Height and distance-squared functions on implicit plane curves

Masaru Hasegawa

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arXiv · 2608.19517

Height and distance-squared functions on implicit plane curves

Masaru Hasegawa

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Abstract

We introduce families of Lagrange functions associated with height and distance-squared functions on implicit plane curves. We show that degeneracies of these families 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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Masaru Hasegawa. 2026-08-20. Height and distance-squared functions on implicit plane curves. https://arxiv.org/abs/2608.19517

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