What if Euclid had been Japanese? There are traditionally stated and proved theorems about origami. And MetaFilter has previously explored modular origami (as well as the boring old artistic kind), which has a geometric foundation. However, origami itself is a powerful mathematical framework that allows one to, for instance, solve the famously insoluable problem of trisecting an angle. More generally: Traditional geometry solves quadratic equations, origami solves cubic ones. (Many more mathematical items about and using origami can be found in the excellent mathematics teachers' book: Project Origami: Activities for Exploring Mathematics, most of which are unfortunately not findable online).
posted by DU on Feb 13, 2007 - 9 comments

Jim Loy's Mathematics Page is (among other things) a collection of interesting theorems (like Napoleon's Triangle theorem), thoughtful discussions of both simple and complex math, and geometric constructions (my personal favorite); the latter of which contains surprisingly-complex discussions on the trisection of angles, or the drawing of regular pentagons.

Similarly enthralling are the pages on Billiards (and the physics of), Astronomy (and the savants of), and Physics (and the Phlogiston Theory of), all of which are rife with illustrations and diagrams. See the homepage for much more.

If you like your geometric constructions big, try Zef Damen's Crop Circle Reconstructions.
posted by odinsdream on Sep 14, 2005 - 8 comments

Euclid in Colour. 'An unusual and attractive edition of Euclid was published in 1847 in England, edited by an otherwise unknown mathematician named Oliver Byrne. It covers the first 6 books of Euclid, which range through most of elementary plane geometry and the theory of proportions. What distinguishes Byrne's edition is that he attempts to present Euclid's proofs in terms of pictures, using as little text - and in particular as few labels - as possible. What makes the book especially striking is his use of colour ... '
posted by plep on Aug 11, 2004 - 15 comments

Euclid's Elements - the ancient Greek mathematicians textbook, presented here with the aid of Java, including Pythagoras' Theorem, and proof that there is an infinite amount of prime numbers.
posted by Orange Goblin on Jan 3, 2004 - 2 comments

The Independent has a report that excavations at Herculaneum has brought forth some 850 papyri and "Among the works, which academics hope to read using the new equipment, are the lost works of Aristotle (his 30 dialogues, referred to by other authors, but lost in antiquity), scientific works by Archimedes, mathematical treatises by Euclid, philosophical work by Epicurus, masterpieces by the Greek poets Simonides and Alcaeus, erotic poems by Philodemus, lesbian erotic poetry by Sappho, the lost sections of Virgil's Juvenilia, comedies by Terence, tragedies by Seneca and works by the Roman poets Ennius, Accius, Catullus, Gallus, Macer and Varus."
posted by stbalbach on Feb 11, 2001 - 20 comments