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PreprintarXiv licencearXiv

Degeneracies of Lagrange functions and geometric interpretations of Lagrange multipliers

  • Masaru Hasegawa
Open at sourcePDFDOICite

Abstract

We introduce Lagrange functions associated with height and distance-squared functions on implicit plane curves. We show that degeneracies of these functions characterize geometric properties of the curves, such as inflections and vertices, and give geometric interpretations of the corresponding Lagrange multipliers in terms of contact with lines and circles.

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Cite

BibTeXRIS
BibTeX
@misc{hasegawa2026degeneracies,
  title = {{Degeneracies of Lagrange functions and geometric interpretations of Lagrange multipliers}},
  author = {Masaru Hasegawa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.19517},
  eprint = {2608.19517},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.19517},
}
RIS
TY  - UNPB
TI  - Degeneracies of Lagrange functions and geometric interpretations of Lagrange multipliers
AU  - Masaru Hasegawa
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.19517
UR  - https://arxiv.org/abs/2608.19517
AB  - We introduce Lagrange functions associated with height and distance-squared functions on implicit plane curves. We show that degeneracies of these functions characterize geometric properties of the curves, such as inflections and vertices, and give geometric interpretations of the corresponding Lagrange multipliers in terms of contact with lines and circles.
ER  -