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JT
Posts:
1,388
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 > <d6885fa13a344e7da18eb85727a65...@w5g2000vbd.googlegroups.com>, > > 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.



