All Questions

Let R be a region on a hypersphere. Each point A of the hypersphere is associated with a vector pointing to A and with origin at the centre of the hypersphere. So let me identify each point with a ...

I was fascinated by the solutions of Problem 8 of the IMC 2021 contest, which can be summarized as: Theorem 1. Let $v_1,\dotsc,v_N$ be distinct unit vectors in $\mathbb{R}^n$ such that among any three ...

I need an efficient method to construct a (hyper)rectangle inside a polytope with a lot of dimensions (say $100 < d < 1000$). Ideally I'd want the biggest possible rectangle, but as I don't ...

I've found a formula for a scalar product in barycentric coordinates which I think is pretty cool. I hope that it's new. Is it? Suppose that you have points $x_1,\dots,x_n$ sitting in general position ...