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In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian asserts that the phase-space distribution function is constant along the trajectories of the system—that is that the density of system points in the vicinity of a given system point traveling through phase-space is constant .

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The equation of the circle is simplest if the centre of the circle is at the origin. However, we derive below the equation of the circle with a given centre and radius (Fig 1 ). Given C (h, k) be the centre and r the radius of circle. Let P(x, y) be any point on the circle (Fig). Then, by the definition, | CP | = r. By the distance.