Multi-linear dimension of inscribed polygons

Chuqi Ren

doi:10.1117/12.2627570

22 April 2022 Multi-linear dimension of inscribed polygons

Chuqi Ren

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121633X (2022) https://doi.org/10.1117/12.2627570
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

Previously, people explored that there is a derivative relationship between area and perimeter of some regions in ℝ² (in ℝ³, it becomes volume and surface area, respectively) which satisfies dA(a) /da = λP(a) (dV(a) /da = λS(a) in ℝ³) and λ is a constant. They called such 𝑎 as a linear dimension of the region. In this paper, we further explore the partial derivative relationship of some regions in two-dimension and three-dimension. That is, discuss the situations when A and P (V and S) depend on several variables. We show that the multi-linear dimensions, which are the distances between the circumcenter and each side of the polygons, exist for some kind of irregular polygons. The necessary conditions are the polygon is inscribed in a circle, and the circumcenter cannot lie on any of its sides.

Citation Download Citation

Chuqi Ren "Multi-linear dimension of inscribed polygons", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121633X (22 April 2022); https://doi.org/10.1117/12.2627570

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