Compass and Straightedge
I include here both pages about the classical Greek compass-and-straightedge style of construction, other topics involving Greek mathematicians such as Pythagoras and Euclid, as well as the three famous problems they found impossible to construct with these tools.
Angle trisection, from the geometry forum archives.
Animated proof of the Pythagorean theorem, M. D. Meyerson, US Naval Academy.
Oliver Byrne's 1847 edition of Euclid, put online by UBC. "The first six books of the Elements of Euclid, in which coloured diagrams and symbols are used instead of letters for the greater ease of learners."
Cinderella multiplatform Java system for compass-and-straightedge construction, dynamic geometry demonstrations and automatic theorem proving. Ulli Kortenkamp and Jürgen Richter-Gebert, ETH Zurich.
Constructing a regular pentagon inscribed in a circle, by straightedge and compass. Scott Brodie.
Equivalents of the parallel postulate. David Wilson quotes a book by George Martin, listing 26 axioms equivalent to Euclid's parallel postulate. See also Scott Brodie's proof of equivalence with the Pythagorean theorem.
Euclid 3:16. Fun geometry T-shirt sighting, from Izzycat's blog. I want one.
Euclid's Elements, animated in Java by David Joyce. See also Ralph Abraham's extensively illustrated edition, and this manuscript excerpt from a copy in the Bodleian library made in the year 888.
An extension of Napoleon's theorem. Placing similar isosceles triangles on the sides of an affine-transformed regular polygon results in a figure where the triangle vertices lie on another regular polygon. Geometer's sketchpad animation by John Berglund.
Gauss' tomb. The story that he asked for (and failed to get) a regular 17-gon carved on it leads to some discussion of 17-gon construction and perfectly scalene triangles.
Greek mathematics and its modern heirs. Manuscripts of geometry texts by Euclid, Archimedes, and others, from the Vatican Library.
Hippias' Quadratrix, a curve discovered around 420-430BC, can be used to solve the classical Greek problems of squaring the circle, trisecting angles, and doubling the cube. Also described in St. Andrews famous curves index, Xah's special curve index, Eric Weisstein's treasure trove, and H. Serras' quadratrix page.
Jim Loy's geometry pages. With special emphases on geometric constructions (and non-constructions such as angle trisection) as well as many nice Cinderella animations.
Pi curve. Kevin Trinder squares the circle using its involute spiral. See also his quadrature based on the 3-4-5 triangle.
PolyMultiForms. L. Zucca uses pinwheel tilers to dissect an illustration of the Pythagorean theorem into few congruent triangles.
Pythagoras' Haven. Java animation of Euclid's proof of the Pythagorean theorem.
Pythagorean theorem by dissection, part II, and part III, Java Applets by A. Bogomolny.
Quadrature. Michael Rack finds what appears to be an accurate numerical approximation to pi using compass and straightedge.
Romain triangle theorem. An analogue of the Pythagorean theorem for triangles in which one angle is twice another.
A small puzzle. Joe Fields asks whether a certain decomposition into L-shaped polyominoes provides a universal solution to dissections of pythagorean triples of squares.
Squaring the circle. BNTR finds a pretty geometric visualization of Gregory's Series for pi/4.
Straighten these curves. This problem from Stan Wagon's PotW archive asks for a dissection of a circle minus three lunes into a rectangle. The ancient Greeks performed similar constructions for certain lunules as an approach to squaring the circle.
Three classical geek problems solved! Hauke Reddmann, Hamburg.
Trisecting an angle with origami. Julie Rehmeyer, MathTrek.
Wonders of Ancient Greek Mathematics, T. Reluga. This term paper for a course on Greek science includes sections on the three classical problems, the Pythagorean theorem, the golden ratio, and the Archimedean spiral.
Zef Damen Crop Circle Reconstructions. What is the geometry underlying the construction of these large-scale patterns?