parametric example
Parametric Surface Graph: Saddle Patch
A saddle written as a two-parameter patch.
z = x^2 - y^2Teacher prompt
What are u and v doing here?
They directly become x and y coordinates.
min z 0.00max z 0.0060 samples
What this graph represents
This shows how common z=f(x,y) examples are also parameterized surfaces.
Where it appears in calculus
Use it to connect graphing calculators and vector calculus notation.
Embed this graph
Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.
Open embed pageRelated graphs
Open another surface page and compare shape, slices, and contour behavior.
Torus
z = sin(sqrt(x^2 + y^2))A donut-shaped parametric surface used in geometry and visualization.
Mobius Strip
z = atan(y / (x + 0.001))A one-sided strip with a half twist.
Helicoid
z = atan(y / (x + 0.001)) + 0.15*sqrt(x^2 + y^2)A screw-like minimal surface.
Wave Sheet
z = sin(x) * cos(y)A parametric sheet whose height is a wave product.