Parametric Surface Graph: Helicoid
A screw-like minimal surface.
z = atan(y / (x + 0.001)) + 0.15*sqrt(x^2 + y^2)Quick facts
- Formula: z = atan(y / (x + 0.001)) + 0.15*sqrt(x^2 + y^2)
- Category: parametric
- Tags: parametric, surface, vector calculus
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.
How to use this graph
- Rotate the surface by dragging with your mouse or finger
- Use the Embed button to copy an
<iframe>for your LMS or lesson page - Click PNG to export a classroom-ready image
- Click Formula or LaTeX to copy the equation for your notes
Embed this graph
Use the Embed button in the calculator to copy a ready iframe for blogs, LMS pages, and lesson notes.
Open embed pageTeacher prompt
Question: What motion creates the helicoid shape?
Answer: A point moves outward while rotating and rising like a screw.
Related graphs
Explore more parametric examples and compare shapes, 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.
Spherical Cap
z = sqrt(max(0, 16 - x^2 - y^2))A cap from a sphere parameterized by angles.
Spiral Ramp
z = atan(y / (x + 0.001)) + 0.2*sqrt(x^2 + y^2)A ramp that rises as it rotates.
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