Compass and straightedge angle construction

[trini]

Ok so couple questions, what is the use of this method of creating angles? does being able to construct an angle using only this method give that angle any special properties in physical situations, or is it just a matter of being a backup plan in case you for some reason happen to have a compass and ruler on you, and no protractor, and need to construct said angle? Also,is it possible to trisect a 120 degree angle?

[lurflurf]

It is a game. This supposedly started when people realized that some constuctions could be constructed with only a few tools, so it was decided that when a construction could be accomplished without a tool it would be better to not use it. It was further decided that since preforming constructions with minimal tools was preferable that constuctions that require minimal tools would be prefered to those that required more.

[HallsofIvy]

The early Greek's were very good at geometry, but not very good at algebra (their lack of a good numeration system handicapped them)-, and used geometry to define numbers. There would be no point in using a protractor labeled with angles or a ruler labeled with distances since that would assume the numbers a-priori.