Perfectly Packing an Equilateral Triangle by Equilateral Triangles of Sidelengths n-1/2-ϵ.
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| Title: | Perfectly Packing an Equilateral Triangle by Equilateral Triangles of Sidelengths n-1/2-ϵ. |
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| Authors: | Januszewski, Janusz1 (AUTHOR) januszew@pbs.edu.pl, Zielonka, Łukasz1 (AUTHOR) lukasz.zielonka@pbs.edu.pl |
| Source: | Discrete & Computational Geometry. Sep2025, Vol. 74 Issue 2, p286-301. 16p. |
| Subjects: | Packing problem (Mathematics), Triangles, Geometry, Mathematics, Geometric shapes |
| Abstract: | Equilateral triangles of sidelengths 1, 2 - t , 3 - t , 4 - t , ... can be packed perfectly into an equilateral triangle, provided that 1 / 2 < t ≤ 37 / 72 . Moreover, for t slightly greater than 1/2, squares of sidelengths 1, 2 - t , 3 - t , 4 - t , ... 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 . [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | Equilateral triangles of sidelengths 1, 2 - t , 3 - t , 4 - t , ... can be packed perfectly into an equilateral triangle, provided that 1 / 2 < t ≤ 37 / 72 . Moreover, for t slightly greater than 1/2, squares of sidelengths 1, 2 - t , 3 - t , 4 - t , ... 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 . [ABSTRACT FROM AUTHOR] |
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| ISSN: | 01795376 |
| DOI: | 10.1007/s00454-024-00654-w |
