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Topic: Calculate angles, sides and areas for any regular polygon without
using trig functions and Pi

Replies: 9   Last Post: May 29, 2013 9:55 PM

 Messages: [ Previous | Next ]
 JT Posts: 1,448 Registered: 4/7/12
Re: Calculate angles, sides and areas for any regular polygon without
using trig functions and Pi

Posted: May 28, 2013 11:09 PM

On 29 Maj, 03:11, Ken Pledger <ken.pled...@vuw.ac.nz> wrote:
> In article
>
>  JT <jonas.thornv...@gmail.com> wrote:

> > Do you think i could calculate all the angles in turns and the lengths
> > of sides(perimeter) and area of any regular polygon without using
> > trigonometric functions and Pi?

>
> The perimeter of a regular hexagon  -  yes.
> The perimeter of any other regular polygon  -  no.
>
> The area of a square or regular dodecagon  -  yes.
> The area of any other regular polygon  -  no.
>
>    Ken Pledger.

So even by doing it for a 12 sided regular polygon i would surprise
you? You do realise that i can divide isoceles into right angled
triangle, using hypotenuse length i can extend the opposite side of
triangle and there will be a new right angled triangle formed with
known opposite and adjacent side and using them we get the new side
(it will be the hypotenuse). This we can do recursively for
6,12,24,48,96... and so on i hope your realise that. But we can also
calculate the triangles calculate for 18 30 36 42.. and so on.

And you did see 30 come up it will be handy since it will be used to
calculate the perimeter for 5 sided polygon.
I think i could write the program for multiples of hexagon in a day,
doing all the others require some thought so maybe a week or a month.
But it will be recursive solution so i expect when i solved it for 5,
it will be solved for all other primes.

Date Subject Author
5/28/13 JT
5/28/13 JT
5/28/13 Scott Berg
5/28/13 Ken.Pledger@vuw.ac.nz
5/28/13 JT
5/28/13 JT
5/29/13 RGVickson@shaw.ca
5/29/13 JT
5/29/13 JT
5/29/13 Brian Q. Hutchings