Mathematical Musings, Memorabilia and Personalities
 

Today we hold in remembrance the 84th. death anniversary of the 20th century Indian mathematical genius Srinivasa Ramanujan F.R.S.

His legend lives on in Hardy's 'Collected papers' and the 'Lost Note Book'.
For Mathematicians the world over, he belonged to the league of legends such as Fermat, Karl Jacobi and leonhard Euler.

Personally, I hold in reverence his remarkable approximation of pi correct to twleve places of decimals given by the simple, elegant and symmetric formula
when written in math symbols. Here I can only put it as the one fourth root of 2143/22 or the more elegant sqrt. of sqrt. of 2143/22.

For those interested in further details of his life and times I refer him to the excellent biography by Robert Kanigel entitled "The Man who knew infinity"

Many of the results he jotted down are still being verified today and many have been the the subject of thesis for Ph.D.

Ramanujan died comparatively young as many good mathematicians do.
His is a story of a nobody living in obscurity rising to the pinnacle of achievement and glory in so short a time!

Mally.

[QUOTE=mfgoode]Today we hold in remembrance the 84th. death anniversary of the 20th century Indian mathematical genius Srinivasa Ramanujan F.R.S.[/QUOTE]

:bow: :bow: :bow:

A real and complex genius.

Luigi

[QUOTE=mfgoode]His legend lives on in Hardy's 'Collected papers' and the 'Lost Note Book'.
For Mathematicians the world over, he belonged to the league of legends such as Fermat, Karl Jacobi and leonhard Euler.
[/QUOTE]

I really think that Euler was important, but do you really think that he contributed more to the mathematical society then Gauss?
Tho Gauss was more important than the three stated above, but of course he came after Euler and Fermat, maybe if you also consider this in your judgement, you come to the conclusion that Euler and Fermat contributed more.

The thing what made the work of Fermat so extraordinary IMHO was that he was a judge and used math only as a hobby and yet achived so much. Maybe he made number theory more popular than it was. Who knows what would be if he hadn't written down his famous conjecture. I guess number theory would not have attracted so many people in the past centuries :o)

Sory maybe this is not appropriate here, because all of the stated people relly where genius and all of them did a great work, but I was just wondering why you chose these three :o)

[QUOTE=juergen]I really think that Euler was important, but do you really think that he contributed more to the mathematical society then Gauss?
Tho Gauss was more important than the three stated above, but of course he came after Euler and Fermat, maybe if you also consider this in your judgement, you come to the conclusion that Euler and Fermat contributed more.

The thing what made the work of Fermat so extraordinary IMHO was that he was a judge and used math only as a hobby and yet achived so much. Maybe he made number theory more popular than it was. Who knows what would be if he hadn't written down his famous conjecture. I guess number theory would not have attracted so many people in the past centuries :o)

Sory maybe this is not appropriate here, because all of the stated people relly where genius and all of them did a great work, but I was just wondering why you chose these three :o)[/QUOTE]



:smile:
Why I picked the legendary names of Pierre Simon Fermat (1601-1665)
Leonhard Euler (1707-1763) and Carl Gustav Jacob Jacobi (1804-1851) to put Srinivasa Ramanujan (1887-1920) on par with them is because the common threads of mathematics links the four of them.
With Fermat and Euler it was the Theory of numbers. Admittedly with Fermat it was entirely recreational but built of the highest class. so it was with Ramanujan. With Jacobi it was work on Elliptic functions which they both excelled at.

Every nation prides in it national heroes especially when they attain international status.
My selection suited these men of four different nationalities viz: in order French, Swiss, German and Indian so you will admit its a fair comparison.

However great these four may be they cannot be compared to Karl Friedrich Gauss (1777-1855) whose quality of work in different sciences far surpasses his quantity. In sheer quantity Euler reigns supreme even till today
and like Ramanujan their works are still being collected.

