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 Aug 2 comment Generalizations of winding numbers yeah, your post gave me the same idea, which lead me to the idea of using the medial axis to give a metric. See if you like it. Aug 2 comment Generalizations of winding numbers Good idea for the star case, although I was hoping for something for general simple-closed boundaries. Aug 1 comment How many different shapes can I make with this toy? It might be interesting to see what upper bounds can be discovered for this, as I imagine it would be hard to come up with the actual number. I spent a pleasant afternoon once discussing a similar problem: how may shapes could one have in a game of n-tris, a generalization of tetris where the shapes were all comprised of n connected squares with no holes. Aug 1 comment Generalizations of winding numbers @johnmangual, the fact that winding numbers are integers covers a multitude of rounding and truncation errors, but if I wanted to work harder I'd use a more robust method like vector crossing counts. I was using winding numbers as a quick way to get Mathematica's RegionPlot function to work with a fairly simple boundary. Anyway, my question is more one of curiousity, it's not tied to my work. Nov 1 comment Name this concept: Comparing equal sized vectors vs. comparing features You might want to ask this on astronomy.stackexchange.com. I think they do something similar to align sequences of images in order to get an enhanced composite image. Sep 29 comment circle that touch quadrantal internally @J.M.: I'm assuming kim want's the inscribed circle Sep 26 comment Why is this curve convex? Are you sure they want you to use polar coordinates? You could put $\theta$ on the x axis and r on the y axis. Sep 21 comment 4 items add up to and multiply to 7.11 what are the value of the items? @anon: Right you are! (duh!) Sep 21 comment 4 items add up to and multiply to 7.11 what are the value of the items? @anon: if $\pi$ is too expensive, maybe I can just buy a piece? Sep 21 comment 4 items add up to and multiply to 7.11 what are the value of the items? Hmmm, the prime factors of 711 are 3*3*79. There aren't many choices for the prices here, and none of them add up to 711. For example, 1*1*9*79 = 711, but the sum isn't even close. Sep 21 comment 4 items add up to and multiply to 7.11 what are the value of the items? Hint: This is a Diophantine problem. Besides the sum and product, you also have that the answers (expressed in cents) are integers. Sep 21 comment Curvature of the image of a curve projected onto a surface I haven't tried yet, but will sometime in the next week (or two). I don't see why it wouldn't though. I'll post the Mathematica results here when I do. Sep 20 comment Curvature of the image of a curve projected onto a surface Thanks, I appreciate the effort you put into this. I really like the idea of creating an orthogonal basis in the tangent space. I can make this work. Sep 20 comment Curvature of the image of a curve projected onto a surface Thanks for this. I'm not clear why you say that I forgot to mention p, k, and d, (as k and d are of your own construction) and I don't know what you mean "it's a pullback". I'm not I can I turn this into a finished solution for d given that S is unknown in advance (we are only guaranteed that we can inquire it's derivatives). Sep 20 comment Curvature of the image of a curve projected onto a surface It's not clear to me that the construction as you describe it gives the correct curve. Can you justify the idea that there is a locally aligned parametrization that has the second derivative projection properties? Unfortunately I have to award the bounty soon, so please answer quickly. I'll give it some further thought myself. Sep 18 comment Curvature of the image of a curve projected onto a surface @alex: the surface will generally be a NURBS surface, so there is no hope of an implicit form. Thanks for the suggestion. Aug 31 comment “Mathematical Induction” ODEs do it for me every time! Aug 25 comment Curvature of the image of a curve projected onto a surface @anon: Thanks for this. I intend to see if I can get it to work in Mathematica, but I haven't gotten to it yet. Aug 18 comment Curvature of the image of a curve projected onto a surface I modified the question to avoid references to derivatives in $C_S$. Aug 18 comment Curvature of the image of a curve projected onto a surface @Jesse: Hmmm, that didn't come out very nice, did it. I guess you can't use html in comments? How did you get your subscripts?