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[
,
, 
].
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