A STEM Project: Slice Forms of Common Quadric Surfaces Part #3

Slice Form of an Elliptic Paraboloid

Side View

I made slice forms of six different quadric surfaces: Hyperbolic Paraboloid aka Monkey Saddle, Ellipsoid, Hyperboloids of One Sheet, Cone, Hyperboloids of Two Sheets and Elliptic Paraboloid.   This post is the third of three posts about quadric surface slice forms.  It is the slice form of an Elliptic Paraboloid. 

Quadric surfaces are the graphs of any equation that can be put into the general form

$$A{x}^2+B{y}^2+C{z}^2+Dxy+Exz+Fyz+Gx+Hy+Iz+J=0$$

where $A$, … , $J$ are constants. 

I made all of the slice forms by using this formula. I graphed the quadric surface with the Desmos online graphing calculator, https://www.desmos.com/calculator.  The image created represents the traces needed to form each slice. The slices were then divided by a constant interval of 0.5 inches to create the slits.

Here is the PDF.  I used a good quality 65 lb. cardstock.  The paper needs to be stiff and should not curl.  Otherwise the slices will curl. The slice forms are assembled by sliding the two center slices together.  Next, all of the upward facing slices are slid onto the center slices.  Lastly, all of the downward facing slices are slid onto the center slices.

https://drive.google.com/file/d/1aZ9xnPZwBghJBTY-PJHkoN4K32NdpvVU/view?usp=sharing

Here is the .Studio file.

https://drive.google.com/file/d/1eKuxM1maJGsjTgzaAcMiRh_CNrfJExI_/view?usp=sharing

Here is the SVG. The SVG file goes beyond the viewable area.  To see the entire file, zoom out.

https://drive.google.com/file/d/1FeShzutZHU9Bz-YrJuNwGx1oTjWB8CZm/view?usp=sharing

Elliptic Paraboloid

An equation of an elliptic paraboloid. 

• The horizontal cross sections are circles, if a and b are equal. If a≠b, the cross sections are oval.

$$\mathrm{x2a2+y2b2=\; z}$$

To make an elliptic paraboloid slice form, with a and b equal(circular base), I used its formula and graphed the surface.  I made traces at constant intervals of 0.5 inches.  These traces represent the slices of the figure.

Elliptic Paraboloid Slice Form lying flat