Parallel packing a square with isosceles right triangles and equilateral triangles
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910249454141440 |
|---|---|
| author | Su, Chen-Yang |
| author_facet | Su, Chen-Yang |
| contents | Suppose that $I$ is a unit square. Let $T$ (resp. $Δ$) be an isosceles right triangle (resp. an equilateral triangle). We prove that any collection of triangles homothetic to $T$ (resp. $Δ$), whose total area does not exceed $\frac{1}{2}$ (resp. $\frac{\sqrt{3}}{4}$), can be parallel packed into $I$. These upper bounds are tight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09406 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parallel packing a square with isosceles right triangles and equilateral triangles Su, Chen-Yang Combinatorics Suppose that $I$ is a unit square. Let $T$ (resp. $Δ$) be an isosceles right triangle (resp. an equilateral triangle). We prove that any collection of triangles homothetic to $T$ (resp. $Δ$), whose total area does not exceed $\frac{1}{2}$ (resp. $\frac{\sqrt{3}}{4}$), can be parallel packed into $I$. These upper bounds are tight. |
| title | Parallel packing a square with isosceles right triangles and equilateral triangles |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.09406 |