Some fans that are considered "brushless motors" or "magnetic motors" are Permanent Split-Phase Capacitor motors and require a solid state motor control of the Triac variety. (Vortex, CanFan, Fantech are some)

A Triac type controller sends out specific wavelengths of current to prevent the current from rising and possibly damaging the motor windings.

A variac is a variable transformer that lowers the voltage to the motor, but a lower voltage results in a higer current and can potentially be a problem at very low speeds (under 30%) because of the reduced cooling and higher amperage.

Always check with a fan manufacturer to find out their motor type and if they require a solid state controller.