Larry, you've got a LOT to learn. Meanwhile please stop disseminating misinformation and above all stop contradicting me and others with nonsense. The "short answer" for you is you can get an education by watching me sleep. Until and unless you have spent 30+ years studying RF communications the best you can do for yourself and others is keep your eyes on the monitor and your hands off the keyboard.
Now go back and READ what I wrote, then compare it with what YOU wrote. Then compare BOTH with the expert engineers' writings in the ARRL Antenna Handbook, the graphics will help your understanding. Which is closer to what's in the book? Eyes are for studying, brain is for understanding, mouth is for feeding eyes and brain. Misuse of body parts results in confusion.
Just to set you straight on a point of misinformation you "educated" us with, a vertical or horizontal (the only difference is polarization) dipole most certainly HAS a counterpoise "ground". Take that groundplane with the radials at 90 degrees (52 ohms) and bend them down to 180 degrees and you have a dipole with a feedpoint impedance of 75 ohms, NOT 300 ohms! FYI, a dipole doesn't need a balun to operate, it's function is providing an unbalanced feed from a balanced one, it's a BALanced-UNbalanced device which decouples the transmission line from the antenna reducing or eliminating feedline radiation. We can discuss turns ratios, current, voltage and choke baluns when you learn enough basic electrical theory to have a grasp of the more advanced subject material.
Good luck with your studies, "a mind is a terrible thing to waste".