Wednesday, April 30, 2008

Common sense thoughts about geometry

The month April has nearly come to an end and I haven't posted any line to my blog! These past two months, I used all my spare time to ponder over famous geometric problems like the angle trisection or the doubling of the cube. These are "proven" to be impossible to solve with the classical "euclidean tools" that are the compass and the unmarked straightedge. The more I digg into it, the more I feel that such impossibility proofs are just ways to reassure ourselves about our advanced scientific tools.

If an angle exists, the third of an angle also exists. A simple solution hides somewhere beyond scholar hindrances. The same for the double of a cube. If a cube of unit volume exists, a cube with double volume is determined. Or take the squaring of a circle. If a circle has some physical meaning, any other figure may be constructed departing from the area of the circle. Impossibility "proofs" just obstruct the road to a solution. Solutions may be found by playing, playing with real objects, following our intuition.

For an intuitive solution of the squaring of the circle, have a look at the tools of dakhiometry originated by Nguyen Tan Tai.