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You have to start with a basic 2 element array of two fed dipoles. The dipoles are 1/4 wave apart and they are fed with coaxial cables which differ in length by a 1/4 wave. In one direction the signals from the two will combine because they arrive in phase. In the opposite direction they cancel out because they arrive in antiphase.. 1/2 wave (180 deg) out of phase. So all to do with coherent sources, phasing and interference patterns.
Max Roberts suggested:
You describe what I would call a “phased dipole array.” Dr. Yagi certainly built many kinds of antennas. The one that his name stuck to -- at least on this side of the Atlantic -- is the design with one driven dipole element and and two, or more, parasitic elements. (I’ve used aluminum tubing and, alternatively, copper wire -- with equally good results.) The dipole “driven element” is of resonant length. The director is 5% shorter than the driven element. The reflector is 5% longer. The resonant length for the driven dipole element is given by:
I only mentioned a phase array so as to lead on to how a Yagi works.