##
Archive for the ‘**Math**’ Category

### Tribute to Hero’s: G. H. Hardy

Posted February 7, 2009

on:Some quotes:

1. Asked if he believes in one God, a mathematician answered: “Yes, up to isomorphism”.

2. “I have never done anything ‘useful’. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.”

Wikipedia :

It is never worth a first class man’s time to express a majority opinion. By definition, there are plenty of others to do that.

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

Quoting one of the mathematicians, C Snow, that Hardy worked with:

A mathematicians apology is, if read with the textual attention it deserves, a book of haunting sadness. Yes, it is witty and sharp with intellectual high spirits: yes, the crystalline clarity and candor are still there: yes, it is the testament of a creative artist. But it is also, in an understated stoical fashion, a passionate lament for creative powers that used to be and that will never come again. I know nothing like it in the language: partly because most people with the literary gift to express such a lament don’t come to feel it: it is very rare for a writer to realize, with the finality of truth, that he is absolutely finished.

Hardy was a sort of purist mathematician, one who did his mathematics not for the sake of its applicability to anything, but for the sake of doing great mathematics. Hardy, along with Littlewood and Ramanujan, is also mentioned in Apostolos Doxiadis’ “Uncle Petros and the Goldbach Conjecture”. The link above gives a short summary on his life.

### Prime Numbers between 1 & 1000

Posted February 4, 2009

on:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73 ,79, 83 ,89, 97 ,101, 103, 107, 109 ,113 ,127,131, 137, 139, 149, 151, 157, 163 ,167, 173 , 179, 181, 191, 193, 197, 199, 211, 223, 227, 229 ,233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349 ,353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463 ,467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673 ,677, 683, 691, 701, 709, 719, 727, 733 ,739, 743, 751, 757, 761, 769, 773, 787, 797, 809 , 811,821, 823, 827 ,829, 839 ,853, 857, 859, 863 ,877, 881, 883, 887, 907, 911, 919 ,929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997

- In: India | Math | Tribute to Hero's
**1**Comment

Today is the 121 Birth Anniversary of Srinivas Ramanujan,a famous Indian Mathematician,who, with almost no formal training in pure mathematics, made substantial contributions to mathematical analysis,number theory,infinite series and continued fractions.Recently his contributions have found applications in crystallography and string theory.

In the memory of Ramanujan, Tamil Nadu every year celebrates 22 December as ‘State IT Day’. His contributions to Mathematics are well known.The contribution of G.H. Hardy a famous mathematician is also equally important, but when some body asked him what was his biggest contribution to Mathematics, Hardy told, Ramanujan was his biggest contribution to Mathematics,such was the genius of Ramanujan.

Here is his brief Profile.

Profile

Born : 22 Dec 1887

Died : 26 April 1920

Birth Place : Erode, Tamil Nadu, India

Contributions to Mathematics :

1. Landau- Ramanujan Constant

2. Mock Theta Fuction

3. Ramanujan Prime

4. Ramanujan – Soldner Constant

5. Rogers- Ramanujan Identities

Applications of his contributions :

1. Crystallography

2. String Theory

I wrote this post to pay tribute to him & his genius.

### Classic: Algebraic Proof of 1=2

Posted April 11, 2008

on:- In: General | Math
**5**Comments

- In: Math
- Leave a Comment

Here is a nice Song i found on the Net, which reminds us about the Famous Unsolved Mathematical Problem P = NP .

its a love story

of two strange people

who never knew they could

fall for each other

when they first met

they only ended up fighting

but slowy it became clear to them

that they sure shared something

a small problem happened

when pride overtook him

he thought she was

less smarter than him

she would solve a puzzle

and he would solve it again

he would tell her

that she was simply

an idea away from him…

he said that he always gets this idea

and then he does all that she can

and probably much more…

one day she decided

his behaviour had to be checked

she thought for a while and

then she said…

fine, then you sure

can do everything

but if you are strictly more smart

you have to do the following

think of some puzzle

that you can easily do

and then give it to me

to solve and lets see if

i can’t do….

all the king’s men and

all the king’s horses

could not come up

with a puzzle like this

the duo got closer and

the world around more curious

today as it stands

the puzzle is still not found

and hence the duo

lives happily close bound

they two are well known

as simply, inseparable

P is the queen and

NP the king of our fable…

Hope you all enjoy it…….

