## Thursday, 29 November, 2007

### Beauty of Maths

Beauty of Math!

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10 = 1111111111

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

Brilliant, isn't it?

And look at this symmetry:

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

This I got by a mail from my friend. Nice one..
By the way, are the results correctly?
So, from next time onwards, if any one asks you to write a program to print the pyramid of numbers, instead of writing using junk loops, use Maths to print it.

Insanity said...
This comment has been removed by the author.
Insanity said...

hmm.. I shud disagree with u if u want to print thru code. do u want to give a complex math instead of simple loop with single statement

printf("%d",i);

Look the number of clock cycles in both the cases.

Maths is beautiful, but logic is more beautiful.

Vishnu said...

I agree that this takes lot of cycles.. 'm not asking you to include this in your project :) but, you ought to appreciate the beauty of maths. It shows how innovative you are if you write a piece of code in different ways.. I guess I can term this as one "out of box" thinking way to write a pyramid program.. may be some of those at present aweful ways may lead to different useful ways later.. :)
ok.. just out of curiosity to learn, can you suggest me where this calculations can be used?