距离几何历史上的六个数学瑰宝
Six mathematical gems from the history of Distance Geometry
摘要：
这是距离几何迷人历史的一部分。我们不要求完整性，但我们确实承诺展示令人眼花缭乱的美丽的初等数学。证明了Heron公式，Cauchy关于多面体刚性的定理，Cayley将Heron公式推广到高维，Menger关于抽象半度量空间的刻画，Goedel关于球面上度量空间的一个结果，Schoenberg距离与正半定矩阵的等价性，这是多维标度的基础.
英文摘要：
This is a partial account of the fascinating history of Distance Geometry. We make no claim to completeness, but we do promise a dazzling display of beautiful, elementary mathematics. We prove Heron's formula, Cauchy's theorem on the rigidity of polyhedra, Cayley's generalization of Heron's formula to higher dimensions, Menger's characterization of abstract semi-metric spaces, a result of Goedel on metric spaces on the sphere, and Schoenberg's equivalence of distance and positive semidefinite matrices, which is at the basis of Multidimensional Scaling.
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