Reg,

Your math example does not illustrate the reality that the impedance
change produced by a ~5/8" OD brass pin inserted radially into the
dielectric space of coaxial transmission line can match that line into an
adjacent termination of fairly high SWR (1.3:1 or so), at frequencies as
low as 54MHz.

As I wrote earlier, this technique is widely and successfully used to match
the main transmission line of broadcast TV and FM stations to the net input
impedance of their antenna (including its input elbows).

- RF