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.
trisection, from the geometry forum archives.
- Animated proof
of the Pythagorean theorem, M. D. Meyerson, US Naval Academy.
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
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.
- 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.
Elements, animated in Java by David Joyce. See also
manuscript excerpt from a copy in the Bodleian library made in the year 888.
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.
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
Andrews famous curves index,
Xah's special curve index,
Weisstein's treasure trove, and
- Jim Loy's
geometry pages. With special emphases on geometric constructions
(and non-constructions such as angle
trisection) as well as many nice
curve. Kevin Trinder squares the circle using its involute spiral.
See also his quadrature
based on the 3-4-5 triangle.
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.
theorem by dissection,
and part III, Java Applets by A. Bogomolny.
Michael Rack finds what appears to be an accurate numerical
approximation to pi using compass and straightedge.
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.
the circle. BNTR finds a pretty geometric visualization of Gregory's
Series for pi/4.
these curves. This problem from Stan Wagon's
asks for a dissection of a circle minus three lunes into a rectangle.
The ancient Greeks performed
as an approach to
squaring the circle.
- Three classical geek problems solved!
Hauke Reddmann, Hamburg.
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.
Damen Crop Circle Reconstructions. What is the geometry underlying
the construction of these large-scale patterns?
From the Geometry Junkyard,
and recreational geometry pointers.
Send email if you
know of an appropriate page not listed here.
from a common source file.