Double Integrals

Over 60 Models Included! Print a Progression!

These are terrific for my Calculus III class, and the added bonus is that my younger students started asking questions about higher-order mathematics as well!

These models represent approximations for double integrals that find volume for a circular paraboloid and a hyperbolic paraboloid. I made approximately 30 model files for each shape that show more and more refinement. The number in each filename matches the number of squares across the diameter in the model.

The photos show the models that I chose to print for both shapes. These correspond to numbers 3, 7, 11, 25, and Smooth. I prefer the look of the odd numbers since they have a distinct middle square.

The files are in the downloadable .zip folder, but I included copies of "CircularParaboloid-20" and "HyperbolicParboloid-20" outside the folder for the 3D model preview. The animations included among the photos show each of the numbered models. Smooth models for both shapes are also in the .zip folder.

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Mathematical Models

• This model is featured in my 3DWithUs article!
  3D Printable Math Models for Teaching Complex Concepts

• Find more models for mathematics in my Math Surfaces, Solids, Etc. Collection.

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