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Mathematical Expression Editor
Learn how to draw an elliptic and a hyperbolic paraboloid.
At this point, you should get to know elliptic paraboloids and hyperbolic paraboloids.
For both of these surfaces, if they are sliced by a plane perpendicular to the plane ,
the cross-section looks like a parabola, hence the name paraboloid.
One way to get to know these surfaces, is to practice drawing them.
Drawing an elliptic paraboloid
We’ll start with elliptic paraboloid that opens up, like . You begin by drawing a set
of axes:
Now draw a parabola in the -plane:
Now add-in an ellipse:
To draw an elliptic paraboloid opening down, like you draw something like this:
Drawing a hyperbolic paraboloid
Most folks find the hyperbolic paraboloid more difficult than the elliptic paraboloid
to draw. Time to teach you the tricks of the trade. Let’s draw Note here, as the
absolute value of increases, the -values increase. As the absolute value of increases,
the -values decrease. We’ll see this in our drawing. You begin by drawing a set of
axes:
Now draw a parabola in a -plane that contains some positive -value.
Now draw a curvy line:
And another parabola:
Finally, add in the base:
And you have a hyperbolic paraboloid! In our picture above, we can literally see that
as the absolute value of increases, the -values increase and that as the absolute value
of increases, the -values decrease. Cool!
