A standard English snooker table is 6' x 12'. We know that the
shortest path between any two points on the table is given by the
straight line between them. How do we figure out the shortest
distance between two points if the ball must bounce off one wall?
What if it must bounce off 2 walls? 3 walls?
If you want to try one yourself, let the bottom left hand corner
of the pool table be the origin. Consider the case when the cue
ball is at (5,5) and the target ball is at (10,2). Which wall gives
the shortest path to the target?
Getting a class cast error. so I am commenting this all
out. -E If you have a java enabled browser you
can use at the interactive version below. The interactive diagram
below has two labelled points, A and B. What is the shortest path
from A to B if you bounce off one cushion? In the diagram, you can
click on the "Show" buttons to draw the four possible paths from A
to B. Which is the shortest? You may move A and B around by
clicking on them.
What is the shortest path from A to B using exactly two
cushions? The interactive diagram below shows the eight possible
paths from A to B. How would you calculate the shortest
path?
To experiment further with this problem, download a copy
of Geometer's Sketch
Pad.