The Ptolemaic approach of using cycles and epicycles was becoming strained: there seemed to be no end to the mushrooming growth in complexity required to account for the observable phenomena. Johannes Kepler was the first person to abandon the tools of the Ptolemaic paradigm. He started to explore the possibility that the planet Mars might have an elliptical orbit rather than a circular one. Clearly, the angular velocity could not be constant, but it proved very difficult to find the formula describing the rate of change of the planet's angular velocity. After many years of calculations, Kepler arrived at what we now know as the law of equal areas.