Historical Activities for Calculus - Module 3: Optimization Problems Then and Now

Module 3: Optimization Problems Then and Now

Perhaps the most important application of the differential calculus is the solution of optimization problems, where one wants to find the value of a variable that maximizes or minimizes a certain quantity. In this module we look at the history of some of these problems and their solutions.

• 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

References

Paul J. Nahin, When Least is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible, Princeton University Press, 2004.

V.M. Tikhomirov, Stories about Maxima and Minima; translated from the Russian by Abe Shenitzer, American Mathematical Society/Mathematical Association of America, 1990.