On the Properties of Curves and Parametrization-Independent Isoperimetric Inequality

Kazuhisa Nakasho; Yasunari Shidama

doi:10.2478/forma-2024-0016

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On the Properties of Curves and Parametrization-Independent Isoperimetric Inequality

Formalized Mathematics

Volume 32 (2024): Issue 1 (August 2024)

By: Kazuhisa Nakasho and Yasunari Shidama

Open Access

|Dec 2024

Abstract

In this article we formalize in Mizar several properties of curves. We introduce the definition of the ArcLenP function and define arc length parametrization with its fundamental properties. Finally we prove an isoperimetric inequality that holds regardless of the curve’s parametrization.

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Articles in this issue

DOI: https://doi.org/10.2478/forma-2024-0016 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 195 - 201

Accepted on: Dec 14, 2024

Published on: Dec 31, 2024

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

isoperimetric theorem,

differential geometry,

parametric curve

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2024 Kazuhisa Nakasho, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Volume 32 (2024): Issue 1 (August 2024)