TITLE: Can a line of π lengths be drawn with a compass and straight edge?
QUESTION [5 upvotes]: I've drawn two random points on a two dimensional plane. If the distance between these two points is one unit, can a line of π units be drawn using a compass and straight edge?
Or, is there a proof that shows this is impossible?

REPLY [5 votes]: No (to your first question). A constructible number  must be  algebraic. However  $\pi$ is  not an algebraic number ($\pi$ is  a transcendental number). Also of interest with regards to this is the famous 
 "squaring the circle"  problem.