It's based on the Roman salute. American culture draws heavily on the psuedo-Greco-Roman aesthetic of the enlightenment, and copied a wide variety of trappings from them. For instance, the Venetian architect Andrea Palladio can be honestly credited with providing the inspiration for the White House with his Villa Rotonda, which in turn, obviously, draws from Greek (the pillars) and Roman (the central building) influences.

Fasces, the symbol consisting of a bundle of sticks and an axe wrapped together, are a common element in American heraldry, though obviously few are added today.

In fact, it could be argued that the Facists drew heavily on American iconography, although it is more plausible that this is simply an example of parallel evolution.

That said, Hitlers planfor a new Berlin resembled a sort of combination of Washington DC and Paris, although because Hitler had a tiny penis and only on testicle, he demanded that it be much larger - the domed hall at the back of that image was to be something like sixteen times the size of Saint Peter's Basilica in Rome.