Last time I introduced a neat little question: Is it true that every infinite path in contains arbitrarily long arithmetic progressions? For example, in the following path, the squares colored in red have coordinates , which form an arithmetic progression of length 3, where every two consecutive points differ by . As it turns out, … More Arithmetic progressions in space!
Here is a neat question that I stumbled upon during my academic random walk. A sequence of vectors is called an arithmetic progression of length k if there exists a vector such that . In other words, an arithmetic progression in is exactly the generalization you would expect of your good ol’ high-school arithmetic progression … More Arithmetic progressions in space?