Area Regular Polygons

Originally posted by @humy
how does that make the formula wrong?
Why is the formula wrong if it is based on the radius and not the side?
The formula is correct; just not the one you asked for.
This is just semantics but you should say that as "correct but not the one I ask for" (or alternative words of that effect) and not just "wrong". I apologize for being annoyingly pedantic; 🙂 I do that a lot.

He was making reference to my comment about the cot term in the link's formula.

He referenced the wrong formula.

My use of tangent is directly linked to the polygon. The link's use of cot must be a substitution that makes things work neatly but does not make sense simply looking at a polygon.

Originally posted by @sonhouse
Still, you have to hand it to him for coming up with a way different from the approved method.

I did a similar thing with gravitational lensing, I came up with a formula for calculating focal length based on radius and mass, introducing a new constant in it only to be told here it was not original, but at least it was my own work independent of the pape ...[text shortened]... He is no doubt very busy right now with a dozen students and his own ongoing research projects.

I developed a method of finding the equation for a polynomial based sequence a few years ago. It uses subtraction of terms, the rebuild using integration. It required one more term than the degree of the polynomial.

Or I should say reinvented a technique.

Originally posted by @eladar
The purpose was to find the area using perimeter and specifically perimeter.

Radius and apothem based formulas are common enough.

Isn't that easy? Perimeter P of a regular n-gon with sides of length s is simply P=n*s, so replace s with P/n in the formula.

Originally posted by @soothfast
Isn't that easy? Perimeter P of a regular n-gon with sides of length s is simply P=n*s, so replace s with P/n in the formula.

Yep, that was the idea. Then after squaring one set of n's cancel, leaving p squared over 4n. Taking the limit as n approaches infinity would result in the area of a circle. Have no clue how that would work out.

Originally posted by @eladar
Yep, that was the idea. Then after squaring one set of n's cancel, leaving p squared over 4n. Taking the limit as n approaches infinity would result in the area of a circle. Have no clue how that would work out.

Even the old Greeks knew that...

Originally posted by @fabianfnas
Even the old Greeks knew that...

Yes, but they did not know how to take linits and were limited to measurements to calculate circumference.

As for your original response of clarity, it shows you have no clue how my tangent term was derived.

Just did a quick set of calculations and if they are right, using the link's nicer trig component....

The limit as n approaches infinity of n*tan (180/n) equals pi.


Fixed, forgot to square my 2.

Originally posted by @eladar
Just did a quick set of calculations and if they are right, using the link's nicer trig component....

The limit as n approaches infinity of n*tan (180/n) equals pi.


Fixed, forgot to square my 2.

Just tested it in my ti84 and it works.

So sweet. I always wondered how you can calculate pi from an equation and I derive one.

Interesting that if I use my original equation which calculates pi with n/tan ((180-360/n)/2), the ti 84 gets an error with 99999999 but an answer for the tan (180/n)

Originally posted by @eladar
The purpose was to find the area using perimeter and specifically perimeter.

Radius and apothem based formulas are common enough.

Does your formula work in non-Euclidean spaces, too?

Originally posted by @moonbus
Does your formula work in non-Euclidean spaces, too?

I've never studied them so I don't know. Based on what little I just read about them I doubt it. Distances are not consistent so no distances formulas should work.

The post that was quoted here has been removed

Yep, apothem is trivial. I did it only with a side, not apothem. Evidently an adult female was unable to see that.

Originally posted by @eladar
Yes, but they did not know how to take linits and were limited to measurements to calculate circumference.

Still old news...