In regards to the difference between American and European billion/trillion/etc:

  // These number terms were described by N. Chuquet and De la Roche in the 16th
  // century as being successive powers of a million.  These definitions are 
  // still used in most European countries.  The current US definitions for these
  // numbers arose in the 17th century and don't make nearly as much sense.

Huh? Admittedly I'm biased, being American, but how do the American definitions not make nearly as much sense?

By the time "billion" was defined by Chuquet and De la Roche, the concepts of "ten thousand" and "hundred thousand" were in widespread use. Those were followed by "million". So there's already a precedent for "we multiply things by a hundred before coming up with a new name". How does it make sense to change that to "but after a point, we multiply things by a thousand before coming up with a new name"?

I could see a couple systems that would arguably make more sense:

* ten, hundred, thousand, million, billion, trillion... (no multipliers)

* ten, hundred, ten hundred, thousand, ten thousand, hundred thousand, million, ten million, hundred million, thousand million, billion..., million billion, trillion... (use all previous multipliers before creating the next new name)

Admittedly, the US uses neither of those systems. But sticking with the precedent of "a hundred is the highest multiplier" makes sense.