Intereting Posts

Elementary number theory: sums of primes and squares
Showing that $f = 0 $ a.e. if for any measurable set $E$, $\int_E f = 0$
Understanding the proof of $|ST||S\cap T| = |S||T|$ where $S, T$ are subgroups of a finite group
Isomorphism from $\mathbb{C}$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.
How a group represents the passage of time?
A probabilistic game with balls and urns
A golden ratio series from a comic book
Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$.
Prove that the congruence $x^2 \equiv a \mod m$ has a solution if and only if for each prime $p$ dividing $m,$ one of the following conditions holds
Product of Two Metrizable Spaces
Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$
Catalan numbers – number of ways to stack coins
reference for multidimensional gaussian integral
Calculating a basis of vector space $U \cap V$
Isotropic Manifolds

I’m looking for the algorithm that determines the fact that a polygon has self intersection or hasn’t. I’m not needed in calculation of the intersection points coordinates or how many intersection points there are.

- Find intersection of two lines given subtended angle
- $7$ points inside a circle at equal distances
- Finding point coordinates of a perpendicular
- Find the number of simple labeled graphs which have no isolated vertices
- Is it possible to divide a circle into $7$ equal “pizza slices” (using geometrical methods)?
- Is there a Möbius torus?
- Partition the points
- Prove if there are 4 points in a unit circle then at least two are at distance less than or equal to $\sqrt2$
- Maximum number of equilateral triangles in a circle
- Algorithms for Finding the Prime Factorization of an Integer

There is the obvious algorithm of comparing all pairs of edges, which is $O(n^2)$ but probably is ok for small polygons. There is the Bentley–Ottmann algorithm sweep algorithm, which is $O(n \log n)$ but is harder to implement and probably only needed if $n$ is large. I think there is a $O(n)$ algorithm by Chazelle, which is very likely to be impractical.

In any case, note that you can test whether two line segments intersect *without* finding the intersection point. It’s a simple matter of comparing signs of a few determinants. See http://algs4.cs.princeton.edu/91primitives/.

- Smallest positive element of $ \{ax + by: x,y \in \mathbb{Z}\}$ is $\gcd(a,b)$
- Exercises on Galois Theory
- How to find a function mapping matrix indices?
- Reference request for Algebraic Number Theory sources for self-study
- Finding a pair of functions with properties
- For every integer $n$, the remainder when $n^4$ is divided by $8$ is either $0$ or $1$.
- Existence of Holomorphic function (Application of Schwarz-Lemma)
- Meaning of mathematical operator that consists of square brackets with a plus sign as a subscript
- Ideal Generated by Three Elements in Polynomial Ring
- Volterra integral equation with variable boundaries
- Johann Bernoulli did not fully understand logarithms?
- What are Quantum Groups?
- Compute center, axes and rotation from equation of ellipse
- When is $x^{\alpha}\sin(x^{\beta})$ uniformly continuous for $\alpha, \beta > 0$?
- Variety generated by finite fields