Ben Alpert
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# 66 Comments

 Jul 30 comment Counting how many hands of cards use all four suits This is a fantastic solution that I hadn't thought of. Thanks! Jul 30 comment Are the “proofs by contradiction” weaker than other proofs? Related: math.stackexchange.com/questions/198. Jul 27 comment Proof of Angle in a Semi-Circle is 90 degrees Nice! Hadn't seen this proof before. Jul 25 comment Probability that two people see each other at the coffee shop Tom Stephens: In Mathematica, you can generate the above plot by running RegionPlot[x - 1/3 < y < x + 1/3, {x, 0, 1}, {y, 0, 1}, FrameTicks -> {{0, 1/3, 2/3, 1}, {0, 1/3, 2/3, 1}}] then selecting Save Graphic Asâ€¦ from the right-click menu to make a PNG. If you don't have Mathematica, you'll need to find some other tool. Jul 25 comment How can I randomly generate trees? And now there's no http://, which you need to make it a link. (I had it in my comment but it was stripped out.) Jul 25 comment Probability that two people see each other at the coffee shop I don't know which classes you're taking where this is a common homework question, but I just really like the graphical solution for this problem and so I thought I'd ask it so that someone could put up the solution. Jul 25 comment Picking cakes if we need at least one of each type I'd always heard this as a "ribbon cutting" problem, but that doesn't seem to be a standard term online. Looks to me like everyone teaches the including-zero variation first, but I find this one much more intuitive. Jul 25 comment Picking cakes if we need at least one of each type This is a variant on Casebash's question that can be solved by changing this problem slightly to fit into that problem's constraints and using that formula, but there's another solution that doesn't require changing the problem. Jul 25 comment How can I randomly generate trees? I think that link should just be www-cs-faculty.stanford.edu/~uno/fasc4a.ps. Somehow you got the Google tracking page in there when you copied the link. Jul 25 comment Probability that two people see each other at the coffee shop Nice. It's funny we both used Mathematica and then uploaded to imgur for the region plot. Jul 25 comment Probability that a stick randomly broken in two places can form a triangle All right. That's basically what I did to check your answer; I guess I was just thrown off by your change in names. Thanks for the clarification. Jul 25 comment Probability that a stick randomly broken in two places can form a triangle I'm actually confused as to how you arrived at 1/4 using your method. If you use the three inequalities from my answer (below), only 1/8 of the unit square satisfies all three. This doesn't work out for essentially the same reason as the Monte Carlo simulation, except this time, both x and y are chosen uniformly and 1-x-y is forced into a tiny range of values. How'd you get 1/4? Jul 25 comment What property of certain regular polygons allows them to be faces of the Platonic Solids? Oh, I misread your question completely! I thought you were asking, "Why is it that only regular polygons can be faces of the Platonic solids?". Jul 25 comment Probability that a stick randomly broken in two places can form a triangle Thanks! I was about to go to sleep but then I stumbled upon your question and the opportunity to solve it and figure out the mystery was just too great to pass up. :P Jul 25 comment Your favourite maths puzzles V pnyphyngrq gur ahzore bs cbffvovyvgvrf sbe obgu, naq vg ybbxf gb zr yvxr gurl'er gur fnzr. V'z fher gurer'f n terng rkcynangvba ohg V'z abg frrvat vg evtug abj. Jul 25 comment Your favourite maths puzzles Kaestur Hakarl: That's the fastest way that I know of. Jul 25 comment Balance chemical equations without trial and error? Just edited; better now? Jul 24 comment How many knight's tours are there? Tomer Vromen: I'd repost that as an answer. Jul 24 comment Why is the derivative of a circle's area its perimeter (and similarly for spheres)? This doesn't explain why the coefficients match up. Jul 23 comment Your favourite maths puzzles If the size is fixed, it's easy to create a tiling that prevents finding a monochromatic triangle, but if I remember correctly, the answer is unknown in the general case.