My Math Forum Derivation of Alternative Viète Formula (digits of pi)

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December 14th, 2013, 06:29 PM   #1
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Derivation of Alternative Viète Formula (digits of pi)

Hello all,

Maybe you have heard of Viète's Formula http://en.wikipedia.org/wiki/Vi%C3%A8te's_formula,

which if you don't remember, has an alternative version: $\pi= \lim_{n\rightarrow\infty}2^{n}\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2+...}}}}}$

Expressions of this type are usually weaseled through some tricky trig identity, or by Euler's formula, which is fun. I present here a purely geometrical "derivation", if you mathematicians don't my mind my laziness as a physicist. Please see the attached PDF.

AND... if you know of a place where this exact derivation is already done in detail, please show me.
Attached Files
 Pi as Nested Roots (WFB).pdf (143.1 KB, 11 views)

 Tags alternative, derivation, digits, formula, viete

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