I need to find: a spherical line that passes through the points 0,0 and 8,8 and the distance of the line between those two points must be exactly 12 I imagine the answer will b …

Inspired by this question, I would like to determine the probability that a random knot of 6 unit sticks is a trefoil. This naturally leads to the following question: Is there a …

Are there tetrahedra which can be subdivided into three parts similar to the original? I believe this would require splitting one face into three parts. I know some types of tetrah …

In A Generalization of Brouwer's Fixed Point Theorem by Shizuo Kakutani, he defined $S^{(n)}$ be the $n$-th barycentric simplicial subdivision of $S$. In which $S$ is an $r$-dimens …

I have a unit cube, and operating in the continuum limit (i.e. not on a lattice), I sequentially place spheres of some radius $r$ inside the cube until a filled volume "jamming lim …

Let $ \Omega $ be an open and bounded subset of $ \mathbb{R^n} $, and let $ f:\Omega \to \mathbb{R} $ be a continuous function. I'm looking for some (preferably, minimal) condition …

This problem cropped up in the context of scale-insensitive methods for generating random variables. Let $X=R^n \cup \{\infty\}$. Suppose we consider a set of transforms $\cal{T} …

By  lattice  I'll mean  Birkhoff lattice. The two classical equational classes of lattices are modular lattices and distributive lattices. The old problem used to b …

I'm interested in some instances of the following problem. Let $n \geq 2$, and suppose we draw $k \geq 2$ vectors $v_1, \dots, v_k$ uniformly at random from the $n$-dimensional …

The Minkowski-Hlawka theorem (as stated by Gruber in his lovely book Convex and Discrete Geometry) says that if $S$ is a Jordan measurable set in $\mathbb{R}^n$ with volume < 1. …

Is it true that of all $n$-simplices with edge lengths greater than or equal to some parameter $s$, the regular simplex with edge lengths $s$ has the smallest circumradius? It seem …

I am looking for an elementary derivation of the formula for the area of a geodesic triangle lying in a surface of constant curvature $\kappa$, depending on the angles and side len …

I have two boundaries of two planar polygons , say,B1 and B2 of polygons P1 and P2(with m and n points in Boundaries B1 and B2). I want to find out if the Polygons overlap or not.I …

Mamikon's visual calculus (see Mamikon, Tom Apostol, Wikipedia) is a very beautiful and surprisingly efficient tool. The basis is Mamikon's theorem. The area of a tangent swee …

When trying to develop an algorithm for a program, I got with the following problem: Determine the approximate location of $O$, if you can take finite samples $P_n$ from known loc …