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Jul
22
comment A shape that covers all box with certain side lengths
In two dimensions, your shape looks like this (red is $b_2 \in \big[\!\frac12,\frac34\!\big]$, blue is $b_2 \in \big[\!\frac34,1\big]$), while this arrangement has smaller area, so the former is not optimal.
Jul
22
comment Minimization of function with large dimensions
The asker didn't say anything about constraints, so neither the KKT conditions nor duality apply.
Jul
22
comment Check if two 3D vectors are linearly dependent
@copper.hat is right. If you're working with floating-point numbers, I would say checking for linear independence is an ill-posed problem. Perhaps there is another way to do whatever you're trying to achieve without this linear independence check.
Jul
20
comment Solve $dy/dx = e^{x^2}$
@J.M. Honest question: what does closed form mean if not elementary?
Jul
20
comment Why is the amortized time for path compressions approximately $\mathcal{O}(1)$?
What does "approximated amortized complexity" mean? The amortized complexity of union-find with path compression is $O(\alpha(n))$, where $\alpha(n)$ is the inverse of the Ackermann function, and this is not $O(1)$. In any case, searching for "union find ackermann" on Google turns up a number of results, for example these course notes by (I think) Dexter Kozen, which contain a proof.
Jul
19
reviewed Approve Using the substitution $p=x+y$, find the general solution of $dy/dx=(3x+3y+4)/(x+y+1)$.
Jul
19
comment Geometric explanation of centroid of triangle
That's okay. I would still like to know your definition of "moment of mass about the origin".
Jul
19
comment Geometric explanation of centroid of triangle
...And what is your definition of moment, please?
Jul
19
comment Geometric explanation of centroid of triangle
What is your definition of the center of mass? Does it involve calculus? :)
Jul
19
comment Geometric explanation of centroid of triangle
I don't follow what you mean by "the[y] would fall to one side or the other". Also, any point on the triangle lies on some line through the vertex; I don't see how that tells you anything. What you are assuming later is that the line through the vertex and the center of mass is the same as the line through the midpoint and the center of mass, but you need to justify that.
Jul
18
comment Properties of the matrix $JD$
"Of course $JD$ is going to be anti-symmetric." Are you sure about that? Let $D = \begin{bmatrix}a & b & c \\ b & d & e \\ c & e & f\end{bmatrix}$, for example...
Jul
15
comment Calculating distance in a hexagonal grid map
Can you explain what you mean by a "conditional algorithm" that you don't want? An explicit formula will probably need a few cases, but can be done without a full-fledged graph search.
Jul
15
answered Functional equations of (S-shape?) curves
Jul
15
comment Functional equations of (S-shape?) curves
It would be best if you could elaborate on how the things you've looked up so far didn't match your needs. Your problem as given is underspecified (there are lots of functions that will do the job), and it would help to get an idea of what "soft" or "aesthetic" features you're looking for to pick the best one.
Jul
15
comment Functional equations of (S-shape?) curves
Presumably you also want the function to never go outside the range $[0,1]$, right?
Jul
15
reviewed Approve Prove if $x^{2}-5xy-3$ is even, then $x+y$ is odd, where $x,y \in\mathbb{Z}$
Jul
15
answered Is it valid to consider average rate of change as a 3 variable function?
Jul
15
comment Generating generalised Venn diagrams
Did you check the references in the Wikipedia page? The first link has a section called A General Construction for Symmetric Venn Diagrams.
Jul
15
answered How to find the area of green region in terms of yellow, blue and red region in the following figure?
Jul
14
revised Figure out if a fourth point resides within an angle created by three other points
thinko: a point lines *in* a half-plane or on one side of a *line*, not on one side of a half-plane :/; deleted 3 characters in body