I have followed straight dope for about 10 years now and I have been haunted by a geometry question for about 20 years. I never thought to link the two until I saw another math post today. Maybe the clever people here can end my torment.

The scene … I was 19 years old and at the Royal Navy school of engineering and for some reason found myself working for a week in an office full of math(s) instructors - mostly Oxford & Cambridge graduates. Every morning the head of math(s) would set the instructors a puzzle of the day. I was able to solve most of them but failed at one and it has stuck in my mind ever since.

Here’s the question…

How do you bisect a line with just a compass ? ( a pair of compasses for english readers ).

He gave us a clue - that I was the only one in the room with insufficient math knowledge to solve the problem. (That should have been my hint to give up 20 years ago).

Every now and again, I drag this out and work on it for a couple of weeks or share it with friends - I sometimes feel I am close to a solution but … I just end up with mounds of crumpled paper covered in circles.

I even tried writing a program to find the answer by exhaustion - that was fun, but equally unsuccessful.

I gave up a couple of years ago and started posting the question to prominent math web sites and newsgroups but I was either ignored or was told to draw two arcs and use a ruler to join the two intersections … but you guys of course realize that that is the point … there is no ruler - only a compass.

Can anyone put me out of my misery ? I am sure the answer will turn out to be “it’s not possible” - a proof would be nice if that’s the case.

I was hoping at least the cabbage people might be able to help me out …