论文标题
对称的声音
The sound of symmetry
论文作者
论文摘要
本说明首先是对M. KAC 1966年在《美国数学月刊》中普及的倒数等语态问题的介绍，“有人可以听到鼓的形状吗？”尽管答案已有二十年了，但仍然存在许多开放问题。读者旨在为普通观众提供挑战，要在整个对反光谱理论的交互式介绍中完成练习。引入之后，收集和讨论用于逆光谱问题的主要技术。然后使用这些证明可以听到以下形状：平行四边形，急性梯形和常规的N-GON。最后，我们表明，人们可以在所有凸出的n gon中实际听到常规N-基因的形状，因为它是由有限数量的特征值决定的。真的可以听到对称性的声音！
This note begins with an introduction to the inverse isospectral problem popularized by M. Kac's 1966 article in the American Mathematical Monthly, "Can one hear the shape of a drum?" Although the answer has been known for some twenty years now, many open problems remain. Intended for general audiences, readers are challenged to complete exercises throughout this interactive introduction to inverse spectral theory. Following the introduction, the main techniques used in inverse isospectral problems are collected and discussed. These are then used to prove that one can hear the shape of: parallelograms, acute trapezoids, and the regular n-gon. Finally, we show that one can realistically hear the shape of the regular n-gon amongst all convex n-gons because it is uniquely determined by a finite number of eigenvalues; the sound of symmetry can really be heard!
