Project 6.6

Euclid clearly made a distinction between the definition of a figure and the proof that such a figure could be constructed. Two very famous problems in mathematics focus on this distinction:
1. Trisect an angle using only a straightedge and compass.

Reference:

Trisecting:
http://www.geocities.com/CapeCanaveral/Launchpad/5577/musings/trisect.html

2. Square a circle: Using only a straightedge and compass, construct a square with an area equal to the area of a given circle.

Reference:

http://mathforum.org/isaac/problems/pi3.html
This site has an interesting interactive component to help you to understand the problem. There are also links to other sites. Other sites are:

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Squaring_the_circle.html

These problems have been proved to be impossible (as compared with unsolved problems that might be possible). Write a paper discussing the nature of an unsolved problem as compared with an impossible problem.

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