Recent content by scienalc

Let's say there is a set of n elements, S. P is a subset of S, with m elements, and satisfies some conditions, i.e. c1 < f(P) < c2 and g(P) < c3, where f and g are some functions on the elements of P and c1, c2 and c3 are constants. For practical purposes, S is represented as a sorted array of...

Thanks for providing this link, I found it really useful. Basically, the reference points aboard the ship and on Earth can't be treated as equivalent, because the ship has to change inertial frames when turning around, so, after the turn is completed, it needs to readjust its clock. Particularly...

The popular thought experiment states, that if of two identical twins one is left on Earth an the other is embarked on a spaceship and sent into open space at near-c velocity, time for the traveling one will pass slower than for the one left on earth, due to the speed. On the other hand, time...

Hm... that part is perfectly clear. As you state, a 1000 binary and a 8 decimal are the same number, but a different representation. So, if we take the first few decimals of pi 3.1415926535... and I wanted to extract the fourth digit, in this case 5 (decimal), would I be correct to assume using...

Thanks a lot, that helped me. Could you clarify issue 3 a bit (since it effectively summarizes number 1 as well)?

Yes, the wiki article was one of the sources I consulted. However, it did not explain the issues I listed. I did get the idea behind the use of the modulo function, though

Hello everyone, I have trouble understanding how to apply the BBP formula, i.e. actually compute the n-th digit of pi. \pi=\sum\frac{1}{16^{k}}(\frac{4}{8k+1}-\frac{2}{8k+4}-\frac{1}{8k+5}-\frac{1}{8k+6}) where the sum uses k from 0 to ∞. I've read a few explanations how to adapt it...

Thanks a lot, guys. I looked up the n-body problem, seems to very well describe my problem. The relation voko provided is the one mentioned in various sources. Now, regarding the minus sign, I wonder why is the direction of the force/acceleration/velocity determined by rj-ri, and not the...

This is the case. If I have n objects in a system and a new object A enters the system with its velocity v, obviously, everyone of the n objects would interact with A affecting its velocity. My plan was to calculate the isolated effect of each of the n objects on A and then superpose the...

Yes, the notation is what I had in mind, the only thing that confuses me is that you used r cubed. Is that a typo or am I missing something obviously huge? So, then I would have to regard the problem as a differential equation like: Gm2 = r2(t)d2r/dt2 is that correct?

Thanks for the reply. Can you please clarify it a bit more for me. I assumed that in (2) is a situation like in the Law of Gravity, where we have a force (vector) on the left side and on the right we have the distance, a scalar, but one that is associated with a unit vector (in the opposite...

Homework Statement I need to develop a macroscopic gravity simulation software. I have problems with representing vectors in a programming language (c++), because I need do develop my own mathematical infrastructure for the project. I asked for the Cartesian coordinates, but would also have...

Hi, I have to write an ~10 pages essay on Computabilty theory as part of my PhD logic course. Given that that is a very broad topic and that I found very little information on the internet, I would like to ask if anybody has had any experience with that? My primary issue would be which...

thanks a lot again for the quick answer (and the µ of course) :D it's ok, i found my mistake, the correct value for distance should be 33.3m (you get that from the equation x(t) = (µ*g*t^2)/2 which represents traveled distance in dependence of time, and use that t = 3.33s) funny thing, this...

thank you actually, I was assuming that what you said, and took only the frictional force into account: ma = -(mi)mg, then dv = -(mi)gdt, and from there (first integral v1=20 m/s -> v2=0 and second t1=0 -> t2=t) I got v(t) = (mi)gt (1) then the required time i calculated as: t = v1/((mi)g) =...