# Interesting Mathematical Find.

#### jnicholes

Hello,

I wanted to share something I find interesting with you all.

So, I was experimenting with making up math formulas, I like to do that in my spare time. I found something VERY interesting, (at least to me,) while doing this.

I was trying to find out on my own a regular polygon formula, to find out the ratio of the side length to the radius. My idea was to take the perimeter and divide it by the number of sides to get the side length. I then took the side length, squared it, then reversed the Pythagorean theorem to get the other two sides, which are of equal length and is the radius, so I divided the side squared by 2. This gave me the radius squared. I then got the square root of the radius squared. After that, I divided the perimeter/number of sides with the radius. Here is the formula I found.

(P/N)/ the square root of ((P/N)^2 /2)

To my surprise, no matter what I make P, (the perimeter,) and N, (the number of sides,) I always get the same answer. The answer is the square root of 2, which is 1.414213562.

I found this interesting.

If you are confused, here are 2 demonstrations to prove my point. The perimeter equals 17 in this example and the number of sides is 5 in this example.

(17/5)/ the square root of ((17/5)^2 /2)

3.4/the square root of(3.4^2 /2)

3.4/the square root of (11.56/2)

3.4/the square root of 5.78

3.4/2.404163056

1.414213562

Second Example, Perimeter equals 25, Number of sides equals 7

(25/7)/the square root of((25/7)^2 /2)

3.571428571/the square root of(3.571428571^2 /2)

3.571428571/the square root of(12.75510204/2)

3.571428571/the square root of 6.37755102

3.571428571/2.525381361

1.414213562

Whether I found a polygon formula or not, I find it interesting that no matter what P and N are, the answer in this formula is always the square root of 2, 1.414213562.

I hope all of you enjoyed reading this. Please tell me what you think, I dont mind learning more about math.

Jared

#### jnicholes

@Denis, thanks for showing me that. I found it very interesting. So, the square root of 2 is irrational. That was pretty interesting to read.

Thanks for Sharing that.

Jared

#### Denis

Math Team
Me and sqrt(2) are buddies, both being irrational !!

#### jnicholes

Truth be told, my mind is like the square root of 2 also. Sometimes I tend to think irrationally.

Jared