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Subject Item
dbr:Circle_packing_in_a_square
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Circle packing in a square Empilement de cercles dans un carré 정사각형 안에 원 채우기
rdfs:comment
L'empilement de cercles dans un carré est un problème d'empilement bidimensionnel dont l'objectif est d'empiler des cercles unités identiques de nombre n dans le carré le plus petit possible. De manière équivalente, l'objectif est de disposer n points dans un carré visant à obtenir le moins de séparation, dn, entre les points. Pour passer d'une formulations du problème à l'autre, le côté du carré des cercles unitaires sera . Des solutions (pas nécessairement optimales) ont été calculées pour chaque n≤10 000. Les solutions allant jusqu'à n = 20 sont indiquées ci-dessous. Circle packing in a square is a packing problem in applied mathematics, where the aim is to pack n unit circles into the smallest possible square; or, equivalently, to arrange n points in a unit square aiming to get the greatest minimal separation, dn, between points. To convert between these two formulations of the problem, the square side for unit circles will be . Solutions (not necessarily optimal) have been computed for every N≤10,000. Solutions up to N=20 are shown below: 정사각형 안에 원 채우기는 유희 수학의 채우기 문제이다. 목표는 단위원 n개를 가장 작은 정사각형에 채우는 것, 또는 n개의 점을 단위 정사각형에 최소거리 dn가 최대가 되도록하는 것이다. 이 두 문제를 변환하려면 단위 원이 있는 정사각형의 한 변의 길이는 이 된다. 해(반드시 최적은 아님)는 N≤10,000에 대해서 모두 계산되었다. N=20 까지의 해를 아래에 나타냈다.:
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L'empilement de cercles dans un carré est un problème d'empilement bidimensionnel dont l'objectif est d'empiler des cercles unités identiques de nombre n dans le carré le plus petit possible. De manière équivalente, l'objectif est de disposer n points dans un carré visant à obtenir le moins de séparation, dn, entre les points. Pour passer d'une formulations du problème à l'autre, le côté du carré des cercles unitaires sera . Des solutions (pas nécessairement optimales) ont été calculées pour chaque n≤10 000. Les solutions allant jusqu'à n = 20 sont indiquées ci-dessous. 정사각형 안에 원 채우기는 유희 수학의 채우기 문제이다. 목표는 단위원 n개를 가장 작은 정사각형에 채우는 것, 또는 n개의 점을 단위 정사각형에 최소거리 dn가 최대가 되도록하는 것이다. 이 두 문제를 변환하려면 단위 원이 있는 정사각형의 한 변의 길이는 이 된다. 해(반드시 최적은 아님)는 N≤10,000에 대해서 모두 계산되었다. N=20 까지의 해를 아래에 나타냈다.: Circle packing in a square is a packing problem in applied mathematics, where the aim is to pack n unit circles into the smallest possible square; or, equivalently, to arrange n points in a unit square aiming to get the greatest minimal separation, dn, between points. To convert between these two formulations of the problem, the square side for unit circles will be . Solutions (not necessarily optimal) have been computed for every N≤10,000. Solutions up to N=20 are shown below: The obvious square packing is optimal for 1, 4, 9, 16, 25, and 36 circles (the smallest six square numbers), but ceases to be optimal for larger squares from 49 onwards.
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