Below you will find links to examples of differential and difference equations of historical significance studied by the great early masters.More Phaser Modules...

Archimedes' Pi MAP

How Archimedes launched the race to Pi. "Proposion 3: The circumference of any circle is three times the diameter and exceeds it by less than one-seventh of the diameter and by more than ten-seventyoneths" -- fromMeasurement of a Circleby Archimedes (287-212 BC). Difference equations converging to Pi.

Leibniz's Pocket Watch ODE

How Leibniz determined, using a first-order ODE, the trajectory of his pocket watch as he pulled it on a table. "The distinguished Parisian physician Claude Perrault, equally famous for his work in mechanics and in architecture... proposed this problem to me and to many others before me, readily admitting that he had not been able to solve it..." (Leibniz 1693).

Newton's First ODE

How Newton approximated the solutions of a first-order ODE using infinite series. "But this will appear plainer by an Example or two. ..." (Newton 1671) -- After outlining his general method for finding solutions of differential equations. The equation in this module is his first significant example.

(NOTE: The images of the great early masters used here on this site are in the public domain; their copyrights have expired.)