Area Regular Polygons

Science 21 Sep '17 23:29
1. 21 Sep '17 23:29
I developed a formula for finding the area of any regular polygon knowing either the length of one side or its perimeter.

I've not seen it before so I was wondering if anyone here has. I know it is out there but I've not seen it.

Polygon with n sides...

n/4 x side squared x tan((180-360/n)/2)

Going off of memory here while sitting in a parking lot but I think that's it.
2. Soothfast
0,1,1,2,3,5,8,13,21,
22 Sep '17 02:42
I developed a formula for finding the area of any regular polygon knowing either the length of one side or its perimeter.

I've not seen it before so I was wondering if anyone here has. I know it is out there but I've not seen it.

Polygon with n sides...

n/4 x side squared x tan((180-360/n)/2)

Going off of memory here while sitting in a parking lot but I think that's it.
Looks like a general formula is here:

http://www.mathwords.com/a/area_regular_polygon.htm
3. 22 Sep '17 02:50
Originally posted by @soothfast
Looks like a general formula is here:

http://www.mathwords.com/a/area_regular_polygon.htm
Their cot term is much less complicated but much less clear.
4. 22 Sep '17 06:30
Their cot term is much less complicated but much less clear.
n * r^2 * tan(180/n) looks quite clear to me.
5. 22 Sep '17 11:371 edit
Originally posted by @fabianfnas
n * r^2 * tan(180/n) looks quite clear to me.
May look clear to you but it is wrong.

My equation was based on side length not radius.
6. 22 Sep '17 12:034 edits
May look clear to you but it is wrong.
how so?

My equation was based on side length not radius.

That doesn't make that formula wrong.
If you can deduce (which I haven't) the maths relation between the radius and the length of the side then you should be able to algebraically derive the formula based on the length of the side from that link formula.
7. 22 Sep '17 12:09
Originally posted by @humy
how so?
I explained why. Formula based on side length not radius.
8. 22 Sep '17 12:10
Originally posted by @humy
how so?

My equation was based on side length not radius.

That doesn't make that formula wrong.
If you can find the maths relation between the radius and the length of the side then you should be able to algebraically derive the formula based on the length of the side from that link formula.
You are trying to reframe the topic.
9. 22 Sep '17 12:138 edits
I explained why. Formula based on side length not radius.
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; ðŸ™‚ I do that a lot.
10. sonhouse
Fast and Curious
22 Sep '17 13:181 edit
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; ðŸ™‚ I do that a lot.
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 paper pointed out and I think my formula still a bit simpler due to the use of a new constant.

As an aside, I have not heard from Gandhi about your distribution problem. He is no doubt very busy right now with a dozen students and his own ongoing research projects.
11. 22 Sep '17 19:414 edits
Originally posted by @sonhouse
Still, you have to hand it to him for coming up with a way different from the approved method.
yes, I do.
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 paper pointed out .

I repeatedly have had a similar experience but not with physics; I again and again totally independently came up with what I thought was a totally original way to solve a computer problem or do a computation more efficiently and got really excited thinking it was worth me writing about it and making it public but only to find out a bit later its an old idea and someone else has beat me to it by several decades. I got wise to that and now I am always careful to check if any of my independently derived ideas are really original before trying to do something with them. That is why I keep asking on these forums words vaguely of effect "...but is this really new? ".
12. Soothfast
0,1,1,2,3,5,8,13,21,
22 Sep '17 20:071 edit
May look clear to you but it is wrong.

My equation was based on side length not radius.
You have to make a simple substitution to get the formula in terms of side length: area A is given in terms of radius of circumcircle R, but on the same page R is given in terms of side length s:

R = (s/2)csc(180/n).
13. Soothfast
0,1,1,2,3,5,8,13,21,
22 Sep '17 20:111 edit
Originally posted by @humy
yes, I do.
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 paper pointed out .

I repeatedly have had a similar experience but not with physics; I again and again totally independently ca ...[text shortened]... That is why I keep asking on these forums words vaguely of effect "...but is this really new? ".
If you believe you've discovered something exciting in mathematics that took less than a week to derive, chances are there's either a mistake in your work or someone has already discovered it.
14. 22 Sep '17 20:235 edits
Originally posted by @soothfast
If you believe you've discovered something exciting in mathematics that took less than a week to derive, chances are there's either a mistake in your work or someone has already discovered it.
I usually discover its the latter. However, I know for a fact (because I did thorough checks) that at least some of by discoveries (that will be published) are original and I have checked the validity of each in several completely different ways (always both algebraically (preferably in at least 2 different ways; 3 ways if I can manage it) and numerically and in many cases even with computer simulations) to make sure it isn't a mistake. I wouldn't DARE put anything in my book that I haven't so checked to make absolutely sure it is correct else if just one of the things in my book is wrong then that would be a horrible blemish on my work. If I cannot be absolutely sure of it, I throw it out.
15. 22 Sep '17 22:361 edit
Originally posted by @soothfast
You have to make a simple substitution to get the formula in terms of side length: area A is given in terms of radius of circumcircle R, but on the same page R is given in terms of side length s:

R = (s/2)csc(180/n).
The purpose was to find the area using perimeter and specifically perimeter.

Radius and apothem based formulas are common enough.