English

Hilbert's Error?

History and Overview 2019-01-23 v2

Abstract

It is well known that a center of a given circle cannot be constructed using only a straightedge and that this was proven by David Hilbert. Still it is not so clear what kind of object is proven to be non-existing. We analyze different attempts to define a geometric construction appearing in the literature and observe that none of them is really satisfactory and that Hilbert's proof needs to be corrected (as noted by Akopyan and Fedorov)

Cite

@article{arxiv.1801.04742,
  title  = {Hilbert's Error?},
  author = {Alexander Shen},
  journal= {arXiv preprint arXiv:1801.04742},
  year   = {2019}
}
R2 v1 2026-06-22T23:45:09.148Z