Whhhhattt? Black hole in maths? Yup.. In maths a black hole is a number to which an operation on any of the elements of UNIVERSAL set finally leads to... figuratively speaking everything "BOILS DOWN TO THAT ELEMENT.."
The following are two of the mathematical BLACK HOLES... The Sisyphus String: 123 Suppose we start with any natural number, regarded as a string, such as 9288759. Count the number of even digits, the number of odd digits, and the total number of digits. These are 3 (three evens), 4 (four odds), and 7 (total of seven digits). So, use these digits to form the next string or number, 347. Now repeat with 347, counting evens, odds, total number, to get 1, 2, 3, so write down 123. If we repeat with 123, we get 123 again. The number 123 with respect to this process and universe of numbers is a mathemagical black hole. All numbers in this universe are drawn to 123 by this process, never to escape. Will every number really be sent to 123? Try 122333444455555666666777777788888888999999999. The numbers of evens, odds, and total are 20, 25, and 45, respectively. So, our next iterate is 202545, the number obtained from 20, 25, 45. Iterating for 202545 we find 4, 2, and 6 for evens, odds, total, so we have 426 now. One more iteration using 426 produces 303, and a final iteration from 303 produces 123. Narcissistic Numbers: 153 It is well known that, other than the trivial examples of 0 and 1, the only natural numbers that equal the sum of the cubes of their digits are 153, 370, 371, and 407. Of these, only 153 has a black-hole property. To create a black hole, we need to define a universe (set U) and a process (function f). We start with any positive whole number that is a multiple of 3. Recall that there is a shortcut to test whether you have a multiple of 3. Just add up the digits and see whether that sum is a multiple of 3. For instance, 111111 (six ones) is a multiple of 3 because the sum of the digits, 6, is. However, 1111111 (seven ones) is not. Since we are going to be doing some arithmetic, you may wish to take out a hand-calculator and/ or some paper. Write down your multiple of 3. One at a time, take the cube of each digit. Add up the cubes to form a new number. Now repeat the process. You must eventually reach 153. Moreover, once you reach 153, another iteration just gets you 153 again. Let's test just one initial instance. Using the sum of the cubes of the digits, if we start with 432 – a multiple of 3 – we get 99, which leads to 1458, then 702, which yields 351, finally leading to 153, at which point, future iterations keep producing 153. Note also that this operation or process preserves divisibility by 3 in the successive numbers. __________________________________ Do you Yahoo!? Yahoo! Small Business - Try our new resources site! http://smallbusiness.yahoo.com/resources/ Yahoo! Groups Links Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/tech4all/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
