Rahul
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 Nov 10 comment For all unit vectors $\mathbf u$ and a positive definite $\mathbf C$, what surface do vectors $\mathbf u \mathbf u^\top \mathbf C \mathbf u$ form? I don't know, but it creates some pretty odd-looking surfaces in 3D: i.stack.imgur.com/5M2Ua.png Nov 10 comment For all unit vectors $\mathbf u$ and a positive definite $\mathbf C$, what surface do vectors $\mathbf u \mathbf u^\top \mathbf C \mathbf u$ form? It's easier if you choose a coordinate system along the eigenvectors of $\mathbf C$. Then the polar equation of the curve is just $r=\lambda_1\cos^2\theta+\lambda_2\sin^2\theta$ where $\lambda_1$ and $\lambda_2$ are the eigenvalues of $\mathbf C$. Nov 7 comment rotating a sigmoidal curve The inverse of the logistic function is the logit function $\log x - \log(1-x)$. Nov 7 awarded Popular Question Nov 5 comment Length of an arc of a circle when the angle is infinitesimally small This is a problem of units. If $\mathrm d\theta$ is in radians then the length is $r\,\mathrm d\theta$. But if $\mathrm d\theta$ is in degrees, the length is $r\pi\,\cfrac{\mathrm d\theta}{180^\circ}$... Nov 3 comment A curve that will be perpendicular to all $c \sin x$ Just take $d$ to be very small but positive. The radius is roughly $\sqrt d$. Nov 3 comment A curve that will be perpendicular to all $c \sin x$ Half the curves are missing, but you can get them back by taking the absolute value inside the log: $y=\pm\sqrt{2\ln\lvert\cos x\rvert+d}$. Nov 2 comment find arc between two tips of vectors in 3D @Herman: No, it doesn't. Do you mean $\phi=\pi$? Nov 2 answered find arc between two tips of vectors in 3D Oct 28 comment How do I know by looking at a formula that I should use the chain rule? I always use the chain rule to differentiate $f(x)/g(x)$ because I already know the product rule and the chain rule by heart (you can't do any calculus without them) and I can't be bothered to remember the quotient rule. Oct 21 comment How does this differential equation define an oscillation from a to b? Some possibly helpful intuition: You should get the equation $\ddot y=(a^2+b^2-2y^2)y$. This is the equation of a unit-mass particle under a spring-like force which is zero when $y=y^*=\sqrt{(a^2+b^2)/2}$, and pulls the particle towards $y^*$ otherwise. Therefore, it is an oscillation. To find the range of the oscillation, find out when $\dot y=0$: this happens when $y=a$ or $y=b$. Oct 17 comment Proof that a common brain teaser is wrong (Burning Rope) This doesn't answer the posted question, which is why a rope burned at both ends burns out in time $T/2$. Oct 17 comment Points on ellipsoid with maximum Gaussian curvature/mean curvature. Surely for the ellipsoid the maximum Gaussian and mean curvatures both occur at the extreme points, i.e. if $a<\min(b,c)$ then $(\pm1/a,0,0)$, and so on. I don't have a proof, but isn't there a way to compute curvatures directly from the $f(x,y,z)=0$ form of the surface? Oct 15 comment 3-D Geometry - line You're forgetting the square roots in the denominators. Oct 14 comment Name of shape with constant distance to a line segment A "discorectangle" is a quadrilateral accompanied by '70s music. Oct 14 comment Why does a root only have a positive output? Also Why is the even root of a number always positive?, Can the square root of a real number be negative?, Square root confusion? We seem to have a lot of these. Oct 12 comment Minimization Optimization Have you tried anything at all yourself? Oct 12 comment Name of shape with constant distance to a line segment The term "capsule" that Mark mentioned is pretty commonly used in computer graphics to refer to the 3D analogue, a cylinder capped by two hemispheres. Oct 11 comment How to change $d^{log_2{n}}$ to be in the form $n^?$ Try calculating what $\log_2(d^{\log_2 n})$ is, and see where you can go from there. Oct 8 awarded Nice Answer