The Problematic
Four Bugs Problem –
An Ellipse, a Carpenter's Square and a Circle (pdf of 3/06/2010)
Draft paper on geometry motivated by observation of tendrils that grow on a California native plant known to hikers in coastal chaparral as "California Manroot". (See related slide shows.)
The exercise of imagining how a classic discovery in mathematics may have been made, though fanciful, can lead to discoveries about the history of mathematics. An example was in reconstructing the consequences of Kepler's Laws. After deriving the inverse-square law from Kepler's Laws — and how they in turn imply Kepler's laws — I looked to see how the results were discovered originally. Here are my notes on Kepler's Elliptical Orbits of the Planets and Newton's Inverse-square Law of Gravitation. The talk Hey, who really discovered that theorem! was drawn from such exercises.
Another exercise of imagination led to questions about the history of discoveries — finding the graph of a hanging chain without knowing about cosh and sinh. This has resulted in three talks regarding the solution published by Leibniz in a 1691 issue of Acta Eruditorum; these are linked on the home page.
Remembering Ray Redheffer.
(Last modified May 30, 2017)