Everyone who has been around a math department awhile has seen an ominous bulging manila envelope arrive in the department mail. On the outside of the envelope is written something like "Do you care about the truth?" Inside is a 256-step procedure for trisecting a general angle, using only compass and straightedge. The author wants somebody to spend time to check through this, in order to verify that nothing is wrong.

I will explain why it's not necessary to check through this. More precisely, what do we mean when we say one cannot trisect a general angle with compass and straightedge? This question leads to another interesting topic, the notion of a constructible number. Everyone is welcome. No special background is needed for the talk.