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December 2021 Parallel packing of triangles with squares
Zhanjun Su, Manman Lu, Xi Liu
Rocky Mountain J. Math. 51(6): 2209-2216 (December 2021). DOI: 10.1216/rmj.2021.51.2209

Abstract

Suppose T1 (resp. Δ1) is an isosceles triangle with base length 1 and with height 122 (resp. 132). Let S be a square with a side parallel to the base of T1 (resp. Δ1) and let {Sn} be a sequence of the homothetic copies of S. We first determine the bound of sums of areas of squares from the sequence {Sn} that permits a parallel packing of T1 (resp. Δ1). Then we generalize the results about packing T1 (resp. Δ1) with squares to some other triangles. Finally, we consider the parallel packing of the right triangle T2 (with leg lengths 1 and 2) with squares.

Citation

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Zhanjun Su. Manman Lu. Xi Liu. "Parallel packing of triangles with squares." Rocky Mountain J. Math. 51 (6) 2209 - 2216, December 2021. https://doi.org/10.1216/rmj.2021.51.2209

Information

Received: 29 January 2021; Revised: 27 April 2021; Accepted: 27 April 2021; Published: December 2021
First available in Project Euclid: 22 March 2022

Digital Object Identifier: 10.1216/rmj.2021.51.2209

Subjects:
Primary: 05B40 , 52C15

Keywords: isosceles triangle , parallel packing , right triangle , square

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 6 • December 2021
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