Recent content by damoclark

Pi From a geometric point of view, Pi is what is it due to how unit area is defined. It's just so happens that on planet earth, humans decided to define a unit of area as a little square box with sides of unit length. In another corner of the galaxy, some other intelligent life form might...

DH- Thanks, that's an interesting equation. Is the proper time, the time elasped for a person in the rocket, or for a person on earth? So if I accelerated straight out into space, for 2 years at 1g, then turned around and came back traveling at 1 g, then how could you calculate how many...

Well, i thought after 1 day you would be traveling much faster than the speed of light. v = 4.9 * Seconds in one day^2 = 4.9 * 86400^2 = 36,578,304,000 m/s >> c = 299,792,458 m / s The above equation would imply that you would reach the speed of light after 2 and a bit hours.

I wish to accelarete out into space at 9.8m/s/s for 1 day. The reason I want to accelerate at 9.8m/s/s is because I want to feel the normal effects of gravity as I travel. After accelerateing for one day, I want to look out my rocket window, and take a snap shot of our sun, then I want to...

On another planet, where the aliens have 12 fingers, Earth's 0.333333 recurring is written as 0.4

Maybe this will help, although I don't surely know cause I haven't tried it yet, but I recall a method I used to solve a similar problem once. Set: f(x) := c_1 + c_2x + c_3x^2 + c_4x^3 + c_5x^4 + ... where c_k are the co-efficients you originally defined. Then expand the...

I will try to explain my problem which prompted me to ask the original question. The question that I originally possed, came up while I was working on a problem to do with the stucture of numbers. Where as in binary you can represent any integer, with a sequence of two symbols, those...

Thanks for the links Shmoe, and salthydog for the reference to PARI Can I calculate Pi(344481421025753789822679967) practically, though? where Pi(x) is the prime counting function. From the methods I've looked at, I figure I would need a powerful computer and about 1 million years of free...

That is very helpful, thanks. I was wondering if all the factors could be written down as nth primes, for example 7 is equal to the fourth prime. I guess that 344481421025753789822679967 can't be written down as an nth prime, as the number of prime numbers under this number is unknown. Is...

CAn anybody help me with this problem. I am trying to factor 2^{128}+16+1 My version of MATLAB can't handle such big numbers, although I have managed to find some small factors. The problem is the larger factors, of which I don't know whether are even prime. If anyone has a good...

There's a nice data base of integer sequences at : http://www.research.att.com/~njas/sequences/ that you can search. I played around with the sequence you have given, but couldn't figure anything much out. Do you know anymore of the terms?

If you mean "How many cube faces does a hyper-cube have"? then 8, possibly otherwise your question doesn't make sense, as there is no number of 3-dimensional cubes that we could put inside a hypercube.

Thanks for the links Robert. So if you know the Bernoulli numbers or Bernoulli polynomial in advance you can write down the formula quickly, I assume.But I wonder if there's another way to do, maybe involving a infinite series that's converges fast...

Thanks Shmoe, I'll check out the "Euler-Maclaurin summation formula". So the Sum could be calculated with a polynomial of order 11, which would mean I would have to substitute the value of 10^3, for the polynomial variable, to calculate the answer. I've been looking at the function y =...

Can anyone help me with this sum 1^10 + 2^10 + 3^10 ... +998^10 + 999^10 + 1000^10 = ? I read that when Gauss was a kid at school he solved the simplier problem of summing all the numbers in his head between 1 and 100, before the teacher and all the other kids, by the observing the...