I’d like to discuss the issue of error and error propagation in the constructions of classical geometry. How does error propagate in these constructions? How sensitive are the familiar classical constructions to small errors in the use of the straightedge or compass? Let me illustrate what I have in mind by considering the classical construction of Apollonius of the perpendicular bisector of a line segment $AB$.  One forms two circles, centered at $A$ and $B$ respectively, each with radius $AB$....