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Topic: Calculating Pi using polygon sides sum / radius
Replies: 40   Last Post: Aug 2, 2013 5:27 PM

 Messages: [ Previous | Next ]
 JT Posts: 1,448 Registered: 4/7/12
Re: Calculating Pi using polygon sides sum / radius
Posted: Jul 31, 2013 7:02 AM

Den onsdagen den 31:e juli 2013 kl. 09:30:10 UTC+2 skrev William Elliot:
> On Tue, 30 Jul 2013, jonas.thornvall@gmail.com wrote:
>
>
>

> > If you create a hexagon with the radius of one, and recursively double the
>
> > number of vertices of the hexagon(have same radius as side length)
>
> > Maybe this is a valid way to calculate Pi?
>
> Given a regular n sided polygon, with distance from center to the vertices
>
> of r, the length of one side is 2r.sin pi/n and the total length of all the
>
> sides is 2rn.sin pi/n =
>
>
>
> Now lim(n->oo) 2r.pi.(sin pi/n)/(pi/n)
>
> = lim(n->oo) 2r.pi.(sin pi/n)/(pi/n) = 2pi.r
>
>
>
> For n = 6, sin pi/6 = 1/2, so 2*6r(1/2) = 6r is a crude first approximation
>
> for the circumference of a circle of radius r, giving approximately 3 for pi.

Well if you iterate in a loop double up the vertices you do a lot better then 3, smooth.

Date Subject Author
7/30/13 JT
7/30/13 JT
7/30/13 Peter Percival
7/30/13 JT
7/30/13 Richard Tobin
7/30/13 JT
7/30/13 Peter Percival
7/30/13 JT
7/30/13 JT
7/30/13 JT
7/30/13 JT
7/31/13 William Elliot
7/31/13 JT
7/31/13 Peter Percival
7/31/13 William Elliot
8/1/13 JT
8/1/13 JT
8/1/13 Virgil
8/1/13 Virgil
8/1/13 JT
8/1/13 JT
8/1/13 Virgil
8/1/13 JT
8/1/13 Virgil
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8/1/13 Shmuel (Seymour J.) Metz
8/1/13 Virgil
8/2/13 JT
8/2/13 JT
8/2/13 Virgil
8/2/13 JT
8/2/13 Virgil
8/2/13 Brian Q. Hutchings
8/2/13 Brian Q. Hutchings
8/2/13 Virgil
8/2/13 JT
8/2/13 Shmuel (Seymour J.) Metz
8/1/13 JT
8/1/13 Virgil
8/1/13 JT
8/1/13 Virgil