2  A Sea of Mirrors

Program the geometry and start with the initial conditions to, say, 50 digits. Then Mathematica's automatic precision control will show how precision is lost (about 3 digits per reflection). Starting with 50 digits is enough to get the answer to 10 digits. We can get 500 digits easily. The answer is  0.9952629194433541608903118094267216210294669227341543498032088580729861796228306320991749818976188760.

Created by Mathematica  (June 27, 2004)