What is your G? 1,2,3 or 4? Confused? Are baba... I mean what is your mobile technology? 2G, 2.5G or 3G? No Idea? Want know more??? Here is a small note on what these terms are...
G in 2G, 3G etc stand for generation en marking the time period during which the technology developed.
Sunday, October 16, 2011
MI - not Machine Impossible but most indulging!
Being the kick start post, I gave much thought on what to write. Finally decided to go with a simple concept of MI. This is not Machine Impossible but Most Indulging Mathematical Induction. Here it goes...
Monday, May 10, 2010
Kaprekar's Constant
Guys do you remember specialty of 1729? Most of you might know. 1729 is called as Hardy–Ramanujan number. Named after Srinivasa Ramanujan, A Profound Indian Mathematician. 1729 = 1^3 + 12^3 = 9^3 + 10^3
(^ - Stands for "power of" operation. a^b means a to the power of b)
There is a small story associated with it. In Hardy's words:
“I remember once going to see him when he was 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.”
Just like 1729 there is one more number named after famous Indian Mathematician D. R. Kaprekar.
6174 is known as Kaprekar's constant.
This number is notable for the following property:
1. Take any four-digit number with at least two digits different. (Leading zeros are allowed.)
2. Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2.
The above operation, known as Kaprekar's operation, will always reach 6174 in at most 7 steps and it stops there. Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 3524:
5432 – 2345 = 3087
8730 – 0378 = 8352
8532 – 2358 = 6174
The only four-digit numbers for which this function does not work are repeated digits such as 1111, which give the answer 0 after a single iteration. All other four-digits numbers work if leading zeros are used to keep the number of digits at 4:
2111 – 1112 = 0999
9990 – 0999 = 8991 (rather than 999 - 999 = 0)
9981 – 1899 = 8082
8820 – 0288 = 8532
8532 – 2358 = 6174
One of the numbers terminating in 7 steps is 9831:
9831 - 1389 = 8442
8442 - 2448 = 5994
9954 - 4599 = 5355
5553 - 3555 = 1998
9981 - 1899 = 8082
8820 - 0288 = 8532 (rather than 882 - 288 = 594)
8532 - 2358 = 6174
495 has the same property for three-digit numbers.
For example, choose 598:
985 − 589 = 396
963 − 369 = 594
954 − 459 = 495
For five-digit numbers and above, the function does not settle down to a single value, but instead cycles through one of several series of values.
(^ - Stands for "power of" operation. a^b means a to the power of b)
There is a small story associated with it. In Hardy's words:
“I remember once going to see him when he was 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.”
Just like 1729 there is one more number named after famous Indian Mathematician D. R. Kaprekar.
6174 is known as Kaprekar's constant.
This number is notable for the following property:
1. Take any four-digit number with at least two digits different. (Leading zeros are allowed.)
2. Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2.
The above operation, known as Kaprekar's operation, will always reach 6174 in at most 7 steps and it stops there. Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 3524:
5432 – 2345 = 3087
8730 – 0378 = 8352
8532 – 2358 = 6174
The only four-digit numbers for which this function does not work are repeated digits such as 1111, which give the answer 0 after a single iteration. All other four-digits numbers work if leading zeros are used to keep the number of digits at 4:
2111 – 1112 = 0999
9990 – 0999 = 8991 (rather than 999 - 999 = 0)
9981 – 1899 = 8082
8820 – 0288 = 8532
8532 – 2358 = 6174
One of the numbers terminating in 7 steps is 9831:
9831 - 1389 = 8442
8442 - 2448 = 5994
9954 - 4599 = 5355
5553 - 3555 = 1998
9981 - 1899 = 8082
8820 - 0288 = 8532 (rather than 882 - 288 = 594)
8532 - 2358 = 6174
495 has the same property for three-digit numbers.
For example, choose 598:
985 − 589 = 396
963 − 369 = 594
954 − 459 = 495
For five-digit numbers and above, the function does not settle down to a single value, but instead cycles through one of several series of values.
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