@sarielhp Yeah, it was Erel who asked me the question (I hadn't seen his post). This is the solution Erel and I came up with: If the polygon has holes make some cuts so you get a simple polygon, as you say. Then triangulate the polygon, and connect the triangle centers so you get a tree T. T cuts the polygon into a topological annulus. You can continuously sweep the annulus as in your answer
BTW that still-life he smashes the glider at, at 3:14 in the video, is mine😀
Derek Muller's latest Veritasium video is simply amazing! In half an hour he accurately explains Cantor, Gödel, and Turing, with beautiful animations. All the more amazing given that his original background is physics https://youtu.be/HeQX2HjkcNo
@11011110 Nice! The article on Kirchberger's theorem could mention the following equivalent formulation: If the convex hulls of two point sets intersect, then there exist subsets of them, of total size d+2, whose convex hulls also intersect
@11011110 At my institution the administration got so excited about online classes that they want to keep them after covid is over :)
Tomorrow I'll be talking about fusible numbers and Peano Arithmetic at the Steklov Math Institute's logic seminar, in Moscow. Via Zoom
Exit strategy idea that might beat the coronavirus: Make people alternate between one week of activity and one week of lockdown. That way, most infected people will become infectious when they're in lockdown.
In these days in which "exponential growth" has such ominous connotations, we are pleased to announce our new paper which includes fast-growing functions in a much lighter setting. Fusible numbers and Peano Arithmetic. https://arxiv.org/abs/2003.14342 . Joint work with @jeffgerickson and @alreadydone
For the first time in history, the EuroCG workshop is being held in online-only format. Here is my talk: https://youtu.be/5X_0I3GqI4U
Consider the algorithm "M(x): if x<0 return -x, else return M(x-M(x-1))/2". This algorithm terminates for all real x, though this is not so easy to prove. In fact, Peano Arithmetic cannot prove the statement "M(x) terminates for all natural x". Paper to come! Joint work with @jeffgerickson and @alreadydone
@bremner Me, a Mathematica user for decades: Why yes, (#^%%)! & /@ %%% seems like a perfectly reasonable thing to write, why do you ask?
@11011110 Right. There are many other difficulties. Even for the ACSF itself, existence and uniqueness of the flow past singularities has not been proved, only for the CSF.
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