Four Reflected Directions and a Fixed Quarter-Point

Four distinct line directions define reflected points and projected feet. If the feet lie on a line parallel to the initial axis, the mean of the reflected points is the fixed quarter-point of that axis. Complex and Euclidean proofs include zero-height configurations, and the range of admissible nonzero heights is determined.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23887920
Primary Topic
Mathematics and Applications
Type
preprint
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preprint

Four Reflected Directions and a Fixed Quarter-Point

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

Four Reflected Directions and a Fixed Quarter-Point

Ziping Guo
preprint en

Abstract

Four distinct line directions define reflected points and projected feet. If the feet lie on a line parallel to the initial axis, the mean of the reflected points is the fixed quarter-point of that axis. Complex and Euclidean proofs include zero-height configurations, and the range of admissible nonzero heights is determined.

Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
DOIOpen Access PDFOpenAlex
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Four Reflected Directions and a Fixed Quarter-Point — Ziping Guo · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS