The author delves into the issues of error and error propagation in classical geometry constructions. Through the example of the classical construction of Apollonius’ perpendicular bisector, the sensitivity of these constructions to small errors using compass or straightedge placement is highlighted. The author illustrates how errors in these placements can accumulate and propagate throughout the construction, impacting the accuracy of the final result. The discussion raises questions about the sensitivity of classical constructions to errors and proposes potential improvements, such as using larger circles to reduce variations. The author also touches on the concept of error estimation through probability distributions and suggests repetition or convergence algorithms to enhance accuracy.
https://jdh.hamkins.org/propagation-of-error-in-classical-geometry-constructions/