這篇論文中我們探討的是 Chenciner, A. 所提出的一個問題中的某個情況，Chenciner, A.提出的問題是：「共圓而且質心在其外接圓圓心的中型構形是否一定是正多邊形？」，這個問題在三體的情況是對的，不難證明；在四體的情況，由 Hampton, M. 在2003年給了肯定的答案；而我們討論的是五體且對稱的情況，並且證明「對稱、共圓且質心在其外接圓圓心的五體中心構形一定是正五邊形。」

In this paper, we study co-circular five-body central configurations with their center of mass at the center of the circumscribed circle. We shall show that in the symmetric case, the only central configuration satisfying these conditions is the regular pentagon with equal masses.

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