We consider regular n-gons with a fixed circumference 4. Let rn and an respectively be the distances from the center of such an n-gon to a vertex and to an edge.
(a) Determine a4,r4,a8,r8.
(b) Give an appropriate interpretation for a2 and r2
(c) Prove that a_{2n}\equal{}\frac{1}{2} (a_n\plus{}r_n) and r_{2n}\equal{}\sqrt{a_2n r_n}.
(d) Define u_0\equal{}0, u_1\equal{}1 and u_n\equal{}\frac{1}{2}(u_{n\minus{}2}\plus{}u_{n\minus{}1}) for n even or u_n\equal{}\sqrt{u_{n\minus{}2} u_{n\minus{}1}} for n odd. Determine n→∞limun. limitalgebra proposedalgebra