用边长为 $$n^{-1/2-\epsilon }$ 的等边三角形完美包装等边三角形

Pub Date : 2024-05-11 DOI:10.1007/s00454-024-00654-w
Janusz Januszewski, Łukasz Zielonka
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引用次数: 0

摘要

边长为 1、(2^{-t}\)、(3^{-t}\)、(4^{-t},\ldots \)的等边三角形可以完美地组合成一个等边三角形,前提是(\1/2<t \le 37/72)。此外,对于t略大于1/2的情况,边长为1、(2^{-t}\)、(3^{-t}\)、(4^{-t},\ldots \)的正方形可以完美地打包成一个正方形(S_t\),使得一些正方形的边平行于(S_t\)的对角线,其余的正方形的边平行于(S_t\)的边。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Perfectly Packing an Equilateral Triangle by Equilateral Triangles of Sidelengths $$n^{-1/2-\epsilon }$$

Equilateral triangles of sidelengths 1, \(2^{-t}\), \(3^{-t}\), \(4^{-t},\ldots \ \) can be packed perfectly into an equilateral triangle, provided that \(\ 1/2<t \le 37/72\). Moreover, for t slightly greater than 1/2, squares of sidelengths 1, \(2^{-t}\), \(3^{-t}\), \(4^{-t},\ldots \ \) can be packed perfectly into a square \(S_t\) in such a way that some squares have a side parallel to a diagonal of \(S_t\) and the remaining squares have a side parallel to a side of \(S_t\).

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