Help with math and science of tri-wiring?

I would think that they all need to be connected to the same tap. This is because:
each "ohm" tap is to allow for the same amount of power to match the paticular speaker. For example the 8 ohm tap will supply more voltage but less current than the 4 ohm tap. Gain of an amp = output Volts / input Volts. If you connected the woofer to a different tap then the midrange, it would see a different signal gain and the sound level would be off by that amount.

Amfibius,
The impedance of the individual sections of your speakers was set by the designer to have the correct volume when the same voltage levels are going to each section as when they are not bi or tri-wired. If you want to bi or tri-wire then you still need to feed each with the same voltage level, which will only happen if you connect them all to the same tap.