http://en.wikipedia.org/wiki/Compass-and-straightedge_construction http://en.wikipedia.org/wiki/Compass-and-straightedge_constr... Things you can't do with thi

http://en.wikipedia.org/wiki/Compass-and-straightedge_construction http://en.wikipedia.org/wiki/Compass-and-straightedge_constr... Things you can't do with this tool: > Squaring the circle: Drawing a square the same area as a given circle. > Doubling the cube: Drawing a cube with twice the volume of a given cube. > Trisecting the angle: Dividing a given angle into three smaller angles all of the same size. Understanding why we can know that these things are absolutely impossible is an important part of understanding what formal systems mean and, therefore, the philosophy of mathematics as a whole. OTOH, getting into arguments with people who claim to have solved those problems is a wonderful introduction to what 'crankery' means in a mathematical context. http://www.nytimes.com/1999/02/09/science/genius-or-gibberish-the-strange-world-of-the-math-crank.html?pagewanted=all&src=pm http://www.nytimes.com/1999/02/09/science/genius-or-gibberis... http://www.crank.net/maths.html http://www.crank.net/maths.html http://rationalwiki.org/wiki/Pseudomathematics http://rationalwiki.org/wiki/Pseudomathematics http://scientopia.org/blogs/goodmath/tag/cantor-crank/ http://scientopia.org/blogs/goodmath/tag/cantor-crank/ http://meta.math.stackexchange.com/questions/136/how-to-deal-with-cranks http://meta.math.stackexchange.com/questions/136/how-to-deal...