This project was developed for a class in nanotechnology. The project's purpose was to display two principles--building items that you could not see and what volume under the curve in calculus really represented. This program uses Mathematica. It allows the student to enter in two polynomial functions where the degree of the polynomial function is not larger than the 3rd power. The screen will then show a representation in both 2- and 3-dimensions. Using a slider on the picture, another view shows the volume as it would appear if one was to build the figure from the bottom up. This view can be made into a slide show to build a 3D object that represents this volume.
Using the slide show feature on your computer, a data projector, a magnifying glass, and a purchased or homemade elevator to move a container of photosensitive liquid up and down, you can make a 3D printer to get a 3-dimensional prototype of the volume (the area under the curve that is rotated around the y-axis). This prototype will be small enough to fit on a quarter and the cost for everything should fit into even a small school's budget.
Part of the program can be used by any group of students that are learning about graphing linear or quadratic equations. It is easy to see how changing the y-intercept and slope affects a linear equation and also how the coefficient of the squared term in a quadratic changes the width of a parabola.