Problems of the following type, and their solution techniques, were first studied in the 18th century, and the general topic became known as geometric probability. * (Buffon's needle) What is the chance that a needle dropped randomly onto a floor marked with equally spaced parallel lines will cross one of the lines? * What is the mean length of a random chord of a unit circle? (cf. Bertrand's paradox). * What is the chance that three random points in the plane form an acute (rather than obtuse) triangle? * What is the mean area of the polygonal regions formed when randomly oriented lines are spread over the plane?