RE: [tech4all] MATHEMATICAL BLACK HOLE

Fri, 29 Apr 2005 11:01:32 -0700

we can consider 4 as 004 as well as 4-
 1(even) ,  0(odd), 1(total)
repeating,
3(e) , 0 (o) , 3(t)
1 2 3


"Abinanthan.B" <[EMAIL PROTECTED]> wrote:

IS 0 A EVEN NUMBER?

 

WHAT IF I TAKE THE STRATING NUMBER ITSELF AS "0"?

 

From: [email protected] [mailto:[EMAIL PROTECTED] On Behalf Of vijay gopinath
Sent: 29 April 2005 12:39
To: [email protected]
Subject: RE: [tech4all] MATHEMATICAL BLACK HOLE

 

222 -----

No: of even numbers - 3

No: 0f Odd numbers - 0

Total number - 3

Therefore 303 -----That leads to again

No of even Numbers -1

No of odd numbers -2

Total number - 3

Therefore "123 "

 

Same with 4 too

 

Thanks ,

 

Vijay

"Abinanthan.B" <[EMAIL PROTECTED]> wrote:

what about 222 or 4?

-----Original Message-----
From: [email protected]
To: [email protected]; [EMAIL PROTECTED];
[EMAIL PROTECTED]
Sent: 28/04/2005 15:36
Subject: [tech4all] MATHEMATICAL BLACK HOLE

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.

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