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
Therefore 303 -----That leads to again
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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