论文标题
切蛋糕和亲吻圈子
Cutting cakes and kissing circles
论文作者
论文摘要
要将蛋糕分成相等的碎片，大多数人都使用刀和运气和敏捷的混合物。这些尝试通常取得了不同的成功。通过用刀子代替欧几里得直立的精确几何构造，而无需使用指南针，我们可以找到解决某些蛋糕切割问题的方法。由于不知道其中心时，不可能完全将圆形蛋糕划分为圆形蛋糕，因此我们的结构需要使用多个蛋糕。使用三个圆形蛋糕，我们提出了一种简单的方法，用于将每个蛋糕脱离它们或找到它们的中心。此外，鉴于带有明显中心的蛋糕，我们提出了将其切成n尺寸n = 3,4和6的N块的方法。我们的方法是基于Steiner和Cauer的建筑，从19世纪和20世纪初。
To divide a cake into equal sized pieces most people use a knife and a mixture of luck and dexterity. These attempts are often met with varying success. Through precise geometric constructions performed with the knife replacing Euclid's straightedge and without using a compass we find methods for solving certain cake-cutting problems exactly. Since it is impossible to exactly bisect a circular cake when its center is not known, our constructions need to use multiple cakes. Using three circular cakes we present a simple method for bisecting each of them or to find their centers. Moreover, given a cake with marked center we present methods to cut it into n pieces of equal size for n=3,4 and 6. Our methods are based upon constructions by Steiner and Cauer from the 19th and early 20th century.
