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 Oct 31 awarded Autobiographer Jun 5 awarded Notable Question Mar 22 awarded Popular Question Mar 10 answered Is the invariant correct? Sep 5 answered Proof of trigonometric identity $\cot \theta \sec\theta= 1/ \sin\theta$ Aug 24 revised Understanding how a differential equation is solved with distributions added 14 characters in body Aug 23 revised Understanding how a differential equation is solved with distributions added 4 characters in body Aug 23 asked Understanding how a differential equation is solved with distributions Aug 5 comment Geometric minimal distance path between 2 points via 1 area yes in particular cases, a straight line works Aug 5 awarded Curious Aug 5 revised Geometric minimal distance path between 2 points via 1 area deleted 99 characters in body Aug 5 comment Geometric minimal distance path between 2 points via 1 area @achillehui nice intuition, I could also have put a more generalized elliptic sea line, and the idea is maybe to find the largest ellipse that fits in the other Aug 5 comment Geometric minimal distance path between 2 points via 1 area it can be the longer path or shorter path, I think. If my assumption is right, the other parallel tangent below the circle is the longer path possible Aug 5 revised Geometric minimal distance path between 2 points via 1 area added 85 characters in body Aug 5 comment Geometric minimal distance path between 2 points via 1 area One fire, one plane at an initial location, on straight sea line that the place must each before getting to the fire Aug 4 asked Geometric minimal distance path between 2 points via 1 area Jul 14 suggested rejected edit on Expected Number of Coin Tosses to Get Five Consecutive Heads Jul 4 comment Combinatorics: Mean and Variance of an indicator function of items arranged in a circle. confirmed by this matlab quick test: n=25; b=10; X = zeros(10000,1); for i=1:length(X) B = sort(randsample(n,b)); % blue balls C = diff([B; B(1)+n]); % differences to right neightbor clock-wise D = circshift(C, 1); % differences to left neightbor clock-wise X(i) = sum(C>1 & D>1); end E = mean(X) % 3.8182 V = var(X) % 2.8490 Jun 28 comment Combinatorics: Mean and Variance of an indicator function of items arranged in a circle. I think with a circle, all $X_i$ are equivalents, the same problem with balls on a straight line would be more difficult Jun 27 comment Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$ @Tunk-Fey contour integration comes with the study of holomorphic functions (functions continuous in $\Bbb C$)