Sarve Janaha Sukhino Bhavanthu......Raghavan.......

MATEHMATICS OF A TELEPHONE NUMBER
AND
HARDY RAMANUJAM NUMBER...





MATHEMATICS OF A TELEPHONE NUMBER......
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I give some clues in Mathematical language ...find out the telephone number.....

NUMBER OF DIGITS.......CUBE OF BASE OF BINARY NUMBERING SYSTEM.......

THE TELEPHONE NUMBER IS MADE OF REAL NUMBERS CONSISTING.......

1.ARITHMETIC PROGRESSION OF 3 NOS WITH SMALLEST EVEN INTEGER IN ASCENDING ORDER WITH COMMON DIFFERENCE 2

2.ARITHMETIC PROGRESSION OF 3 NOS WITH HALF VALUE OF EACH DIGIT AS ABOVE IN ASCENDING ORDER.....

3.NUMERAL ,MEANING NOTHING....IT IS AN INTEGER BETWEEN +1 AND _1......

4.CUBE OF SMALLEST EVEN INTEGER.....

THE TELEPHONE NUMBER STARTS WITH SMALLEST EVEN REAL NUMBER AND ENDS WITH CUBE OF SAME NUMBER.......

SORRY IF I HAVE CONFUSED ALL...

PLEASE WORK OUT THE SOLUTION...

MEANTIME SOMETHING ABPOUT RAMANUJAMS NUMBER

Ju

1729 is known as the Hardy-Ramanujan number, after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Aiyangar Ramanujan. In Hardy's words [1]:

I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

In fact

1729 = 1³+12³ = 9³+10³

as both men would have verified mentally; but it is much less obvious that this is the smallest example.

Two things have been observed regarding the anecdote, both of which detract from the surprise element. Firstly, Ramanujan didn't discover the taxicab property on-the-spot; it has been found in one of his notebooks dated years before the incident. Secondly, Hardy possibly knew it as well, and pretended not to only to cheer up the ailing Ramanujan. Indeed, such behaviour would have been in keeping with Hardy's self-deprecating character.

[edit] Quote

"Every positive integer is one of Ramanujan's personal friends" -- J. E. Littlewood, on hearing of the taxicab incident.

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