Inertial frames of reference and nonrotating frames of reference are discussed. Using geometric algebra as the principal mathematical tool, the Thomas precession of torque‐free gyroscopes in special relativity is then derived in an exact fashion in two different ways. First, the equations of Fermi–Walker transport are employed to derive expressions for the precession; second, a torque‐free reference frame is compared to one in which the coordinate axes are forced by torques to remain parallel to a fixed direction. The precession of a freely falling gyroscope in a gravitational field concludes the paper.