The Problem

Important Update

My remarkably simple method of exact trisection “cheating” has now been acknowledged by the mathematical fraternity. Professor W. Kahan of the University of California at Berkeley, amongst others, has pronounced my construction valid, and has declared it “slightly simpler” than the most famous method of all, that of Archimedes of Syracuse. A paper describing my method has now been published In The Mathematical Association of America’s March 2007 issue of The College Mathematics Journal. See two separate proofs.




If you know anything at all about geometry, you will know how to bisect an angle with a compass and ruler. But do you know how to trisect it? I'm sure you don't. The surprising truth is that it can't be done. You simply cannot trisect an arbitrary angle with only a compass and unmarked ruler. Well, not without cheating.

Although it has been known for nearly 200 years that compass-and-ruler trisection is a mathematical impossibility, thousands have continued stubbornly to embark on the ancient quest of finding a way to do it. I am one of them.

I have two excuses for such an apparent waste of time. Neither involves a disdain for the pronouncements of mathematics or science. Although I am not a scientist, I have the utmost respect for science - so much so that I believe our threatened world would be a very much better place if the scientific approach to solving problems were universally applied by individuals and institutions. Science works. It works because its entire focus is the pursuit of truth by observation and reason. It doesn’t mind being challenged. In contrast to many other areas of human thought, it demands that it should be, for its respect for the truth is so steadfast that it welcomes the exposure of its own inadvertent falsehoods.

This provides me with my first excuse, for science does make mistakes. It is quite sensible for fresh minds to revisit its pronouncements in case it has misconstrued or overlooked anything.

My second excuse is that the intellectual challenge of trying to do the impossible can be a rewarding one - as long as it is not done out of ignorance and contempt for the probabilities and realities of mathematics and physics and logic. One invariably develops a deep understanding of the science underlying the insoluble problem with which one is wrestling. And occasionally - just very occasionally - one might glean an original and perhaps useful insight. Over the years I have gleaned a number of such useful insights in many different fields. My groundbreaking method of trisection is just one of them.