1
vote
1answer
25 views

How does one solve arbitrary polygons, in the same sense as one solves a triangle?

Let us say you are given a polygon, and also are given some, but not all, of its angle measures and side lengths. How would one compute the following: If there is a finite number (zero inclusive) of ...
2
votes
1answer
38 views

Area of the intersection of regular pentagons

I was playing around in Geogebra and came up with an interesting problem. Take an arbitrary point $A$ and draw a circle with center $A$. Then draw any line through $A$. Call the points where the ...
0
votes
1answer
67 views

Calculating perimeter of n-sided regular polygons using only height?

Say you were drawing n-sided regular polygons on a square grid (first side you drew being flat always). You wanted any polygon you drew to be 100 units high, aka the uppermost point being y = 100. ...
0
votes
1answer
143 views

Internal polygon formed by drawing diagonals in a regular polygon

In an n-sided (n>4) regular polygon, label the vertices {0, 1, ..., n-1}. For each vertex i, draw a pair of diagonals: from i to (i+2) mod n and from i to (i-2) ...
3
votes
1answer
166 views

Polygon sine waves

So I came across this picture on Google+ and I wanted to understand further. I created an equation for the second wave, the one with the square. Here it is: $$y=\frac{\sin x}{\cos(\min(x \mod \pi/2, ...
1
vote
1answer
111 views

Rotation angle of regular polygon that has largest taxicab maginitude between all vertices

Firstly just to apologise, I posted this on mathoverflow before realising it was focused on research level mathematics. If I have a regular polygon that is centred at the origin. Then take the ...
5
votes
1answer
325 views

cyclic polygons & trigonometry

At one vertex of a pentagon inscribed in a circle of unit diameter (unit diameter, not unit radius) let the angles between adjacent diagonals be $\alpha,\beta,\gamma$, at the next, ...