Parameterized Surfaces in Cylindrical Coordinates

You can create cylindrical plots of parameterized surfaces defined by functions such as z(r, θ) = r + cosθ. You plot the parameterized surface r = f (s, t), θ = g(s, t), z = h(s, t) in cylindrical coordinates by entering the expressions for r, θ, and z into a vector $\left(\vphantom{ f(s,t),g(s,t),h(s,t)}\right.$f (s, t), g(s, t), h(s, t)$\left.\vphantom{ f(s,t),g(s,t),h(s,t)}\right)$ and choosing Cylindrical from the Plot 3D submenu.

$\blacktriangleright$ To create a parameterized cylindrical plot

1.
Enter the three defining expressions for r, θ, and z as the components of a vector.


2.
With the insertion point in the vector, from the Plot 3D submenu choose Cylindrical.


The following example shows the ``spiral staircase'' z = θ, a 3D cylindrical plot of the vector $\left[\vphantom{ r,\theta ,\theta }\right.$r, θ, θ$\left.\vphantom{ r,\theta ,\theta }\right]$, with r≤1, 0≤θ≤4π, and.Plot Style set to Hidden Line.

$\blacktriangleright$ Plot 3D + Cylindrical

$\left[\vphantom{ r,\theta ,\theta }\right.$r, θ, θ$\left.\vphantom{ r,\theta ,\theta }\right]$

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