I felt pretty meh about this idea ('triangle of power') when I encountered it before. If anything, I'd keep the triangle *predicate* (x^y = z) (ditching the function symbols) & write it as a sort of morphism to avoid the *excess* symmetry that an equilateral triangle suggests
A lot of Ramanujan identities would be very hard to write in this notation.
math.stackexchange.com/a/165…
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The result has a more reasonable set of essential identities:
(x ->^{y} z is the symbol that means x^y = z, or equivalently, to better show off why "morphism composition" works,
ln(x) * y / ln(z) = 1)
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A chain of nested radicals would then just be a sequence of arrows with parenthetical subexpressions. So could write this linearly.
4:42 PM · Dec 2, 2020
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