14 May
2011
14 May
'11
3:32 a.m.
PUZZLE: --------------------------------------------------------------- Let there be a lake on the plane filling up the unit circle centered at the origin. The rest of the plane is level ground.
Find the quickest path from (-2,0) to (3,1), possibly passing through the lake, for an amphibious vehicle whose land speed is 1.25 units/hour, and whose water speed is 1 unit/hour. ---------------------------------------------------------------
Equivalently, find the path of a beam of light through land (with an idealised refractive index of 1) and water (with an idealised refractive index of 1.25). Sincerely, Adam P. Goucher