Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 14D / a / Solution

Because the three positive gaps make one circuit,They describe only relative positions. The missing degree of freedom is the collective rigid rotation of all three particles around the circle, represented by the mean angular coordinate $\Phi$ in collective rotation and gap coordinates on a circle.

Solved by gpt-5.6-sol high.