In the late 1920s, R. H. Park published a change of variables that provided a means of analyzing the performance of synchronous machines. He transformed the stator variables to substitute variables that eliminated the rotor-position-dependent terms from the self-and mutual inductances. This transformation has become the bedrock of machine analysis and simulation; however, Park's derivation involves a maze of three-phase trigonometric identities with generator action and we are left searching for a more concise analytical development. In this paper, a direct connection is established between Tesla's rotating magnetic field and reference frame theory. In particular, an analytical basis for the change of variables is established from the expression of Tesla's rotating magnetic field combined with an expression that relates stationary and rotating coordinates. This leads directly to reference frame theory and an array of transformations that yield the same advantages as Park's transformation. It shows that all transformations used in the analysis of power systems, electric machines, and drive systems have a common origin. Also, the magnetic poles can be analytically located during transient operation and on a phasor diagram during steady-state operation, thereby providing a vivid visualization of machine and drive operation.