Hello, This problem reminds me of a geom. construction. Take 2 circles on the X axis of radius 1 , slide them one into each other until the common area is equal to the 2 others. Think as if you had a Venn diagram. When the 3 areas are equal then the height of the intersection is 0.739. The interesting thing about that is the number 0.739... it is the solution of the transcendental equation cos(x) = x. Funny isn't ? To get that number : go to my Inverter to get many digits or the OEIS to get some other infos : http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?An... But to get a <feeling> of what this number is : -take any scien. calculator like an HP something. -put the mode in RADIANS. -type 1. -Hit the COS button until it converges to the number. Unfortunately, I do not know other constructions that leads to other trans. equations too or the inverse. It is easy to generate trans. equations of course, what is more difficult is to invent a geom. construction to explain it. I had this hint about the geom. construction from Gilbert Labelle that read about it a while ago in the AMM (AMS monthly). Simon Plouffe