Posted at Mar 25/2006 04:42PM:
Sebastian De Vivo: Katie, it was great to see your project take shape (no pun intended!). Your exploration of the compass is well-balanced between the history of mathematics and current applications of the compass and straightedge to mathematical proofs. I especially liked how sensitive you were to the essence of the thing: on the one hand, pure abstraction (incl. Plato's move away from making these things physical at all) and the materiality of the compass, the straightedge, and their products. Wonderful project!

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My homepage/project proposal---> Katie Howard

"As the geometer intently seeks to square the circle, but he cannot reach, through thought on thought, the principle he needs, so I searched that strange sight: I wished to see the way in which our human effigy suited the circle and found place in it."---Dante's Paradiso, Canto XXXIII, Lines 133-139 (Yay IHUM reading!)

This is how Dante describes his hero's encounter with the image of God. The circle represents God's grace and the square is human reason. He uses the squaring the circle simile to show how humans try and try to understand God, but they can never quite get there with logic. The Divine Comedy was written in the 14th century. By then, compass construction problems had been around for a long time, but were still a long way from being proven impossible. This just shows the degree to which these problems were taken seriously. They have been embedded in culture for over 2 millenia, and are still not fully understood.

In this project I will look at the reasons behind all this hype and how a couple of "things" transformed mathematics and abstract thinking.

Euclid's Elements and the Greeks

Other Beginnings

A Theory in an Artifact

Classical Problems

Constructible Figures and Numbers

Mathematical Beauty and Elegance

Compass Design

Ways to Cheat

My Attempts at Constructing

Katie's Compass Store

Concluding Thoughts

Try out some constructions yourself here: http://www.cs.mcgill.ca/~sqrt/cons/applet.cgi?width=580&height=320

Here are my SOURCES

Other Students' Projects---> Ten Things 2006: Projects