All Questions
14 questions
4
votes
1
answer
330
views
Billiard circuits in pentagons
A billiard circuit in a convex $n$-gon is a closed billiard path
of $n$ segments reflecting from consecutive edges of the polygon.
Every regular $n$-gon has such a billiard circuit:
Recently a ...
- 151k
10
votes
0
answers
177
views
Minimum reflection paths in a mirror polygon
Let $P$ be a simple, orthogonal polygon of $n$ edges, i.e., one whose edges meet at right angles,
and is non-self-intersecting;
also known as a rectilinear polygon.
Treat every edge of $P$ as a ...
- 151k
7
votes
1
answer
498
views
Is there a bicyclic irregular pentagon in integers?
Is there a bicyclic irregular pentagon in integers, i.e. is there a pentagon, the length of each side is integer and unique such that it has a circumcircle and an inner circle as well?
If it does ...
- 71
14
votes
0
answers
270
views
Regular $n$-gon with diagonals: bounds on area of largest cell?
Consider a regular $n$-gon of side length $1$ with diagonals. Here is an example with $n=11$ (from geogebra applet).
I've been trying to find, in terms of $n$, bounds on the area of the largest cell, ...
- 3,527
15
votes
2
answers
779
views
How to characterize the regularity of a polygon?
In my research, I've recently started to play with Voronoi tessellations. I currently have a Python code that creates the tessellation and I am trying to color the polygonal regions according to their ...
- 161
4
votes
0
answers
232
views
Illuminating a just-barely irrational polygon
As has been discussed earlier on MO,1,2
recently an impressive advance was proved concerning
internally illuminating a mirrored polygon.
Here is the result:
Let $P$ be a rational polygon.
Then for ...
- 151k
4
votes
1
answer
332
views
Construct closed chain of $k$-gon around $n$ points-$n, k$ are odd primes number
Question 1: I am looking for a proof of the conjectures 1, 2, 3 as follows?
Question 2: In conjecture 3, in general case, I can not give a formula of $X$. But I think, If $n, k$ are odd primes number ...
- 1,776
4
votes
1
answer
266
views
A closed chain of $2n+1$-gon around $2n+1$-points
I posed a generalization of Theorem 3.2 In my paper
Conjecture: Let $P_1, P_2,....,P_{2n+1}$ and $O$ be $2n+2$ points in plane. Construct a chain $2n+1$ regular ${2n+1}$-gons $A_{1\;1}A_{1\;2}...A_{1\;...
- 1,776
6
votes
1
answer
2k
views
Given a set of 2D vertices, how to create a minimum-area polygon which contains all the given vertices?
Not sure whether this question belongs here or math.stackexchange.
You can assume that all the vertices are unique. The given vertices can be the vertices of the polygon, thus they do NOT have to be ...
- 163
10
votes
1
answer
9k
views
Get Largest Inscribed Rectangle of a Concave Polygon
I'm looking for an algorithm to find a set of largest inscribed rectangles of a concave polygon where each rectangle must be collinear with one of the edges of the polygon.
In other words, I want to ...
- 325
6
votes
1
answer
767
views
Using mirrors to make a non-convex polygon visible from a fixed interior point
Take a point $A$ inside a non-convex polygon $P$. Is it always possible to place a finite set of mirrors given by straight segments (not necessarily along the boundary of $P$, any position inside $P$ ...
- 17.9k
32
votes
5
answers
2k
views
Nonconvex manhole covers
One common reason given for the circularity of manhole covers is that they can't fall through the manhole. For convex manhole covers, this property is equivalent to having constant width — if ...
- 5,275
2
votes
4
answers
8k
views
Compute the Centroid of a 3D Planar Polygon
Given a list of 3D coordinates that define the surface( Point3D1, Point3D2, Point3D3, and so ...
- 381
19
votes
5
answers
21k
views
Dividing a square into 5 equal squares
Can you divide one square paper into five equal squares?
You have a scissor and glue. You can measure and cut and then attach as well. Only condition is You can't waste any paper.
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