论文标题
魔术三角形
Magic Triangles
论文作者
论文摘要
魔术正方形是众所周知的整数安排，具有共同行，列和对角线。已经提出了其他各种魔术形状，但是三角形被忽略了。我们在三个方向上介绍了整数的某些三角形安排，我们称之为魔术三角形。对于这些三角形的小尺寸，我们计算独特的魔术三角形的数量，并检查其内部不同位置的整数的分布。虽然我们无法以更大的尺寸列举魔术三角形的数量，但我们提供了一种模拟的退火方法来寻找魔术三角形。
Magic squares are well-known arrangements of integers with common row, column, and diagonal sums. Various other magic shapes have been proposed, but triangles have been somewhat overlooked. We introduce certain triangular arrangements of integers with common sums in three directions, which we call magic triangles. For small sizes of these triangles, we count the number of unique magic triangles and examine distributions of integers at different positions within them. While we cannot enumerate the number of magic triangles at larger sizes, we offer a simulated annealing method for finding magic triangles.
