It seems unlikely to me that 4 is the optimum number. So why not 3, if reducing parts leads to optimization. Or 7 (6 surrounding 1) if more, smaller motors and blades is better?

 

There is a trend for 6. Quad, though, gives good stability and when on the corners, does not obstruct forward or rear views. That arrangement also facilitates inducing yaw.

John

 

It seems unlikely to me that 4 is the optimum number. So why not 3, if reducing parts leads to optimization. Or 7 (6 surrounding 1) if more, smaller motors and blades is better?

You want an even number of rotors, with pairs spinning in opposite directions, in order to cancel counter-torque and minimize gyroscopic effects during flight.

 

Ah, that's a good explanation of why you don't see TRI copters. And four is the minimum. I think we have our answer.