Category Archives: Pretty little things
Here I describe the solution to the problem from the last post. Spoilers!
I came up with what seems quite a beautiful geometric construction solving the problem described below. On a compact convex set consider the function where we denote In other words, “hanging” in the point we measure the “width” of the … Continue reading
Discovered an interesting discussion on math.stackoverflow.
There is an amazing result in the theory of social choice called Arrow’s impossibility theorem. Suppose we have a set of possible alternatives, say, election candidates, and voters. Each voter organizes its individual preference list over that is, a linear ordering of (suppose … Continue reading
Fix an integer Cut hypercube with an arbitrary -dimensional affine subspace of general position. How many vertices has the obtained polyhedron? It occurs that grows polynomially, and not exponentially, with The goal of this … Continue reading
It turned out that the proof of Welch bound for mutual coherence, which I previously mentioned here, is very simple. Apparently it can also be obtained from Gershgorin circle theorem.
Found a nice Greek-style purely geometrical proof of the main property of stereographic projection, the fact that it preserves circles.