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 Okay, lets see who can work out what is so special about this number: 142857 Time's a tickin'
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 × 2 = 285714 142857 × 3 = 428571 142857 × 4 = 571428 142857 × 5 = 714285 142857 × 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.
