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 Aug 5 comment Geometric minimal distance path between 2 points via 1 area yes in particular cases, a straight line works 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 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 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 $\Bbb C$) Jun 25 comment partial derivatives of Dirac functions right, indeed, $\delta = \delta_0$ and $x_i$ is null Jun 21 comment Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$ Thanks, awesome answer, the trick is to take this quarter circle Jun 20 comment Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$ I guess you take a half-circle as contour, I can't get your first equality with $\sqrt i$, could you expand please? Jun 14 comment How many are possibilities to build count $n$ summing $k$ other counts? you forgot 5+0+0 Jun 14 comment How many are possibilities to build count $n$ summing $k$ other counts? What are the scores for (5,3), (5,4), (5,5), (5,6)? Jun 4 comment Multiplying using reciprocal, addition and subtraction Are you sure it isn't $*/*$ (division of any pair) instead of inverse $1/*$? May 27 comment Why does a circle enclose the largest area? merci @Pierre-Yves it's clear May 26 comment Why does a circle enclose the largest area? Could you explain the last equality $\sum_{n\in\mathbb Z}\ n^2\ |c_n|^2=1$? May 1 comment Normal Distribution Quantiles and Value at Risk Also, don't smoke Mar 7 comment What Is Exponentiation? isn't $a^{\pi} < max(a^3,a^4)$ enough to say it's convergent (since it's also increasing with your decomposition) Dec 2 comment Calculate interests I'm currently googling to know which option is commonly used, thx Dec 2 comment Calculate interests yes r: yearly interests of the loan and m: monthly payback, @AndréNicolas I have edited the question with what you suggested can you have a look? Dec 2 comment Calculate interests I don't agree, at the end of first year, the loan is N less 12 paybacks, and you add the interests