Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Calculate circumreference and area of circle without Pi is easy
Replies: 12   Last Post: May 9, 2013 12:49 AM

 Messages: [ Previous | Next ]
 JT Posts: 1,434 Registered: 4/7/12
Re: Calculate circumreference and area of circle without Pi is easy
Posted: May 6, 2013 10:43 PM

On 7 Maj, 04:23, JT <jonas.thornv...@gmail.com> wrote:
> On 7 Maj, 04:18, donstockba...@hotmail.com wrote:
>
>
>
>
>
>
>
>
>

> > On Monday, May 6, 2013 9:03:27 PM UTC-5, JT wrote:
> > > Knowing that a hexagon built by isocles we can split them into right
>
> > > triangles and have hy^2-0.5hy^2=b^2.
>
> > > And from there we create a new dodecagon knowing the difference
>
> > > between base and hypotenuse we can calculate required heights of new
>
> > > vertices, we plug it in and get hypotenuse of triangle forming new
>
> > > vertice.
>
> > > We repeat all this splitting hexagon, dodecagon, 24, 48, 96, 192...
>
> > > recursively until sought smoothness of the circle is aquired while
>
> > > adding vertices and triangle areas.
>
> > Only one calculation is needed if you just know pi.
>
> Yes but Pi is approximation, my answer would be a fraction and
> therefor exact for the sought and aquired smoothness.

Well a vertice dependent fraction relative the original hypotenuse of
hexagon. So if we set hypotenuse to 1 for any radius we get a general
solution fraction for the required smoothness, that need just be
multiplicated with the the split hexagon hypotenuse length to get the
circumreference.

Date Subject Author
5/6/13 JT
5/6/13 JT
5/6/13 donstockbauer@hotmail.com
5/6/13 JT
5/6/13 JT
5/7/13 JT
5/7/13 Richard Tobin
5/7/13 JT
5/7/13 Brian Q. Hutchings
5/8/13 Brian Q. Hutchings
5/8/13 JT
5/8/13 JT
5/9/13 Brian Q. Hutchings