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Certain hyperbolic regular polygonal tiles are isoperimetric
Geometriae Dedicata ( IF 0.5 ) Pub Date : 2021-02-20 , DOI: 10.1007/s10711-021-00605-2
Jack Hirsch , Kevin Li , Jackson Petty , Christopher Xue

The hexagon is the least-perimeter tile in the Euclidean plane. On hyperbolic surfaces, the isoperimetric problem differs for every given area. Cox conjectured that a regular k-gonal tile with 120-degree angles is isoperimetric for its area. We prove his conjecture and more.



中文翻译:

某些双曲正则多边形块是等参的

六边形是欧几里得平面中最小周长的图块。在双曲表面上,对于每个给定区域,等渗问题都是不同的。考克斯推测,具有120度角的规则k角形图块是等面积的。我们证明他的猜想等等。

更新日期:2021-02-21
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