Some of my Favorite Calculus Projects...
I am a big fan of using technology in the classroom. In the calculus sequence,
I use the computer algebra system Maple for visualization, computation,
and discovery-based learning. I enjoy writing interactive computer-based
projects to motivate mathematical concepts and pique student interest. Projects
involving an element of design and/or competition are particularly popular
with students. Two such examples are given below. The Goblet Project was
developed by my colleagues here in the Mathematics Department (not by me).
1. The Goblet Project -
In second semester calculus students are asked to design a wine goblet that meets the following requirements.
(1) To reduce the cost, the wineglass will be molded using a symmetric mold: therefore, the goblet must be a solid of revolution.
(2) The goblet must hold 150 cm^3 of wine.
(3) The goblet should not be easily tipped over. Therefore, the height H of the center
of mass must be suitably related to the base radius R. It's required that H/R <= 3.
(4) It requires no more than 150 cm^3 of glass to manufacture the wine goblet.
(5) The stem thickness must be at least 1/4 cm at its thinnest point.
Any goblet design meeting all five of the requirements is then entered into a competition; the competition is judged on aesthetic value only. Judges are usually members from the faculty or administration at Kenyon, and the winning entry earns a famous gourmet pizza made by the master chef Eric Holdener!!!
STUDENT WORK (all from the Spring, 2000 course offering):
2. The Parametric Plot Project -
The following artwork was done by Kenyon students in Multivariable Calculus. They were asked to create a pretty picture with Maple after a brief introduction to parameterizations of lines, ellipses, and functions. You can find an online version of the project here .
The Winning Entry in the Spring of 2004 - by Christopher White
A parametric rendition of Bill Watterson's Calvin and Hobbes comic strip using 234 lines of code!
If you are interesting in learning more about my use of art and design in calculus projects, you can read my paper Art and Design in Mathematics which was published in the Journal of Online Mathematics and its Applications in June of 2004.
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Last Modified: August 17, 2005