Circle packing in a right isosceles triangle is a packing problem where the objective is to pack n unit circles into the smallest possible isosceles right triangle. Minimum solutions (lengths shown are length of leg) are shown in the table below. Solutions to the equivalent problem of maximizing the minimum distance between n points in an isosceles right triangle, were known to be optimal for n < 8 and were extended up to n = 10. In 2011 a heuristic algorithm found 18 improvements on previously known optima, the smallest of which was for n = 13.
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| - Relleno con círculos de un triángulo isósceles rectángulo (es)
- Circle packing in an isosceles right triangle (en)
- Empilement de cercles dans un triangle isocèle rectangle (fr)
- 직각이등변삼각형에 원 채우기 (ko)
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| - Circle packing in a right isosceles triangle is a packing problem where the objective is to pack n unit circles into the smallest possible isosceles right triangle. Minimum solutions (lengths shown are length of leg) are shown in the table below. Solutions to the equivalent problem of maximizing the minimum distance between n points in an isosceles right triangle, were known to be optimal for n < 8 and were extended up to n = 10. In 2011 a heuristic algorithm found 18 improvements on previously known optima, the smallest of which was for n = 13. (en)
- El relleno con círculos de un triángulo isósceles rectángulo es un problema de empaquetado donde el objetivo es acomodar n círculos de radio unidad en un triángulo isósceles rectángulo lo más pequeño posible. (es)
- L'empilement de cercles dans un triangle isocèle rectangle est un problème d'empilement bidimensionnel dont l'objectif est d'empiler des cercles unités identiques de nombre n dans le triangle isocèle rectangle le plus petit possible. Les solutions minimales sont indiquées dans le tableau ci-dessous. Des solutions optimales sont connues pour n < 8. En 2011, un algorithme heuristique a trouvé 18 améliorations sur les optimum connus précédemment, le plus petit étant pour n < 13. (fr)
- 직각이등변삼각형에 원 채우기는 가장 작은 직각이등변삼각형을 n 개의 단위원으로 채우는 채우기 문제이다. 최소해(길이는 빗변의 길이이다)를 아래의 표에 나타냈다. 직각이등변삼각형안에 n개의 점들간의 최소거리를 최대화하는 문제의 해와 같은 최적해는 n< 8일 때 최적임이 증명되었다. In 2011년에 이 이전에 최적이라고 알려진 해에서 18개의 개선점을 찾아냈으며, 그 중 가장 작은 것은 n=13일 때이다. (ko)
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| - Circle packing in a right isosceles triangle is a packing problem where the objective is to pack n unit circles into the smallest possible isosceles right triangle. Minimum solutions (lengths shown are length of leg) are shown in the table below. Solutions to the equivalent problem of maximizing the minimum distance between n points in an isosceles right triangle, were known to be optimal for n < 8 and were extended up to n = 10. In 2011 a heuristic algorithm found 18 improvements on previously known optima, the smallest of which was for n = 13. (en)
- El relleno con círculos de un triángulo isósceles rectángulo es un problema de empaquetado donde el objetivo es acomodar n círculos de radio unidad en un triángulo isósceles rectángulo lo más pequeño posible. (es)
- L'empilement de cercles dans un triangle isocèle rectangle est un problème d'empilement bidimensionnel dont l'objectif est d'empiler des cercles unités identiques de nombre n dans le triangle isocèle rectangle le plus petit possible. Les solutions minimales sont indiquées dans le tableau ci-dessous. Des solutions optimales sont connues pour n < 8. En 2011, un algorithme heuristique a trouvé 18 améliorations sur les optimum connus précédemment, le plus petit étant pour n < 13. (fr)
- 직각이등변삼각형에 원 채우기는 가장 작은 직각이등변삼각형을 n 개의 단위원으로 채우는 채우기 문제이다. 최소해(길이는 빗변의 길이이다)를 아래의 표에 나타냈다. 직각이등변삼각형안에 n개의 점들간의 최소거리를 최대화하는 문제의 해와 같은 최적해는 n< 8일 때 최적임이 증명되었다. In 2011년에 이 이전에 최적이라고 알려진 해에서 18개의 개선점을 찾아냈으며, 그 중 가장 작은 것은 n=13일 때이다. (ko)
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