# Questions tagged [polygons]

For questions on polygons, a flat shape consisting of straight lines that are joined to form a closed chain or circuit

995 questions
Filter by
Sorted by
Tagged with
28 views

### segments of a parabolic umbrella

I would like to build a kind of parabolic umbrella. Therefore I am trying to calculate the shape of the fabric parts. My mathematical approach to this problem was to slice a parabolic surface along it'...
22 views

### Only 5 platonic hedrons, connectivity only proof?

I am reading a course on discrete differential geometry and found this neat problem: After thinking about it for 15 minutes curiosity got the better of me and I cheated. And here's one possible proof:...
26 views

### Given an n-sided polygon, how would you random sample points within it?

I would like to random sample points within an n-sided polygon. One idea I've thought of is to discretize the area of the n-sided polygon with triangles. I can assign each triangle a unique number in ...
19 views

### Finding perimeter of polygon inscribed in circle

n equally spaced points are taken on the circumference of a circle of radius 1. How do you find the perimeter of the resulting regular polygon obtained by joining the n points in order?
23 views

### Line picking in a regular polygon

What is the average distance between two random points in a regular polygon with $n$ sides? The length of each side is $l$. (Integration is not allowed). We know: If $n = 4$ (square), the answer is (...
11 views

### Raising Polygon Matrices to powers

Suppose we have a matrix $M$ that is of dimension $n * n$. Clearly $M$ has the shape of a square. Considering $M$ can be raised to any $k$-th power, and thus $M^k$ is also a $n * n$ square matrix, is ...
79 views

### Least triangular convex polygon

(This question is based on a question posed in a math riddle post on Reddit.) Let $P$ be a convex polygon. Let the non-triangularity of $P$ be the minimum area of the symmetric difference (shown with ...
60 views

### Convex set that cannot be approximated by a polygon

In $\mathbb{R}^2$, show that there exist no polygon containing the set $C = \{ (x,y) \in \mathbb{R}^2 | y \geq x^2\}$ and included in $C + B(0,1)$ where $B(0,1)$ is the open unit ball. Intuitively, we ...
22 views

### Splitting a convex polygon of n sides into an odd or even number of smaller polygons.

There is a n sided convex polygon.the number of ways in which we can split this polygon into an a)odd number of smaller polygons such that every vertex of the smaller polygon(smaller polygon means ...
71 views

36 views

### planar loop shapes

I know if I stick two pins on a paper, and trace a taut loop around them, I get an ellipse. With one pin, I get a circle. Question is, are there names for shapes I get if I trace a taut loop around 3, ...