| Sohail Maskeen wrote on Wed, 03 November 2004 13:11 |
19=1 !!!!!!!!!!!
Seems to be a false conclusion,in my minds we have to get down these mathematical theories, we must focuse on Quran teachings!!!
|
It is called continous summation.
19 gives us = 1 + 9 = 10
10 gives us = 1 + 0 = 1
Similarly,
19 x 19 gives us = 361
361 gives us = 3 + 6 + 1 = 10
10 gives us = 1 + 0 = 1
19 x 19 x 19 ....... x 19 will result in continous summation = 1.
This algorithm is very well known to mathematicians. If you have taken college level Discrete Mathematics then your professor should have shown you this algorithm. I will illustrate one of the use of this algorithm:
Continous summation algorithm is used to verify multiplication of 2 numbers. This is useful if you are multiplying 2 large numbers. For example, lets take two number 249 and 176 (this two numbers are random, just off the top of my head).
249 x 176 = 43824 (using calculator)
Now let us verify if this is correct using continous summation. Algorithm is like this:
1. Take left hand side two numbers and reduce them to smallest unit using continous summation.
2. Multiply the reduced two numbers and then reduce the resulting number to smallest unit using continous summation. This is your left hand side result.
3. Take right hand side (the result) and reduce it into smallest unit using continous summation. This is your right hand side result.
4. Two sides should equal. If they are not equal then there was error in multiplying the numbers.
Applying the algorithm:
a) Left side continous summation:
249 x 176
=> (2 + 4 + 9) x (1 + 7 + 6)
=> (15) x (14)
=> (1 + 5) x (1 + 4)
=> 6 x 5
=> 30
=> (3 + 0)
=> 3
Thus the smallest unit after continous summation of left side is: 3
b) Right hand side continous summation:
43824
=> (4 + 3 + 8 + 2 + 4)
=> 21
=> (2 + 1)
=> 3
Therefore, left side = right side, thus our multiplication operation of 249 x 176 = 43824 was correct.
If two sides weren't eqaul then we made error in multiplication. This algorithm was very useful during pre-calculator days. Multiplying 2 longs numbers and verifying is a tedious process. But using this algorithm you can easily verify.