I've been trying to make an algorithm to find the number of all possible simple quadrilaterals in a N*M lattice. I already have a brute force solution but since this is a Project Euler problem I ...
Consider an arbitrary $n$- dimensional hypercube: If we select $n - 1$ corners of that hypercube and highlight all $(n - 2)$ dimensional elements that originate from each of the corners is it ...
I'm stuck with this problem. can anyone help me? A finite collection of squares has total area 4. show that they can be arranged to cover a square of side 1.
I want to define a labeling, by small natural numbers, of the 48 symmetries of a cube — affine transformations which do not change the volume it occupies. What is a ...
I have stumbled on an interesting problem. How many congruent rectangles on a plane can be arranged in such a way that they all touch each other but never overlap? I pondered this problem for a few ...
Edited for clarity: I thought I had a complete set of solutions to this: Cut a square into identical pieces so that they all touch the center point. It became clear, after some discussions, ...
Definition: A $n$-gon is simple if it has no self intersection and is in general position if no pair of its edges are parallel. It is clear that by extending the edges of each simple $n$-gon in ...
Assume you have a triangle in the plane defined by its three vertices at $(x_0,y_0)$, $(x_1,y_1)$, and $(x_2,y_2)$. Is there a general expression for the moments of the triangle, where the moments are ...