Riemann Sum Visualization

George Mason University Math 401: Mathematics Through 3D Printing.

This set of objects was created for a project where we explored how a calculus topic could be represented through 3D modeling. I chose Riemann sums as my topic, specifically double sums that are in 3 dimensions. To help guide me, I took a problem from a calculus textbook: "Consider the solid that lies above the square (in the xy - plane) R = [0, 1] x [0, 1], and below the elliptic paraboloid z = 25 - x^2 + xy - 4 y^2. Estimate the volume by dividing R into 9 equal squares and choosing the sample points to lie in the midpoints of each square."

The first object to be created was the model of the Riemann sum, which can be seen in the code of the given OpenSCAD file. The creation for this was relatively simple, I created 9 squares and arranged them in a 3x3 grid. I then put them at the height of the curve given by the problem at their midpoints, as indicated by the problem. Because the region is so small, I scaled it