parametric example
Parametric Surface Graph: Helicoid
A screw-like minimal surface.
z = atan(y / (x + 0.001)) + 0.15*sqrt(x^2 + y^2)Teacher prompt
What motion creates the helicoid shape?
A point moves outward while rotating and rising like a screw.
min z 0.00max z 0.0060 samples
What this graph represents
The height changes as the angle wraps around the origin.
Where it appears in calculus
Use it to connect rotation and height.
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.
Wave Sheet
z = sin(x) * cos(y)A parametric sheet whose height is a wave product.
Ripple Disk
z = sin(sqrt(x^2 + y^2))A circular ripple described naturally with radius and angle.