If sometime something does not work...
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Ceiling fan has a single phase induction motor assembled in it. A single phase induction motor has similar speed-torque characteristics, as that of a 3-phase, only difference is in starting torque. In this case, we dont get any starting torque & so capacitive split phase starting method is applied in this case. So while starting, single phase supply is splitted in two phases, almost 90 degrees out of phase with each other to get a rotating flux & hence a finite starting torque. In regulators for speed control, SCR triacs are used nowadays (instead of rheostats) to change the firing angles of voltage supply to the fan.