Work

Focal Midpoints, Rectangular Hyperbolas, and Orthocentre Reconstruction

Year: 2026

Type: preprint

Abstract: The midpoints of equal-product focal pairs for a nonrectangular cyclic quadruple form a rectangular hyperbola with one excluded point. An orthocentre closure property yields unique focal reconstruction from three admissible midpoints. For a quadruple on a triangle's nine-point circle, the excluded point is the midpoint of the circumcentre and the fourth anchor.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.23887916

Author: Guo, Ziping

Language: English

Topic: Mathematics and Applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225108186

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