Viète in 1543 derived a representation for

involving a sequence of nested square roots. The formula is displayed in the graphic. The underbrace signifies that the expression above it contains

square roots. For finite values of

, the formula represents the perimeter of a regular polygon of

sides inscribed in a circle of unit diameter. For a 1024-sided polygon, corresponding to

, Viète computed the value

, accurate to 6 significant figures. This Demonstration allows you to extend the result up to

. The capability of

*Mathematica* to compute multiply nested functions is exploited. With

, the underbraced form can be computed using

Nest[,, ].