bob.sacamento
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 2d comment What is the area of the shaded region of the rectangle? What do the "2" and "3" mean? Are those the areas of the enclosed triangles? Apr 27 comment How to find $\int \frac {sinh(lnx)} {x}$ $e^{-\ln{x}}=1/x$ Mar 24 comment Transforming points between two polar coordinate systems You can certainly do the transformation, but it cannot be accomplished by a matrix. I think what you are doing is te way to go about it. You might take a look at how you can condense your operations instead of doing a laborious step-by-step process. But conceptually, I don't think you will find anything different from what you are already doing. Mar 22 comment How to express elements of a first and second fundamental forms by their eigenvalues I think more information is needed to answer the question. A simple diagonal matrix with the elements being the eigenvalues represents such a matrix ... in a particular coordinate system. Transforming to other systems requires alot more info. Mar 16 comment Find the equilibria of the discrete dynamical system You have a system of equations in two variables, $x$ and $y$. Just solve it for $x$ and $y$. Although, it does seem like there isn't going to be any "clean" solution. It's not going to be a typically "nice" solution to a textbook problem. Mar 14 comment Frenet-Serret formulas in arbitrary dimensions Sorry, I don't mean to be obtuse. And if you want to give up, I don't blame you. I understand $e^{\prime}_1\cdot e_j=0, j>2$, and I understand $e^{\prime}_2\cdot e_4=-e^{\prime}_4\cdot e_2$. For the life of me, I can't see why $e^{\prime}_2\cdot e_4 = 0$. Mar 14 comment How can I evaluate $\int_{-\infty}^{\infty} e^{-x^2} dx$ without using polar coordinates Seriously, seriously, get used to polar coords. You will suffer if you don't. I speak from experience. Mar 14 comment Frenet-Serret formulas in arbitrary dimensions I'm new at this. The paper you mention is beyond me right now. Mar 14 comment Frenet-Serret formulas in arbitrary dimensions OK, your expression for $e^{\prime}_j$ is exactly where my problem is. My understanding of the frame is such that you start with the various derivatives of the motion, and then perform a Gramm-Schmidt process to get the various $e$'s. And I don't see how that process implies $e^{\prime}_j=−κ_{j−1}e_{j−1}+κ_je_{j+1}$. I mean, I don't see a priori why $e^{\prime}_j$ for the general case can't have components of any number of the other vectors. Am I missing something obvious? Thanks for your help. Mar 14 asked Frenet-Serret formulas in arbitrary dimensions Mar 7 comment Converting from parts of a circle to polar coordinates @Frank Vel The way I see it \$x/4-x^2/4