Section 6.1 Reference Topics
If you want to see a sample page from Euclid's Elements (with
associated links), look at:
http://www.lib.virginia.edu/science/parshall/elementsamp.html
This site is an amazing visual treat! Great examples of symmetry.
http://www.moonstar.com/~nedmay/chromat/fibonaci.htm
Problem 1 presents an optical illusion. If you like this sort
of problem you might enjoy checking out this site.
http://www.billiardworld.com/puzzles.html
You might be interested in the art of M.C. Escher.
http://www.iproject.com/escher/escher100.html
http://www.mathacademy.com/pr/minitext/escher/
This site discusses many of the topics of this chapter.
http://library.thinkquest.org/2647/geometry/geometry.htm
Three great Problems of Classical Geometry:
There are three great problems from classical geometry. The first, Trisecting
an Angle, is mentioned in the text. Here are couple of great sites discussing
this topic.
This site shows an example of a web posting of someone who "almost"
solved this problem:
http://www.geocities.com/CapeCanaveral/Launchpad/5577/musings/trisect.html
The following site gives a history of this classical problem:
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Trisecting_an_angle.html
The second classical problem, Squaring the Circle, involves
constructing a square equal in area to that of a given circle. Whether you
can do this depends on the tools that you allow yourself to use. Plato was
the first to attempt this construction allowing himself only a straightedge
and compass.
http://mathforum.org/isaac/problems/pi3.html
This site presents a proof that this classical problem is impossible: http://www.geom.umn.edu/docs/forum/square_circle/
The following site gives a history of this classical problem:
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Squaring_the_circle.html
The third classical problem, doubling the cube, involves constructing a solid with double the volume of a given solid.
This site presents the problem along with many great links: http://mathworld.wolfram.com/CubeDuplication.html
The following site gives a history of this classical problem:
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Doubling_the_cube.html