It’s impossible to trisect an angle using a compass and a straightedge, but in 1947 Leo Moser showed how to do it with a pocketwatch. At noon align the watch’s hands with one side of the angle (above, XII), then wait until the minute hand has crossed to the other side (III). At that point the hour hand will have measured one-twelfth of the angle. Double that twice and you have your trisection.
“Now you can trisect an angle anytime, anyplace, for anyone who asks,” writes Underwood Dudley in A Budget of Trisections. “But no one ever will.”