The early radio pioneers were schooled in acoustics, mechanics en chemistry.
So they understood quite soon how to resonate the electric version of a wave.
That takes a bit of the mystery away.

Yes, 4 x ¼ = 1 lambda. So a folded dipole is 1 lambda and an open dipole is
a half lambda. But a folded dipole can thus be halved. A sort of trombone shape.

BUT the ends resonate with tension right ? So we have to feed one end with
high impedance also. Next detail and the big question for me; may the other end
be grounded ? In case of a situation where no counterpoise can be installed.

Because of the folded dipole which is earthted in the straight middle, i think the
half wave end fed can be earthed. Agreed ? The idea is to topfeed a mast which
stands in conductive grounds. So ¼ wire up and the tower is ¼ wave down,
which to my paper insight should work as an ½ wave antenna ? pls say yes. :-) ?