Source : Nutan’s Blog

### NUMB3RS

Posted April 13, 2007

on:- In: Math | Programming
- Leave a Comment

- In: Math | Programming
- Leave a Comment

A prime number (or prime integer, often simply called a “prime” for short) is a positive integer 1″ border=”0″ height=”15″ width=”33″> that has no positive integer divisors other than 1 and itself. (More concisely, a prime number is a positive integer having exactly one positive divisor other than 1.) For example, the only divisors of 13 are 1 and 13, making 13 a prime number, while the number 24 has divisors 1, 2, 3, 4, 6, 8, 12, and 24 (corresponding to the factorization ), making 24 *not* a prime number. Positive integers other than 1 which are not prime are called composite numbers.

Prime numbers are therefore numbers that cannot be factored or, more precisely, are numbers whose divisors are trivial and given by exactly 1 and .

The number 1 is a special case which is considered neither prime nor composite (Wells 1986, p. 31). Although the number 1 used to be considered a prime (Goldbach 1742; Lehmer 1909; Lehmer 1914; Hardy and Wright 1979, p. 11; Gardner 1984, pp. 86-87; Sloane and Plouffe 1995, p. 33; Hardy 1999, p. 46), it requires special treatment in so many definitions and applications involving primes greater than or equal to 2 that it is usually placed into a class of its own. A good reason not to call 1 a prime number is that if 1 were prime, then the statement of the fundamental theorem of arithmetic would have to be modified since “in exactly one way” would be false because any . In other words, unique factorization into a product of primes would fail if the primes included 1. A slightly less illuminating but mathematically correct reason is noted by Tietze (1965, p. 2), who states “Why is the number 1 made an exception? This is a problem that schoolboys often argue about, but since it is a question of definition, it is not arguable.” As more simply noted by Derbyshire (2004, p. 33), “2 pays its way [as a prime] on balance; 1 doesn’t.”

With 1 excluded, the smallest prime is therefore 2. However, since 2 is the only even prime (which, ironically, in some sense makes it the “oddest” prime), it is also somewhat special, and the set of all primes excluding 2 is therefore called the “odd primes.” Note also that while 2 is considered a prime today, at one time it was not (Tietze 1965, p. 18; Tropfke 1921, p. 96).

The th prime number is commonly denoted , so , , and so on.

The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, …

A mnemonic for remembering the first seven primes is, “In the early morning, astronomers spiritualized nonmathematicians”

In the Season 1 episode “Prime Suspect” (2005) of the television crime drama *NUMB3RS*, math genius Charlie Eppes realized that character Ethan’s daughter has been kidnapped because he is close to solving the Riemann hypothesis, which allegedly would allow the perpetrators to break essentially all internet security by factoring large numbers.

The numbers of decimal digits in for , 1, … is given by 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, …

Source :http://mathworld.wolfram.com

### Fibonacci Series……….

Posted April 13, 2007

on:Fibonacci numbers Equation: F(n) = F(n-1) + F(n-2)

Series :`0, 1,1,2,3,5,8,13,21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169`

`1. Fibonacci numbers whose internal digits form a Fibonacci number. Or Fibonacci numbers from which deleting the MSD and LSD leaves a Fibonacci number.`

`0, 1,1``,2,3,5,8,13,21,``34, 55, 89, 233, 610, 987 (``The sequence is finite.)`

`2. `Fibonacci numbers whose external digits form a Fibonacci number. Or Fibonacci numbers whose MSD and LSD form a Fibonacci number.

`0, 1,1``,2,3,5,8,13,21,``34, 55, 89,``121393, 1836311903, 2504730781961, 10610209857723, 10284720757613717413913, 184551825793033096366333, 59425114757512643212875125, 155576970220531065681649693`

`3. ` Fibonacci numbers whose external digits as well as internal digits form a Fibonacci number.

`0, 1,1``,2,3,5,8,13,21,``34, 55, 89`