# Questions tagged [curves]

For questions about or involving curves.

1,854 questions
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### Definition of curves with two variable

I have a question regarding a diagram that I have made. It reflects measurement results. For different duty cycles, a gain factor was measured. The time reflects the turn-on time of transistors. I ...
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### derivative of composition curve

a quick question: Let $(M,g), (N,h)$ be pseudo-Riemannian manifolds, $\gamma:I \rightarrow M$ a curve. $\gamma^{'}(t_0):= d \gamma \dfrac{\partial}{\partial t} |_{t_0}$ Let $F:M \rightarrow M$ be ...
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### All the intersections between two plane curves

In commercial CAD software, one can find ALL the intersections of two plane curves very easily. As it is shown in this case, one of the curve is a B-spline and the other is a polynomial. Both of the ...
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### How do I find the smallest circle enclosing a compact region?

The Four-vertex theorem states that any simple closed plane curve has at least four vertices, i.e $\kappa'(t) = 0$ where $\kappa$ is the signed curvature function. The proof given by Osserman here ...
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### Weighting a cubic hermite spline

I am trying to figure out a function behind the software's curve drawing algorithm. Originally, each node comes with 3 parameters : time, value, and tangent. I have found that it fits cubic Hermite ...
If a curve has unit speed, is the magnitude of its tangent and normal vectors equal to $1$? I am having trouble seeing this. if r is the curve, then the tangent is $r'$. Also, normal vector is $r''/|... 1answer 59 views ### Help with approximation of the length of a curve in$\mathbb{R}^n$I would like to have some hints on this exercise since I struggle to begin. Let$c : [a,b] \rightarrow \mathbb{R}^n$be a curve such that$$l(c) := \sup_{a<t_0<...<t_k<b} \left \{ \... 1answer 59 views ### Is a Weierstrass curve a topological manifold? [duplicate] Obviously a Weierstrass curve is not a smooth manifold, but it seems like a Weierstrass curve should be a topological manifold (which I now see is a suspicion supported by this post), since it is a ... 3answers 31 views ### Trigonometric Curves, Finding Range Sketch the graph of$y=2\sin x + 1$for intervals$0° \leq x \leq 360°$. Hence state the range of values of$x$in this interval which satisfies the inequality$2\sin x + 1 \geq 0$. The graph ... 1answer 37 views ### Secant variety of a curve$\underline {Background}$: Let,$X$be a curve in$\mathbb{P}^{2}$which is not a line.We denote secant variety of$X$to be$\sigma_2(X)\underline {Question}$: To prove$\sigma_2(X)=\...
I've been thinking about this statement for a while, and I think it's true, but I'm not sure of how to prove it. The statement is A Jordan curve $J$ that is symmetric about the origin $p$ does not ...