# Tag Info

### Symbolic area calculation for a parametric self-intersecting closed curve

The plan is first get the "external" contour and then use Green's theorem to find its area. ...
Accepted

ColorFunction and Epilog were around in version 7. However, ColorFunction did get an update ...
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### Finding a parametric curve fitting a two-dimensional dataset

A least squares approach: model = a/((x - x01)^2 + c y^2) + a/((x - x02)^2 + c y^2) $\frac{a}{c y^2+(x-\text{x01})^2}+\frac{a}{c y^2+(x-\text{x02})^2}$ If we ...
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### Plot a function for different parameters

You can use Table for this: Plot[Evaluate@Table[f[a, b, 2, 3], {b, 0, 5, 1}], {a, 0, 1}] And you can also put there multiple ...
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### return {} when the function is given {}

Actually, I want the output to be {} if there is anything wrong with the argument. For this I recommend one or more definitions with patterns that only match a valid argument, and a fall-through ...
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### Solving the Frenet Serret equations for non-constant curvature and torsion, obtaining parametric equations

Okay, this'll be a short answer just to show what you can do. What you are trying for here is essentially an inverse to FrenetSerretSystem, which will give the ...
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### My 3D plot of a Klein bottle doesn't look right

Here's my slight simplification of the Klein bottle parametric equations. I believe the original parametrization is due to Stewart Dickson (whose depiction of the bottle was in the "Graphics Gallery" ...
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### Finding the Period of a Limit Cycle

Although it's primarily designed for ecological models, my EcoEvo package can help. First, you need to install it with ...

### Find eigen energies of time-independent Schrödinger equation

As in version 10.2, there is the NDEigensystem can be used to calculate the eigenstates and eigenvalues of a differential operator. For example in the harmonic ...
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### How do I plot a parametric family of curves given a list of parameter values?

There are a number of ways to do this, e.g.: ...

### Logarithmic scale in an ParametricPlot obtained from ODE boundary conditions

You can use ScalingFunctions. It appears in red but works. ...

### Fitting experimental data by using ParametricNDSolveValue and NonlinearModelFit

A minor change to model eliminates the error cited in the question. (Replace s[t] by s in ...
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### How to draw a 3D point moving along a helical path?

You can add a moving point using a combination of options MeshFunctions, Mesh, and Method as ...

### Parametric plot on multi-dimensional domain

Method 1: unconstrained regions You can easily do it with regions: ...
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You can take a continuous function and evaluate it at the same points that are also used by ParametricPlot3D to create the curve. Here is a way to do it: ...
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### Is Mathematica capable of converting parametric equations into a function? If so, how?

I suspect that there simply isn't a nice equation of the form $y = f(x)$ for these curves. As you note the equation for $x_d$ involves both algebraic and trigonometric terms, and almost all such ...
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### Finding "nice" solution for under-determined system with constraint?

If I understand the question correctly, you wish to obtain a parameterized solution {U2[U1], W2[W1]} from the equation in the question, so that you can vary that ...
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### Shading the surface of the 3D plot

Perhaps, this is what you had in mind. ...
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Curvature of a parabola depends on the position. To find curvature at the maximum point do ArcCurvature[{t,fit[t]},t]/.Maximize[fit[t],t][] (*0.0170112*)

### Finding the Period of a Limit Cycle

Here is a simple approach to get the period of the unknown limit cycle. The idea is to approximate the limitcycle by a circle (1st harmonic) around the mean of the limitcycle: solution ...

### Obtaining the curve parallel to the function a/(x^2+b)

Use FrenetSerretSystem. ...

### 2D cross-section of ParametricPlot3D

We can use the MeshFunctions options and extract the slice data accordingly. ...
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### Solve stiff system by shooting method

The goal of this question, I believe, is selecting Φ[r0] so that the solution connects smoothly to the asymptotic solution at large ...

### Plotting Limit Cycle

Hopf bifurcation analysis The differential system: ...
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### A parametrization for $\frac{\sin(x)}{x}$ as a revolution surface around $y$ axis

Perhaps something like this. Just rotate the original function about the z-axis directly: ...

### My 3D plot of a Klein bottle doesn't look right

Description For fun, thought I give it a try. Below is an example of my attempt to Plot Kleins bottle. Code ...
The plot you were trying to reproduce is a plot of the reduced van der Waals equation; that is, it is using the reduced pressure $P_r=\frac{P}{P_c}$ and reduced temperature $T_r=\frac{T}{T_c}$ as the ...
Here's I think a generalization of what Ulrich gave to an arbitrary $(p, q)$ torus (if I read Wikipedia right): ...