Solutions in which all masses move on the same curve without collisions are called choreographies. A choreography for n = 3 was discovered by Lagrange in 1772 in which three bodies are situated at the vertices of an equilateral triangle in the rotating frame. A figure eight choreography for n = 3 was found numerically by C. Moore in 1993 and generalized and proven by A. Chenciner and R. Montgomery in 2000. Since then, many other choreographies have been found for n ≥ 3.