A Ninth-Intersection Theorem for Isogonal Connector Lines

A three-by-three grid of line intersections gives a nine-point implication for the lines joining a point to its isogonal conjugate. The condition of passing through a fixed point is represented by one homogeneous cubic. A direct divisibility proof supplies the required nine-point argument.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23887902
Primary Topic
Mathematics and Applications
Type
preprint
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preprint

A Ninth-Intersection Theorem for Isogonal Connector Lines

Ziping Guo
2 links
Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
preprint

A Ninth-Intersection Theorem for Isogonal Connector Lines

Ziping Guo
preprint en

Abstract

A three-by-three grid of line intersections gives a nine-point implication for the lines joining a point to its isogonal conjugate. The condition of passing through a fixed point is represented by one homogeneous cubic. A direct divisibility proof supplies the required nine-point argument.

Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
DOIOpen Access PDFOpenAlex
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A Ninth-Intersection Theorem for Isogonal Connector Lines — Ziping Guo · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS