這篇文章我們考慮具有某些等質量的五體中心構型，並且考慮一個關於中心構型的猜想：在平面上有n個構成凸集的質點，那將不可能把第n+1個質點放在邊界上，使得它形成一個中心構型。首先，我們證明在某些對稱的情形之下，此猜想的確是對的。最後，我們給了一個關於這個猜想的反例，說明有這樣的中心構型存在。

In 1990, R.Moekel published a famous work about central configurations, in which he proved Conley′s Perpendicular bisector theorem, and the 45° theorem that provide some information on possible shapes of central configuration.
In this paper we consider the following problem. Suppose (q₁, m₁), (q₂, m₂),..., (qi, mi) form a convex configuration, can we add a mass and position (qi+1, mi+1) on the boundary to make it a central configuration? The answer is false for i=3, as it follows easily from the Conley′s Perpendicular bisector theorem. Is the answer still negative when i >3? In this paper, we discuss the problem with i=4, and with isosceles trapezoid configuration and some equal masses. In the last section we provide a counter-example for this problem.

1.R.Moeckel,On central configurations, Math. Z. 205, no. 499-517.
2.A.Albouy,The symmetric central configurations of four equal masses. Contemp. Math 198 (1996).131-135.
3.Y.Long,S.Sun.Four-body Central Configurations with some Equal Masses. Arch. Rational Mech. Anal. 162. (2002).25-44.
4.N.Faycal.On the classification of pyramidal central configurations. Proc. Amer. Math. Soc. 124. (1996).249-258.