Riemann Sum Visualization

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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 in the X and Y directions by a factor of 50 to make it more visible, and then scaled in in Z by a factor of 2 to make it slightly more visible. The next 2 objects are the same idea, being a visualization of the curve as a comparison. One is meant to be the surface on its own, to be set on top of the Riemann sum model to show how the estimate is close, but not quite correct, and the other is meant to be a proper integral visualization to compare with the Riemann sum. These were made in Mathematica, mostly just by plugging the equation into some modeling equations. These can be seen in the attached text file. The end result was fairly successful, save for some support mishaps with the surface. This did not impact the surface as a visualization tool, but it was really annoying. As seen in the attached images, the Riemann sum and integral are close, but not quite the same, which is the intended purpose, but now it's easier to see.