Compass and Straightedge
I include here both pages about the classical Greek
compassandstraightedge 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 compassandstraightedge construction,
dynamic geometry demonstrations and
automatic theorem proving.
Ulli Kortenkamp and Jürgen RichterGebert, 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 Tshirt 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 affinetransformed 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 17gon carved on it leads to some
discussion of 17gon 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 420430BC, 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 nonconstructions 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 345 triangle.
 PolyMultiForms.
L. Zucca uses pinwheel tilers to dissect an illustration of the Pythagorean
theorem into few congruent triangles.
 Proofs of the Pythagorean Theorem.
 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 Lshaped
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 largescale patterns?
From the Geometry Junkyard,
computational
and recreational geometry pointers.
Send email if you
know of an appropriate page not listed here.
David Eppstein,
Theory Group,
ICS,
UC Irvine.
Semiautomatically
filtered
from a common source file.