[math-fun] Triangle puzzle

Let a, b, m > 0, with m < min{1/a, 1/b}. Let T be the triangle in R^2 with vertices A = (-a,0), B = (b,0), and C = (0,1). Draw the NE-ish segment at slope m from L(0) = (0,0) to BC, and denote its right endpoint as R(1). Draw the NW-ish segment at slope -m from R(1) to AC and denote its left endpoint as L(1). Repeat infinitely many times, obtaining R(2), L(2), etc. What is the total length of all the segments so drawn? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele