Andrew Tomazos
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 Jan 4 comment Confidence interval on extrapolation from sample? It's a real world problem. I'm analyzing a large dataset for properties and I want to analyze a small random sample and then extrapolate, to save processing time, but I want to know how confident I can be in the extrapolation. A typical example of the scale is N is about 200,000,000, M is about 2,000,000, K is 100,000, P is 0.95. Oct 31 comment Winding the faces of a platonic solid? @AndrewD.Hwang: Yes, I'm looking for an algorithm - or at least some rough pattern of formula. Something better than plotting them and doing it by hand. Jan 11 comment Circle intersection in radial coordinates? @leo: I specifically need the $\theta$ for the application. But actually you are right - I could solve in rectangular coordinates and then calculate theta after having the two points (x,y) coordinates. Jan 11 comment Circle intersection in radial coordinates? @Clayton: Then they would not qualify as their interiors would be disjoint. See second sentence of post. Jan 11 comment Two circles overlap? Yes, it seems obvious now. Thank you. Nov 8 comment Derivative of $x \over x+k$? For some embarassing reason I can't explain I thought that because the numerator and denominator shares the $a$ term the Quotient Rule didn't apply. Sorry. Oct 26 comment How is $dx \over dy$ different from $\partial x \over \partial y$? math.stackexchange.com/questions/221755/… Oct 26 comment How is $dx \over dy$ different from $\partial x \over \partial y$? Now I am really confused. If we plot in 3D a surface $x=z_1z_2$, then at a given point on the surface the tangent in the $z_1$ direction will correspond to the partial derivative $\partial x \over \partial z_1$. Does the total derivative have a similiar geometric interpretation? Oct 26 comment How is $dx \over dy$ different from $\partial x \over \partial y$? But for all mechanical purposes all the same rules apply in both cases? We are asking how the "numerator" variable varies with respect to the "denomiator" variable, assuming everything else is held constant. Oct 26 comment How is $dx \over dy$ different from $\partial x \over \partial y$? So what does $dx \over dz_1$ mean? Or is it undefined? If it is undefined why not just use the same notation? Oct 15 comment Generously Feasible? Can you provide the link? It doesn't show in my search results? Sep 21 comment Counting Hexagons in Triangle Grid Recurrence? @BrianM.Scott: What was your technique? Sep 17 comment Counting Hexagons in Triangle Grid Recurrence? This is correct, thanks. I was fooled by the N=4 case into thinking that all hexagons that touch all three sides must have one side of n-2, which is true for N=4 but not true for higher values of N. For example for N=5 we can have a hexagon that results from chopping off triangles of side 2 removed from each corner of the grid. Sep 8 comment N unlabelled balls in M labeled buckets This proves it incorrect, however I still don't see what went wrong in my reasoning. The number of ways to put N labelled balls in M labelled buckets is $M^N$ correct? So why can't I just divide by the number of permutations of N balls to arrive at the unlabelled ball case? Sep 8 comment N unlabelled balls in M labeled buckets Why isn't my expression correct? Aug 28 comment Closed form for $T(1) = K, T(x) = xT(x-1) + x$? Yes $x \in \mathbb{Z^+}$ Aug 27 comment Combinations of nonincreasing sequences within bounds? See my answer for what I was looking for. I guess you were thinking general solution or nothing. I just wanted a way to calculate it. Aug 26 comment Combinations of nonincreasing sequences within bounds? @GerryMyerson: I think you may have misread the problem. I have added an example where $a_1 > a_2$. Aug 26 comment Combinations of nonincreasing sequences within bounds? @GerryMyerson: What do you mean? $a_i$ can be any integer, as can $b_i$. Obviously if for some $i$, $a_i > b_i$ than the answer to the question is zero. Likewise if for some $i$, $b_i < a_{i+1}$ then the answer is also zero. Aug 25 comment Elementary power equation: $k_1k_2^x = k_3k_4^x$ Wow, it seems obvious now - exponentiation becomes multiplication in log space - as multiplication becomes addition