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Spoiler1

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Assuming !! means the double factorial and not the factorial taken twice: 6

Sloppy notation. I'm guessing what you meant was π⁶/(135*ζ(6)), in which case it would be 7

8. Fuck the cross product.

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11 Wait, cos(π/5) = φ/2? What? Holy shit!

This is the only one I don't know how to solve. I could Wolfram it, but ehh.

Fuck you, I'm definitely Wolframing this one. I know how to solve it, but there's no way I can be bothered to. 13

4 real and 4 complex dimensions, or ~262 Hz (Not entirely sure how you'd get "14" out of this one, unless you meant to write E₁₆ or something. I'm pretty sure "C" isn't a number in base 4.)

16 Base i is a good idea.

Funfacts for 11-15:
11: Yep! φ loves showing up in equations involving 5.
12: https://en.wikipedia.org/wiki/Residue_(c..._analysis)
13: Did you know, that if we define f(x)=cos(arctan(x)), then fⁿ(1)=√F_n/F_n+1 (even in the degenerate case of 0 compositions because 1=√1/1=√F₀/F₁)
14: https://en.wikipedia.org/wiki/Catalan_number
15: https://en.wikipedia.org/wiki/Quater-imaginary_base