三体问题与形球
The Three-body problem and the shape sphere
摘要：
[This这是一篇暂时性的文章。我已经把它提交给美国数学月刊了。三体问题定义了平面上三角形空间的动力学。形球是平面三角形的有向相似类的模空间，位于形空间内，形空间是三角形的有向同余类的欧氏三维空间参数化。我们推导和调查的几何形状和动力学诱导这些空间的三体问题。本文提出了两个关于三体问题的定理，这两个定理是通过形空间的观点发现的
英文摘要：
[This is an expository article. I have submitted it to the American Mathematical Monthly.] The three-body problem defines a dynamics on the space of triangles in the plane. The shape sphere is the moduli space of oriented similarity classes of planar triangles and lies inside shape space, a Euclidean 3-space parametrizing oriented congruence classes of triangles. We derive and investigate the geometry and dynamics induced on these spaces by the three-body problem. We present two theorems concerning the three-body problem whose discovery was made through the shape space perspective
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