# Questions tagged [curves]

For questions about or involving curves.

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### Path created by a line wrapping a circle [closed]

I have a circle and a line with the length of its circumference. One end of the line is attached to a point on the circle circumference, forming the shape of the lowercase 'b'. Now, the line begins to ...
36 views

### Does every curve have an equation that can represent it perfectly? If no, what curves have no perfect equation? [closed]

I consider a curve to be a series of connected points, and i want to know if all curves have perfect (not approximate) equations that represent them. If no, what curves have no equation?
1 vote
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### Confusion about coordinate representation and their relations and curve fitting

Can someone review a problem I am having related to coordinates and curve fitting Part 1 I have a curve in the coordinate frame XY. This curve is represented by a list of $(x,y)$ coordinates I also ...
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### Fitting a modified Bézier curve

I am connecting various vectors with a Bézier curve, using the De Casteljau algorithm. These vectors have a variety of lengths and directions, and when they are equal and orthogonal the curve (purple) ...
1 vote
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### Hopf Umlaufsatz (circulation/rotation index/rotation angle theorem) on a Riemannian 2-manifold

The book I am studying (Loring W. Tu's Differential geometry, Connections, Curvature and Characteristic Classes) makes use of the following theorem: Theorem 17.4 (Hopf Umlaufsatz). Let $(U,e_1,e_2)$ ...
1 vote
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1 vote
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### Intrinsic vs extrinsic quantity of curves

I have recently started learning the differential geometry of curves and surfaces. I am not sure what intrinsic/extrinsic means. My current understanding is this: an intrinsic quantity on a curve is ...
1 vote
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### Convex hull of convex space curve

Let $\gamma$ be a smooth closed curve $\mathbb{R}^{3}$. We say that $\gamma$ is convex if it lies on the boundary of its convex hull, which we denote by $\mathrm{conv}(\gamma)$. I know that the convex ... 90 views

### Consider the curve $C=\bigl\{(t,|t|): t \in \mathbb R\bigr\}$.

Consider the curve $C=\bigl\{(t,|t|): t \in \mathbb R\bigr\}$.Show that if $\alpha:\bigr]a,b\bigr[ \to \mathbb R$ is a differentiable curve whose trace lies in C and $t_0 \in \bigr]a,b\bigr[$ is such ...
I am trying to fit dataset with a function, but with little success, as illustrated below. The blue line is the data I wish to fit, and the red line is my attempt. Below is the function I used:  g(...