Why proof by pattern of examples doesn’t work Posted on 21 April 2009 by John Draw a few points on a circle and then draw a straight line from every point to every other point. Count the number of regions created. 2 points, 2 regions. 3 points, 4 regions. 4 points, 8 regions. 5 points, 16 regions. 6 points? See this post from the f(t) blog for the answer.