Constructive Harmonic Conjugates

TL;DR

This paper provides a constructive proof of the invariance of harmonic conjugates in the real projective plane, ensuring their independence from auxiliary choices, based on principles by Errett Bishop.

Contribution

It introduces a constructive proof of the invariance theorem for harmonic conjugates, advancing the understanding of their properties in projective geometry.

Findings

Constructive proof of invariance theorem provided

Harmonic conjugates are shown to be independent of auxiliary elements

Methods follow principles by Errett Bishop

Abstract

In the study of the real projective plane, harmonic conjugates have an essential role, with applications to projectivities, involutions, and polarity. The construction of a harmonic conjugate requires the selection of auxiliary elements; it must be verified, with an invariance theorem, that the result is independent of the choice of these auxiliary elements. A constructive proof of the invariance theorem is given here; the methods used follow principles put forward by Errett Bishop.