Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Trying to find perimeter of a regular pentagon
Replies: 36   Last Post: May 31, 2013 9:26 PM

 Messages: [ Previous | Next ]
 JT Posts: 1,448 Registered: 4/7/12
Re: Trying to find perimeter of a regular pentagon
Posted: May 28, 2013 6:24 PM

On 28 Maj, 23:24, Ken Pledger <ken.pled...@vuw.ac.nz> wrote:
>
>  130bcd <carl.sundqu...@gmail.com> wrote:

> > .... I have unsuccessfully tried to find the perimeter of a pentagon. The "radius"
> > to the vertices is 130, which I tried to convert into 5 triangles but I can't
> > find a formula for determining the length of the 3rd side of an isosceles
> > triangle.

>
> > The two equal length sides would, of course be 130 and the angle between them
> > would be 72....

>
>    If a regular n-gon is inscribed in a circle of radiu r, then each
> side of the n-gon has length  2r.sin(pi/n).  In your case that means
> 260.sin(pi/5)  or  260.sin(36 degrees).
>
>    That can actually be expressed in terms of square roots if you like,
> since  sin(36 degrees) = (1/4)sqrt(10 - 2.sqrt(5)).  Such expressions
> involving sqrt(5) underlie the construction of the regular pentagon by
> straightedge and compasses (Euclid IV.11, or a neater construction by
> Ptolemy).
>
>       Ken Pledger.

I see your formula use Pi so i guess your formula can only calculate
the perimeter to the precision of the given Pi and same would go for
the area?
Would it not be beneficial finding a formula using fractions, that
could calculate the perimeter as well as area exact, without using a
couple of billions of decimalpoints on Pi?

Except from being accurate it sure would put an ease to the
calculation machinwise or humanwise.

Date Subject Author
5/28/13 130bcd
5/28/13 JT
5/28/13 JT
5/28/13 Barry Schwarz
5/28/13 JT
5/28/13 JT
5/28/13 JT
5/28/13 JT
5/28/13 Ken.Pledger@vuw.ac.nz
5/28/13 JT
5/28/13 Ken.Pledger@vuw.ac.nz
5/28/13 David Bernier
5/28/13 Brian Q. Hutchings
5/28/13 JT
5/30/13 RGVickson@shaw.ca
5/31/13 Brian Q. Hutchings
5/31/13 JT
5/31/13 JT
5/31/13 JT
5/31/13 JT
5/31/13 JT
5/31/13 JT
5/31/13 Brian Q. Hutchings
5/28/13 JT
5/28/13 JT
5/28/13 Brian Q. Hutchings
5/28/13 JT
5/28/13 Brian Q. Hutchings
5/28/13 JT
5/29/13 Richard Tobin
5/29/13 JT
5/29/13 Richard Tobin
5/29/13 Brian Q. Hutchings
5/29/13 JT
5/29/13 Brian Q. Hutchings
5/30/13 Graham Cooper
5/30/13 RGVickson@shaw.ca