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 Jan 26 comment What is the meaning of $(x^2+y^2)^n$? Is this an already known geometric object? Thanks. But i am asking only about the LHS. I have edited the question to make it more clear Jan 25 comment What is the meaning of $(x^2+y^2)^n$? Is this an already known geometric object? @ JJacquelin, yes. there is no = in it. i do not want to compare but understand generalization to higher dimensions. Jan 7 comment On notation for derivative of an n-Dimensional Gaussian +1 for the nice answer. Thank you so much Aug 5 comment How to define a surface $z = f(x,y)$ with flat region at centre and sigmoidally tapering towards the edges? So, we have a piecewise defined function covering the 2D plane (well, actually a rectangle since limits are imposed for x and y). What you mean is we can define the above piecewise defined function as a single analytical equation involving sums, if we use the step function. Right? But can you please show an example?(sorry for the amateurish request, i lack the rigor to make this formal) Aug 1 comment How to define a surface $z = f(x,y)$ with flat region at centre and sigmoidally tapering towards the edges? I get the idea. I am curious however if we can define this as a single analytical continuos function over the plane(within the limits)? Jul 26 comment How to define a surface $z = f(x,y)$ with flat region at centre and sigmoidally tapering towards the edges? Thanks for your answer. But the logistic function might satisfy my requirements for the tapering part. Apr 26 comment Bilinearity: what does it mean? + for the link to currying Mar 8 comment Is it possible to find a 2D distribution function such that the higher order moments always exist? Yes. Sorry. So i should have phrased it 'moments of any order, but non-zero. I ve edited the question. Mar 8 comment Is it possible to find a 2D distribution function such that the higher order moments always exist? thanks for your answer. But every distribution whose support is bounded has moments of every order might not be true. As an example, consider a distribution which is symmetric. In this case, some of the 3rd order moments become zero. Is it not? Feb 12 comment Is it possible to find a 2D distribution function such that the higher order moments always exist? And can we ensure those moments are always non-zero even if the support is possitive i.e., for the supports [a,b] and [c,d]? Aug 20 comment How many unit hexagonal tiles can be placed inside a larger hexagon of sides $a,b,c,a,b,c$? And thanks a lot for answering the philosophical questions. To Read: Martin Gardner's math books is on my to do list :-) What an awesome community by the way! Aug 20 comment How many unit hexagonal tiles can be placed inside a larger hexagon of sides $a,b,c,a,b,c$? Brilliant illustration. I loved it. I get it now. The number of tiles on the visible faces is (ab+bc+ca). Then the number of tiles that have been counted multiple times in the previous product (a+b+c) + 1 (the tile at the intersection of the red, green and blue lines). Voilà. Aug 19 comment How many unit hexagonal tiles can be placed inside a larger hexagon of sides $a,b,c,a,b,c$? oops. Sorry Sir.My fault.I have removed that comment saying your answer is wrong. Now, I have upvoted your answer. Although before accepting your answer, i would like to clarify the logic behind. So, $a+(a+1)+...$ is the number of unit hexagons in 1 trapezoid. right? This is an arithmetic progression. How did you find out the last term (a+b-1)? Second, I dont understand how you arrived at $(c−b−1)(a+b−1)$? One more thing is about your assumption. The formula works even when your assumption is violated. a = 985;b=2;c=2 Aug 19 comment How many unit hexagonal tiles can be placed inside a larger hexagon of sides $a,b,c,a,b,c$? hmm.thanks for your quick response. But Sorry the answer is wrong. For a=7,b=8,c=13, the correct answer is 224. Your expression gives 84. Aug 19 comment How many unit hexagonal tiles can be placed inside a larger hexagon of sides $a,b,c,a,b,c$? @copper.hat: I dont get it. How does a>1 remove tiles? Jul 23 comment Multi binomial theorem application yes. I did mean that $v<=alpha$. term. thanks. I got it. But still not sure of how to proceed with the expansion. Jul 23 comment Multi binomial theorem application Thats what i m not sure. Under the assumptions that i have given, we can approximate each of the terms above as (a1/c1)x+(b1/c1)y+1. So should i expand it using multi multinomial theorem? Apr 19 comment Computing the moments of a triangle right! but do you know if i can find a copy of that file somewhere or if you have one, i ll be glad to take it. Apr 19 comment Computing the moments of a triangle The second link is not working.. Oct 28 comment Odd order moments of a symmetrical distribution that was superb!