As prolific author and writer E.T. Bell puts it, this is what he wrote of Gauss.
Quote: Archimedes, Newton and Gauss, these three, are a class by themselves among the great mathematicians, and it is not for ordinary mortals to attempt to range them in order of merit' /unquote

If you are interested in math history I would recommend the book
'A Short Account of the history of mathematics' by W .W. Rouse Ball.
This book is virtually a pocket encyclopaedia of the major figures of mathematicians and their discoveries. Its been reprinted by Dover tho almost 100 years old.

Mally :coffee:

Maths & Mysticism
 

In Hindu philosophy Non-duality can be attttained by a negative approach i.e. "not this", " not this" ... approach until the mind is totally silent.Such a mind
recognises and abides in the reality.
In Maths there is a similar approach: "failure functions"
A Diaphontine eqn. can be solved by this approach.Example:
"A Theorem a la Ramanujan"on site
[url]www.crorepatibaniye.com/failurefunctions[/url]

Devaraj

Maths and Beauty
 

:whistle:

Scientists have narrowed down the concept of perfect beauty to the simple mathematical ratio 1 : 1.618 , otherwise known as Phi, Or divine proportion, to set standards of beauty.
"Only one formula has been consistently and repeatedly present in all things beautiful, be it Art, architecture or nature, but most importantly in facial beauty" The Sydney Morning Herald quoted US. dentist Yosh Jefferson as saying.
Defining the formula he says that if the width of the face from cheek to cheek is 10 inches, then the length of the face from the top of the head to the bottom of the chin should be 16.18 inches to be in ideal proportion
The ratio of Phi also applies to the width of the mouth to the width of the cheek, width (I would say length ) of the nose to the width
of the cheek, the width of the nose to the width of the mouth. :smile:
My own private (pardon the pun) researches reveal that the most perfect women have the distance from the navel to the sole of the foot to the height from head to toe in divine proportion i.e. 1: 1.618
Science fiction writers use the cube, pyramids, etc. as objects of reverence.
I have yet to see a rectangular parallelepiped ( cuboid) which in my opinion is ' perfect ' and having the breadth : length : height in the ratio of
1 : phi : phi^2 as being utilised for the same purpose. :sad:
I have made such enclosures for my bass, hi fidelity speakers which resulted in tremendous sound quality. :showoff:


Mally :coffee:

Remembering digits of PI
 

:rolleyes

Several digits of pi taken in order can be remembered by using rhymes
Then the number of letters in each word of the rhyme will give sucessive digits of pi. These rhymes are known as mnemonics
Here is a mnemonic for pi in letters correct to 12 places of decimals :smile:


"Sir, I have a rhyme assisting, my feeble brain, its tasks oft-times, resisting". (3.141592653589)

Has anyone got any others? French or German mnemonics also welcome :question:

The mnemonic will stop when zero comes along. After how many digits?

Mally :coffee:

[URL]http://membres.lycos.fr/villemingerard/MnemoTe/Phrase.htm[/URL]

[QUOTE=mfgoode]:rolleyes

Several digits of pi taken in order can be remembered by using rhymes
Then the number of letters in each word of the rhyme will give sucessive digits of pi. These rhymes are known as mnemonics
Here is a mnemonic for pi in letters correct to 12 places of decimals :smile:


"Sir, I have a rhyme assisting, my feeble brain, its tasks oft-times, resisting". (3.141592653589)

Has anyone got any others? French or German mnemonics also welcome :question:

The mnemonic will stop when zero comes along. After how many digits?

Mally :coffee:[/QUOTE]

Sir, I bear a rhyme excelling
In mystic force and magic spelling.
Celestial sprites elucidate
All my striving can't relate.


That gives 20 places and is, of course, an old favourite. I used to know the second verse which added another twenty or so places but can no longer remember it.

The usual convention for representing zero is to use a ten-letter word.


Paul

You are missing a digit 3 :)

3,141 592 653 589 793 2[B]3[/B]8 46

[QUOTE=ATH]You are missing a digit 3 :)

3,141 592 653 589 793 2[B]3[/B]8 46[/QUOTE]
You are quite correct. The last line is

All my [b]own[/b] striving can't relate.

Thanks for pointing out this omission.

Paul