John McCoy's Ancient Geometry Stuff

The assistance of Ty Harness in my attempt to make sense of the methodology of the ancient geometers is gratefully acknowledged. Any mistakes or erroneous conclusions found on this page, however, are totally my own doing.

Cubes Pyramids Frustums - pdf file

Eratosthenes' Panel Model - GeoGebra file

Eratosthenes' Panels - interactive html file

Archytas' Constructing Two Means - pdf file

Archytas' 3D Simulation - interactive html file

Archytas Device Animations

Eudoxus and Descartes - pdf file

Menaechmus' Triads - pdf file

Menaechmus' Compass - Physical Model - pdf file

Archimedes' On Conoids - pdf file

Archimedes' On Conoids P7 Three Solutions - GeoGebra file

Apollonian Cone Cevians - interactive html file

Composite Archimedes-Apollonius Model - GeoGebra file

About Conics - Part 1. Angle Chords - html file

Conic Curves - pdf file

Timoshenko Particles - pdf file

Catapults & Cube Roots - pdf file

Frustum Formula, Means and Eratosthenes' Mesolabe - pdf file

This quotation from the 1830's "Penny Cyclopaedia of the Society for the Diffusion of Useful Knowledge" contends that
"Modern writers employ fractions instead of ratios, and with great advantage. But the student who leaves untouched that consideration of ratio which includes incommensurables as well as commensurables will never be more than a mathematician to a certain number of decimal places."
Then in a 2012 conference paper I found this comment about a theorem the author was preparing to discuss.
"...(I first found [it] in a newspaper, sent in by a GEOM (Geometrically Excited Old Man). For some reason, some elderly men continue to be intrigued by geometry, usually in a negative manner, trying to prove every angle can be trisected, etc.)..."
As an octogenarian I feel obligated to disclose that I may be only a two bit mathematician but I am at least half a GEOMeter.

first created: 2014-01-28
last modified: 2016-02-06
page author: jhmc