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

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 $$5$$.

• 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 $u(1-u^2/(3+v^2))/3$. – 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

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