parametric example
Parametric Surface Graph: Spiral Ramp
A ramp that rises as it rotates.
z = atan(y / (x + 0.001)) + 0.2*sqrt(x^2 + y^2)Teacher prompt
Why does height wrap around the center?
Height uses the angular position, so rotating changes z.
min z 0.00max z 0.0060 samples
What this graph represents
Angle creates the spiral height change while radius adds outward slope.
Where it appears in calculus
Good for explaining polar angle in 3D.
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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.