Double Integrals

Model Overview & Print Notes

***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. --- ## Mathematical Models * This model is featured in my 3DWithUs article! [3D Printable Math Models for Teaching Complex Concepts](https://3dwithus.com/3d-printable-mathematical-models-for-teaching-complex-concepts) * Find more models for mathematics in my [Math Surfaces, Solids, Etc. Collection](https://cults3d.com/en/design-collections/abbymath/math-surfaces-solids-etc). --- ## 3D Printing Settings The *x* and *y* dimensions of the models range from 36 mm to 54 mm. The Circular Paraboloid models are 81 mm tall and the Hyperbolic Paraboloid models are 108 mm tall. (The lowest numbered models are rectangular prisms and have somewhat different dimensions.) Note that the Circular Paraboloid models get wider for higher numbers whereas the Hyperbolic Paraboloid models get narrower. I printed with 0.3 mm layer height, 2 perimeters, 3 solid top and bottom layers, and 10% infill. No supports.* \*For the "HyperbolicParaboloid-Smooth" it was clear in my slicer that the top of the model would not print well because it is thin. I tried a couple different orientations and it worked best to rotate it 90 degrees about each of the *x*- and *y*-axes. I used organic tree supports and printed with 0.2 mm layer height (other settings the same as above). See last photo. --- ## Not for commercial use. No derivatives. See © link. ---

Files (3)