论文标题
弦艺术网的数学
The Mathematics of String Art Nets
论文作者
论文摘要
弦艺术是木板上的钉子的布置，这些钉在这些钉子之间，形成了美丽的几何图案。在本文中，我们考虑了一种简单的字符串艺术形式，其中钉在两个不同的轴上，弦线将第一个钉子在一个轴上连接到第二个轴上的最后一个钉子，第二个轴上的第二个钉在第一个轴上与第二轴上的二次peg，等等。最终的模式是由四边形和三角形组成的特殊形状的网，表现出意外的对称性。网的每一行都用其他线分为各个细分，除了相同的长度之一，而另一条长度是另一条长度的两倍。此外，从左上角到右下角沿对角线排列的网中的四边形通常是不一致的，但面积相等，沿网的右上角边界形成的三角形也是如此。最后，我们表明，当轴之间的角度变化时，将保留这些特性，但是仅当轴上的连续钉在等距上时才能保持。
String art is an arrangement of pegs on a board with thread strung between these pegs to form beautiful geometric patterns. In this article, we consider a simple form of string art where pegs are placed on two diverging axes, and segments of string join the first peg on one axis to the last peg on the second axis, the second peg on the first axis to the second-to-last peg on the second axis, and so on. The resulting pattern is a peculiarly shaped net consisting of quadrilaterals and triangles that exhibits unexpected symmetry. Each line of the net is divided by other lines into segments, all but one of the same length, and one of twice the length of the others. Furthermore, quadrilaterals in the net that are arranged along a diagonal from the upper left to the lower right corner are in general incongruent but have equal areas, and the same is true of triangles formed along the upper-right border of the net. Finally, we show that these properties are preserved when the angle between the axes changes, but hold only when consecutive pegs on the axes are equidistant.
