Re: Archimedes Pi Algorithm

dave <davidsnow6767@xxxxxxxxxxx> writes in article <27284186.1138680771203.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx> dated Mon, 30 Jan 2006 23:12:21 EST:
>Hi, I was wondering if anybody could explain to me how to generally use
>Archimedes Algorithm to calculate pi. My main problem is: how can you find the
>perimeters of an n-sided polygon inside and outside a unit circle without using
>trigonometry??? Any help on this would be greatly appreciated!

You can't do it without trig, but you can do enough trig without calculus
to do the approximation.

You probably know the cosine for certain angles (pi/2, pi/3, pi/4, pi/6).
Use the half-angle formula to get as small an angle as you need.

http://mathworld.wolfram.com/Half-AngleFormulas.html

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
.

Relevant Pages

  • Re: Archimedes Pi Algorithm
    ... generally use Archimedes Algorithm to calculate pi. ... how can you find the perimeters of an n-sided polygon inside and outside a unit circle without using trigonometry??? ...
    (sci.math)
  • Re: Veritas
    ... geometry and trig. ... Geometry is at least worth studying for entire semesters at a time. ... using the unit circle. ... And with all due respect to your math professor, ...
    (rec.arts.sf.written)