Newton Diameters and the Deltoid Envelope of a Regular Trifolium

For a regular three-petalled quartic, the mean of four secant intersections lies on an explicit Newton diameter. The envelope is a deltoid scaled by one quarter. Vieta's formula and a separate exceptional-direction calculation establish the diameter identity and the existence of four distinct real intersections in every direction.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23887926
Primary Topic
Mathematics and Applications
Type
preprint
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preprint

Newton Diameters and the Deltoid Envelope of a Regular Trifolium

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

Newton Diameters and the Deltoid Envelope of a Regular Trifolium

Ziping Guo
preprint en

Abstract

For a regular three-petalled quartic, the mean of four secant intersections lies on an explicit Newton diameter. The envelope is a deltoid scaled by one quarter. Vieta's formula and a separate exceptional-direction calculation establish the diameter identity and the existence of four distinct real intersections in every direction.

Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
DOIOpen Access PDFOpenAlex
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Newton Diameters and the Deltoid Envelope of a Regular Trifolium — Ziping Guo · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS