Andrew Tomazos
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 Jan11 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. Jan11 comment Circle intersection in radial coordinates? @Clayton: Then they would not qualify as their interiors would be disjoint. See second sentence of post. Jan11 comment Two circles overlap? Yes, it seems obvious now. Thank you. Nov8 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. Oct26 comment How is $dx \over dy$ different from $\partial x \over \partial y$? math.stackexchange.com/questions/221755/… Oct26 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? Oct26 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. Oct26 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? Oct15 comment Generously Feasible? Can you provide the link? It doesn't show in my search results? Sep21 comment Counting Hexagons in Triangle Grid Recurrence? @BrianM.Scott: What was your technique? Sep17 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. Sep8 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? Sep8 comment N unlabelled balls in M labeled buckets Why isn't my expression correct? Aug28 comment Closed form for $T(1) = K, T(x) = xT(x-1) + x$? Yes $x \in \mathbb{Z^+}$ Aug27 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. Aug26 comment Combinations of nonincreasing sequences within bounds? @GerryMyerson: I think you may have misread the problem. I have added an example where $a_1 > a_2$. Aug26 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. Aug25 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 Aug25 comment Elementary power equation: $k_1k_2^x = k_3k_4^x$ I've always found it unintuitive for some reason that $\log_c(a^b) = b\log_c(a)$. I find it hard to visualize a physical model that demonstrates this. Aug17 comment Maximization of a sum subject to constraints on 3 resources @AngelaRichardson: Information is lost. Your equation is implied by the triple equation, however the reverse is not true.