# 11.934321459

#### LionHearted

Registered Senior Member
Is there anything significant about this number? I noticed that the function f(x) = -x(x+pi)(x-pi)/11.934321459 is the same as f(x) = sin x on the interval (-pi, pi). Is there any good reason for that number to be the denominator?

Its not the same, it just looks the same. It looks like a taylor series expansion for sin(x) up to third order.

Special Numbers

142857

Time's a tickin'

Re: Special Numbers

Originally posted by oxymoron

142857

Time's a tickin'

repeating digits of 1/7

...which also means it's a cyclic number.

Re: Re: Special Numbers

Originally posted by lethe
repeating digits of 1/7

What do you mean by repeating digits of 1/7?

Re: Re: Re: Special Numbers

Originally posted by LionHearted
What do you mean by repeating digits of 1/7?

1/7 = .142857142857142857...

Last edited:

-AntonK

Originally posted by James R
...which also means it's a cyclic number.

what s a cyclic number?

Cyclic numbers are special numbers that when multiplied by an integer produces a number with the same digits but in a different order.

142857 * 2 = 285714

Sum of 142857 = 27

Sum of 142857 * 8 = 27 as well.

However 142857 * 7 = 999999, which means that a cyclic number multiplied by it's fraction-generator gives a string of 9's.

I think these numbers are really cool. Apparently Lewis Carroll worked 142857 one out many, many years ago!

Here is another cyclic number:

588235294117647

142857 &times; 2 = 285714
142857 &times; 3 = 428571
142857 &times; 4 = 571428
142857 &times; 5 = 714285
142857 &times; 6 = 857142

Multiples produce the same digits in a different order.

<a href="http://mathworld.wolfram.com/CyclicNumber.html" target="_blank">Cyclic Numbers</a>

Neat. Math without application is such a lonely thing is it not?

It's like a play that's never acted out, A song that's never played, A dance that's never danced!

It's the best kind of math. All arguements are based on a few simple axioms which must be adhered to, other than that you can do anything you want. Personally I think theoretical physics is much more difficult to grasp than advanced mathemetics. Mathematics is bound by our logic, physics is bound by the logic of mother nature, who seems to be continually changing her mind.

Didn't know about cyclic numbers. They have curious properties that look algorthymically useful. Have we found nature making use of them? (as with Fibonnachi series etc).

Don't know about cyclic numbers, but cyclic permutations have definately been used to describe nature.