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I hereby authorize whoever it may concern to post my comments as answers if they wish, whether as community wiki or otherwise if you like imaginary internet points.


Jul
8
comment Maximum number of vertices in intersection of triangle with box
A box-plane intersection forming a hexagon is shown halfway down this page, and one can easily truncate three of its vertices with a triangle.
Jul
8
comment Is chess Turing-complete?
The question is about a generalization of chess played on an infinite board as stated in the very first sentence.
Jul
8
comment Characterization of sphere.
@user1963: It's not. If you squash the plane down in the $y$ direction, lines parallel to the $x$-axis are now much more likely than lines parallel to the $y$-axis.
Jul
8
comment filling an occluded plane with the smallest number of rectangles
Thanks, that is indeed a productive search query. As for 3D, I'm familiar with BSP trees, but I don't see how one could use them to find the smallest partition rather than just any partition. If the answer is too long for a comment, I can ask a new question.
Jul
8
comment Number of binary trees with N nodes
A binary tree with $k$ internal nodes must have $k+1$ leaves and therefore $2k+1$ total nodes. Ergo, any binary tree with $n$ total nodes is a binary tree with $(n-1)/2$ internal nodes, and you already know how many of those there are. Edit: At least if you're talking about full binary trees where each node has either two or no children.
Jul
8
comment filling an occluded plane with the smallest number of rectangles
+1: I wish this answer had existed five years ago when I was dealing with a related problem! Two questions, if you happen to know the answer offhand: (i) Is the problem easier if the polygon is without holes? (ii) Do the algorithms generalize to higher dimensions?
Jul
8
comment How to slice an area in rectangles optimally?
Joseph O'Rourke has now posted a $O(n^{5/2})$ time solution (where $n$ is the number of vertices) at this duplicate question.
Jul
8
comment How to find the “average” direction of a set of vectors?
It's exactly the "direction of sum of vectors" approach which you said you didn't want. I provided the reference to show that it is a standard approach so you may want to reconsider not wanting it.
Jul
8
comment How to find the “average” direction of a set of vectors?
What about four vectors equally spaced at 90 degrees? What do you expect the average direction to be there? Further reading: mean of circular quantities
Jul
7
comment Non-uniform sampling of N-sphere
Replace $(x_1,x_2,x_3,\ldots,x_n)$ with $(x_1,\lambda x_2,\lambda x_3,\ldots,\lambda x_n)$, then normalize. When $\lambda=1$ you get the uniform distribution on the sphere. When $\lambda=0$ you get all the points at the poles.
Jul
7
comment Two-way matrix optimization
$U\mapsto A-UW$ and $U\mapsto RU-H$ are both linear operators on matrices, and the Frobenius norm is just the $L^2$ norm on the entries of the matrix. So you just have a quadratic minimization problem on your hands.
Jul
7
comment Length of a curve without function?
+1, but the triangles are a little superfluous. You could just say "pick a number of points on the curve, and add up the distances between them".
Jul
7
revised Distinguishing sets according to more fine-grained notions than cardinality.
spelling
Jul
7
comment Positive semi-definite of a matrix composed of semi-definite blocks
@Gal: If you are satisfied with the answer, you can accept it by clicking the check mark on the left.
Jul
7
answered Prove or disprove a statement about testing the convexity of a set using the vertices
Jul
6
revised Extrema homework — maximizing the viewing angle of a picture on a wall
edited title
Jul
6
revised Positive semi-definite of a matrix composed of semi-definite blocks
added 1 character in body
Jul
6
answered Positive semi-definite of a matrix composed of semi-definite blocks
Jul
6
comment Convex hulls for a finite amount of points
There is a difference between understanding what the convex hull is and understanding how to compute it. Wikipedia lists several convex hull algorithms, of which the simplest to understand is probably the gift wrapping algorithm.
Jul
6
comment What is the intutive explanation of why the notation of matrices is as it is?
Very nice answer, but your updated formatting doesn't work for me in Firefox on Mac: i.stack.imgur.com/MBpeB.png ...It's probably best not to use fancy spacing tricks in MathJax because of potential cross-browser rendering inconsistencies.