Historical Activities for the Calculus Classroom

Editors' note:  This article was originally published in Convergence in August of 2007.  We are pleased to "reprint" it in June/July of 2014 with GeoGebra applets hosted by GeoGebraTube. In addition to viewing these applets in the webpages of this article, you may view and download all of the applets that appear in the article directly from GeoGebraTube at http://tube.geogebra.org/m/jdRxWdw6?doneurl=%2F.

The history of the calculus is a fascinating story, inspired by the search for solutions to interesting problems.  We do our students a disservice when we fail to share with them some of this exciting history.  During 2005-07, with support from the National Science Foundation, I developed modules for teaching calculus concepts in a way that integrates the historical evolution of these concepts.  This article contains three examples, which include several interactive applets produced using the software GeoGebra, a free, open-source software package.  In addition, many of the exercises provided require GeoGebra and/or a computer algebra system (CAS) such as Maple, Mathematica, or a Texas Instruments (TI) Voyage 200 calculator.

Module 1:  Curve Drawing Then and Now

Module 2:  Tangent Lines Then and Now

Module 3:  Optimization Problems Then and Now

• Heron's “Shortest Distance” Problem
• Snell's Law and the Principle of Least Time
• L'Hôpital's Pulley Problem and the Principle of Least Potential Energy
• Regiomontanus' Hanging Picture Problem
• Galileo and the Brachistochrone Problem