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arXiv · 1805.06772

A few results on the infimum of regular polygons equal-size split line

Yuyang Zhu
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Abstract

If an n-side unit regular polygon is divided into m equal sized parts, then what is the minimum length of the split line ${l_{m,n}}$? This problem has its practical application in real world. This paper proved that ${l_{2,3}} = \sqrt {\frac{\sqrt 3 π}{12}} $, ${l_{3,3}} = \frac{\sqrt 3 }{2}$, and $\frac{1}{2}\sqrt {nπ{\rm{ctan}}\frac{π}{n}} \le \mathop {\lim }\limits_{m \to \infty } \frac{l_{m,n}}{\sqrt m } \le \sqrt {\frac{\sqrt 3 }{2}n{\rm{ctan}}\frac{π}{\rm{n}}} $

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Yuyang Zhu. 2018-05-15. A few results on the infimum of regular polygons equal-size split line. https://arxiv.org/abs/1805.06772

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