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!!!

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 Scream" - by Chris Fry '99	"Garfield" - By Erin Wimmers '00 and Mark Wilson '00	"Pagoda" - By Atul Varma '01
"The Kenyon Shield" - By Christine Breiner '98 and David Carroll '98	- By Nkululeko Moyo '02 and Stephanie TerMeer '02	"Old Kenyon" - by Sheldon Kimber '00
"Calvin" - By Jada Twedt '01 and Joshua White '01	"The Train" - By Amy Wagaman '03	- By Jeroen Kniep '01
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!

Denise Darlage and Ludovic Ghesquiere	Meghaan Blauvelt	Molly Farrell	Joshua Louria
Thomas Schliekert	Gwen Ockenlaender and Annie Racek	Brian Warner and Robert Snow	Andew Vincent and Ashley Parker