论文标题
为什么肥皂像铁路一样气泡？
Why is a soap bubble like a railway?
论文作者
论文摘要
在某个臭名昭著的茶派对上，疯狂的帽子饰有以下谜语：为什么乌鸦像写作一样？我们不回答这个问题。取而代之的是，我们解决了一个相关的废话查询：为什么肥皂像铁路一样泡泡？答案是两者都可以最小化图形。我们对图形和最小化进行了独立的介绍，从欧几里得平面上的最小网络开始，并以三维泡沫的紧密包装结构结束。在此过程中，我们谈到了算法和复杂性，计算，曲率，化学，填充太空多面体的物理学以及来自其他维度的蜜蜂。唯一的先决条件是高中几何，一些代数和冒险精神。因此，这些笔记应适用于高中富集和床边阅读。
At a certain infamous tea party, the Mad Hatter posed the following riddle: why is a raven like a writing-desk? We do not answer this question. Instead, we solve a related nonsense query: why is a soap bubble like a railway? The answer is that both minimize over graphs. We give a self-contained introduction to graphs and minimization, starting with minimal networks on the Euclidean plane and ending with close-packed structures for three-dimensional foams. Along the way, we touch on algorithms and complexity, the physics of computation, curvature, chemistry, space-filling polyhedra, and bees from other dimensions. The only prerequisites are high school geometry, some algebra, and a spirit of adventure. These notes should therefore be suitable for high school enrichment and bedside reading.
