Woody Dudley Casts a Skeptical Eye on Angle Trisection

November 13, 2009

Trying to trisect an angle with straightedge and compass alone is a dangerous obsession in mathematics, retired DePauw University mathematician Underwood Dudley recently warned. He was speaking to a group of geometry students at Northeastern State University (Tahlequah, Okla.). 

Early on, students learn to bisect angles using the Euclidean―compass and straightedge―method. It's natural to ask whether it's also possible to trisect an angle using the same method. 

"You can't because it's been proved you can't," Dudley said, referring to the work of Pierre Laurent Wantzel in 1837. "That's the beautiful thing about math; once it's proven, it cannot change. Ever." 

Despite the proof, Dudley noted that many mathematicians spend their lives trying to trisect angles using the Euclidean method. Dudley should know. His 1994 MAA book The Trisectors explores the personalities and constructions of these mathematicians.

Through his research, Dudley developed the habit of collecting their various works. "I have the world's largest collection―because I'm reasonably sure it's the only collection―of trisectors," Dudley said. "I have over 200."

In one case, a man spent over 12,000 hours working out a trisection, Dudley said. Showing that trisection to the audience prompted gales of laughter from the large crowd. "As you can see, he came close, but no cigar," Dudley concluded.

"If you leave this university and go out and teach geometry, don't ever, ever bring up the fact that angles cannot be trisected using a compass and straightedge," Dudley said to the students. "Invariably, one of your students will make it their life's work. Which is ridiculous because no one will ever be able to prove that the sum of two even numbers equals an odd number."

Source:  Tahlequah Daily Press, Oct. 8, 2009.