Foucault pendulum sharing the rotation of the earth about its own axis, the suspension point of the pendulum traces out a circular path during one sidereal day. At the latitude of Paris, 48 degrees 51 minutes north, a full precession cycle takes just under 32 hours, so after one sidereal day, when the Earth is back in the same orientation as one sidereal day before, the oscillation plane has turned by just over 270 degrees. If the plane of swing was north-south at the outset, it is east-west one sidereal day later. This also implies that there has been exchange of momentum;
Foucault pendulum direction to Earth, which implies that the trace of the plane of oscillation will undergo parallel transport. After 24 hours, the difference between initial and final orientations of the trace in the Earth frame is , which corresponds to the value given by the Gauss–Bonnet theorem. "α" is also called the holonomy or geometric phase of the pendulum. When analyzing earthbound motions, the Earth frame is not an inertial frame, but rotates about the local vertical at an effective rate of radians per day. A simple method employing parallel transport within cones tangent to the Earth's surface can be used