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.
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.
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.
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.
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.
