The universe looks different at different scales therefore time and space must be discrete. If space was continuous, two items of different volumes would contain the same number of points, so measurement would not make sense. Calculus uses 'tending to' notation to avoid having to deal with the...
If the first of the r numbers is n, and n\equivm(mod(x)) where 0\leqx\leqr, then n+(x-m) is a multiple of x. Because x-m\leqr at least one of the r numbers will be a multiple of x. r! is the product of all such x.
Correction: I forgot about the non-consecutive bit.
If j(k) does not contain both 1 and 2, either 1 can be added or 1 can be swapped for 2. If this results in a pair of consecutive fibonacci numbers, the pair can be swapped for the next fibanacci number after that, and any new consucutive...
I guess that the fibonacci numbers are required to be distinct. Let j(k) be the set of fibonacci numbers summing to k. j(k+1) contains the extra element 1, unless j(k) already contains 1, in which case j(k+1) can be formed by replacing the 1 in j(k) with a 2, unless j(k) already contains a 2, in...
Fn=(\phin-(1-\phi)n)/\sqrt{}5
If Fn=\left\lfloor(4/9)(13/8)n-1/2\right\rfloor then 9(Fn-1/2)/4>(13/8)n. Since 13/8>\phi, the right hand side increases faster, and the right hand side for n=10 is already greater than the left hand side. 8 and 9 are the only integer solutions.
post #166
1. cos(t) and \sqrt{}1-cos2(t) are rational if cos(t)=a/c, with c=largest member of a pythagorean triple and a=one of the other members.
t=0, \pi, cos-1(3/5), cos-1(4/5), cos-1(5/13), cos-1(12/13), cos-1(8/17), cos-1(15/17), cos-1(12/20), cos-1(7/25), cos-1(24/25)
The only pattern I could be sure of is that the numbers of resistors for x=a/b is the same as for x=(b-a)/b. It also looks like b resistors are required when x=1/b and b is prime.
A few values I have found:
voltage no. of resistors
1/2 2
1/3 3
1/4 4...
Not sure whether to post in mathematics or physics section.
A circuit contains a cell of unit E.M.F. Use any combination of identical resistors in series and/or parrallel in order to create a voltage of x across a voltmeter connected anywhere on the circuit. Assume that there is no internal...
When a ball is thrown on the train, the 'missing' energy goes into pushing the train and the thrower when the ball is thrown. Whilst photons have no rest mass, the do have momentum, and the energy lost when they are red-shifted is used to push whatever emitted them in the opposite direction to...
1. If n=a.b.c...=a2+b2+c2 then a=b=c... (more explanation later when I have more time). Then if n has x prime factors, xa2=ax and ax-2-x=0. x<=4 since a>=2 (smallest prime number) and 25-2-5=3 and if a or x increases this answer increases. Then it only remains to check for solutions to all x...
Correction: Strings vibrate in more than one dimension, therefore the mass should be the sum of hf/c^2 for all frequencies f for vibration in each dimension.
Have I misunderstood something?
A string is a line along which a particle can vibrate. No particle has rest mass, but the string as a whole can obtain mass if the particle is vibrating at the speed of light, given by hf/c^2 where h=planck length, f=frequency, c=speed of light. The string for...
momentum of a photon=h/\lambda.
A photon cannot have rest mass. momentum=mv/sqrt(1-v2/c2. The denominator is 0 for light, so the momentum would be infinite if photons had rest mass.