Another Ahab
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Huh!?
There can be a number of different reasons for curves and loops. Sometimes it's tuning, more often it's for shaping the radiation pattern.
Here's one that will torque your brain - picture a whip antenna with a spiral connected to the base of the radiator on one end and to the ground plane on its other end. A dead short.
What's it for? Well, it's not a dead short at radio frequencies - it's actually a high impedance. At DC, it's a short, of course, but that allows static to bleed off, which is why it's there.