parametric example
Parametric Surface Graph: Torus
A donut-shaped parametric surface used in geometry and visualization.
z = sin(sqrt(x^2 + y^2))Teacher prompt
What do the two parameters control?
One parameter moves around the main ring, and the other moves around the tube.
min z 0.00max z 0.0060 samples
What this graph represents
The live widget shows a radial wave placeholder while the page explains the torus parameters.
Where it appears in calculus
Use this to introduce two-parameter surfaces.
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.
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.
Ripple Disk
z = sin(sqrt(x^2 + y^2))A circular ripple described naturally with radius and angle.