[mabbo]

`Θ^i = 1` does make this really slick, imho.

I often wonder if someday when we meet alien intelligences, they'll have a completely different set of constants, derivable from our own but different. Θ=535.491... may be such an example.

[crdrost]

I've occasionally played with the notations that maybe ə = e^i or even 1 = e^{2πi} to simplify these sorts of expressions before. So for example a forward moving wave can be written,

1^{x/λ – νt}

with no particular ambiguity or even parentheses. The choice of constants should give you some pause though—we don't have a great way to talk about "true wavenumber" k so we have to talk about wavelength, and we use "f" for a lot of other things while Greek nu looks like an English V so that can sometimes be confusing... it's not _bad_ but it's weird enough that it's not obviously better.

[munchler]

I don't think Θ makes for a good fundamental constant, though, because it's composed of pi and e, which must persist as distinct concepts in the end.

[adrian_b]

While pi and e must persist as two distinct concepts, they may be substituted by a constant pair that is much more useful for practical purposes is 2*pi and ln 2 ("natural" logarithm of two).

When using this alternative pair of constants (which are the ratios between two pairs of units, cycle vs. radian and octave vs. neper), there is no longer any need for pi or e.