1: Fundamental Algorithms errata to second edition:

Before Fibonacci wrote his work, the sequence F(n) had already been discussed by Indian scholars, who had long been interested in rhythmic patterns that are formed from one-beat and two-beat notes. The number of such rhythms having n beats altogether is F(n+1); therefore both Gospala (before 1135) and Hemachandra (c. 1150) mentioned the numbers 1, 2, 3, 5, 8, 13, 21, ... explicitly.


Well, then why is it named after him? It was the French mathematician Edouard Lucas (1842-1891) who gave the name Fibonacci numbers to this series and found many other important applications.

APPLICATIONS

Every human has two hands, each one of these has five fingers, each finger has three parts which are separated by two knuckles. All of these numbers fit into the sequence.

These patterns within nature were discovered many centuries ago, and until this day, scientists are still studying the pattern of natures numbers. The planets also possess a pattern which relates to the orbital period, which is the time it takes to go once around the Sun to its distance from the Sun. There is much that has been scientifically proven regarding natures numbers and the planet, animal, and human world in which we live.

I wish that this will interest many readers to understand how passion for something leads to greatness. The key thing is the ardent passion with not much forethought given to the end result!

Their lives and lives of many more like them, have lot to teach us and keep us motivated to strive for excellence!

25 comments:

  1. good knowledge yaar

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  2. Thanks a lot! Good that its proving informative! :)

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  3. Something very amazing and new to me. Thanks a lot. I hope this work would continue for long time.

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  4. @Anonymous - Thanks for the encouragement.

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  5. i am sorry... i have a doubt. why did Edourd Lucas give the name of Fibonacci to the sequence? Why can't he give his own name?

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    1. One probable explanation was:

      Leonardo of Pisa is now known as Fibonacci [pronounced fib-on-arch-ee] short for filius Bonacci.
      There are a couple of explanations for the meaning of Fibonacci:
      Fibonacci is a shortening of the Latin "filius Bonacci", used in the title of his book Libar Abaci (of which mmore later), which means "the son of Bonaccio". His father's name was Guglielmo Bonaccio. Fi'-Bonacci is like the English names of Robin-son and John-son. But (in Italian) Bonacci is also the plural of Bonaccio; therefore, two early writers on Fibonacci (Boncompagni and Milanesi) regard Bonacci as his family name (as in "the Smiths" for the family of John Smith).
      Fibonacci himself wrote both "Bonacci" and "Bonaccii" as well as "Bonacij"; the uncertainty in the spelling is partly to be ascribed to this mixture of spoken Italian and written Latin, common at that time. However he did not use the word "Fibonacci". This seems to have been a nickname probably originating in the works of Guillaume Libri in 1838, accordigng to L E Sigler's in his Introduction to Leonardo Pisano's Book of Squares.
      Others think Bonacci may be a kind of nick-name meaning "lucky son" (literally, "son of good fortune").

      Source: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html

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  6. The life history of mathematicians was worth reading...Good!

    Continue your good work to the student community

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  7. it is a very interesting and worthful information

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  8. Interesting! Write something about Kaprekar also.

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  9. Write More About Ramanujan

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  10. Please do write more about Ramanujan

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    1. I guess, both feb and apr remarks are from the same person. I shall pay heed to the suggestion and write a separate post for Ramanujan to do justice! :)

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  11. great thanks yar,for the info. it really helped me.

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  12. hello jaishre ma'am.... very informative n inspirational to read more...... thanku... let d gud work keep goin ahead..

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  13. hello jaishre ma'am..... very informative n inspirational to read more..thanku ... let d gud work keep goin ahead.

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  14. ooh.. ur great.. dat was really usefull !!
    thank u

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  15. Hi, what I appreciate is u started with ramanujan...awaiting more blogs...prasanna

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  16. I am currently reading "The Man who knew Infinity". It is a wonderful book by Robert Kanigel. It is a revelation in itself to read the biography of such a great Indian Mathematician.

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  17. Please write about Stephen hawking

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  18. Rather I think I've read a similar story like that of Ramanujan about another mathematician.

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