What mathematical refinement was introduced by Greek astronomers to reconcile observed wandering motion with the idea of perfect circular orbits?

Answer

Epicycles.

To reconcile data showing planets moving erratically with the belief in perfect circular motion, astronomers developed epicycles—smaller circles upon which planets moved, whose centers tracked along larger circles (deferents) centered around the Earth.

What mathematical refinement was introduced by Greek astronomers to reconcile observed wandering motion with the idea of perfect circular orbits?
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