File:Pythagorean three-body animation.gif

English: The three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation. The three-body problem is a special case of the n-body problem. Unlike two-body problems, no general closed-form solution exists as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required - Wikipedia. This is referred to as the 'Pythagorean three-body problem' because at t=0 the masses are at the vertices of a right-angled triangle. Furthermore, even the masses are Pythagorean, i.e., m1=3m, m2= 4m, m3=5m. Throughout the motion several close approaches are made by the masses. This hopefully brings to light the chaotic nature of the three-body system.