Find the sum of the fiftieth powers of all sides and diagonals of a regular 100-gon inscribed in a circle of radius R.
(In reply to halfway through the general solution
by Michael Kornrade)
I repeat the two important formulas:
Sv = (2*R)^p * SUM( [sin( k * pi / N)]^p ) for k = 0...N-1
S = N * Sv / 2
For the moment, I cannot make the formula more compact, for p > 2...
Go to http://mathworld.wolfram.com/Sine.html to find compact formulas for p = 1 (eq.16 or eq.21) and p = 2 (eq.20).
So, in a Matlab computation for N = 100, p = 50 and R = 0.5 I get:
Sv = 11.2275172659217...
S = 561.375863296086...
Edited on January 10, 2013, 7:09 pm
Edited on January 10, 2013, 7:12 pm