Dan Asimov wrote:

In trying what used to always work -- just copying your text to a primitive editor (Notepad) to an equal-width font, the text no longer reconstructs itself.

Looks OK to me. Will your mail client let you save the message into a file that you can then open in Notepad? Here's the relevant bit of rwg's message with spaces replaced by "." characters; perhaps that will discourage mangling. A.couple.of.years.ago.I.here.gave ...............................................2 .................(cos(c).+.cos(b).+.cos(a).+.1) .........acos(--------------------------------------.-.1). ..............(cos(a).+.1).(cos(b).+.1).(cos(c).+.1) Duh, ....................cos(c).+.cos(b).+.cos(a).+.1 .............2.acos(----------------------------). .............................a......b......c .......................4.cos(-).cos(-).cos(-) .............................2......2......2 Imaginary.result.means.you.violated.the.triangle.inequality...Tsk. --rwg PS,.for.those.interested.in.trig.exercises,.this.started.out.as .....cos(a).-.cos(b).cos(c).........cos(b).-.cos(a).cos(c) acos(----------------------).+.acos(----------------------) .........sin(b).sin(c)..................sin(a).sin(c) .........................................cos(c).-.cos(a).cos(b) ..................................+.acos(----------------------).-.%pi .............................................sin(a).sin(b) The key thing I think you guessed wrong in your rearrangement is that "4 cos a/2 cos b/2 cos c/2" was the denominator; not just abc. :-) -- g