I have the following inequality to solve for $R$ in terms of $\delta$ and $n$, with assumption that $n \geq 3$ and $\delta>0$:
$$-2 < 2 -\frac{16n\delta^{2}}{R^{2}\sin^{2}\frac{\pi}{n}} \left(nR^{2} - R\sin \frac{\pi}{n} - n\delta^{2}\right) < 2$$.
I try to use Reduce command to solve it. My Mathematica code is
Reduce[2 < 2 - 16*n*d^2*f[n, R]/(R^2*(Sin[Pi/n])^2) < 2, R]
which gives False. Trying to solve the two parts of the inequality separately also does not work, i.e. putting
Reduce[2 - 16*n*d^2*f[n, R]/(R^2*(Sin[Pi/n])^2) < 2, R]
gives the output that Mathematica is unable to solve "with the methods available to Reduce".
How could I modify my code to solve the above inequality?
f[n, R]? Also, are you missing a minus sign in the first reduce expression (2 < ...should be-2 < ...)? Can you make any assumptions on the values of the parameters (e.g. real, positive, negative, integer)? $\endgroup$ – MarcoB Jun 22 '16 at 15:58