I am creating the Enneper Surface in Geogebra with the following equations.

Enneper Surface Equation

Is the surface or equation correct, and does the Enneper surface look like this? I'm confused because Wikipedia has a different image of the Enneper surface. In the equation both parameters $u$ and $v$ are varying from $-5$ to $5$.

Enneper Surface

  • 1
    $\begingroup$ I think you must have misread the equations. For example, Wikipedia's equation for the first component is to be interpreted as $u(1-(u^2/3)+v^2)/3$, not $u(1-u^2/(3+v^2))/3$. $\endgroup$ – Rahul Apr 22 at 13:59

As was mentioned in the comments, the issue is that the equations you used are not quite correct. It looks like you distributed incorrectly. They should be

$$\begin{align*} x &= \frac{u}{3}-\frac{u^{3}}{9}+\frac{v^{2}u}{3}\\ y &= -\frac{v}{3} + \frac{v^{3}}{9} - \frac{vu^{2}}{3}\\ z &= \frac{u^2}{3} - \frac{v^2}{3} \end{align*} $$

You can see the difference between the two surfaces on CalcPlot3D.

To get an plot like the one on Wikipedia it is easier to use the polar parameterization:

$$\begin{align*} x &= r\cos(\phi) - \frac{1}{3}r^{3}\cos(3\phi)\\ y &= -\frac{1}{3}r\left[3\sin(\phi) + r^{2}\sin(3\phi)\right]\\ z &= r^{2}\cos(2\phi) \end{align*} $$

Plotting this with $r\in [0,2]$ and $\phi \in [-\pi,\pi]$ will produce a plot similar to the one on Wikipedia. Again, you can see this on CalcPlot3D

enter image description here

  • $\begingroup$ Thank you for spotting the error. Can you suggest the range of u and u so it can look like a surface on Wikipedia $\endgroup$ – Pankaj Solanki Apr 23 at 12:08
  • $\begingroup$ @PankajSolanki see my edits. $\endgroup$ – DMcMor Apr 23 at 15:38
  • $\begingroup$ Thank you very much. $\endgroup$ – Pankaj Solanki Apr 23 at 19:38

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