I've found Dudley's A Budget of Trisections pretty fun in this regard: the book is filled with depictions of various people's attempts to trisect an angle with

I've found Dudley's A Budget of Trisections pretty fun in this regard: the book is filled with depictions of various people's attempts to trisect an angle with straightedge and compass. It turns out that a few steps can get you within arcseconds of the correct result, easily enough to fool the eye.