User blog comment:Plain'N'Simple/A cool geometric connection regarding the fast-growing-hierarchy/@comment-35470197-20191224012438

I did not know such an occurrence of f_2. Now I tried to consider simlar expressions of other numbers, which I do not have an idea on how to relate them to geometry except for trigonometric functions.
 * sin(1/2) = Σ_{n=0}^{∞} (-1)^n/(2n)!f_2(2n+1) = 1/f_2(1) - 1/2f_2(3) + 1/24f_2(5) - …
 * 1-cos(1/2) = Σ_{n=1}^{∞} (-1)^{n-1}/(2n-1)!f_2(2n) = 1/f_2(2) - 1/6f_2(4) + 1/120f_2(6)+ …
 * log(2) = Σ_{n=1}^{∞} 1/f_2(n) = 1/f_2(1) + 1/f_2(2) + 1/f_2(3)+ …
 * √e - 1 = Σ_{n=1}^{∞} 1/(n-1)!f_2(n) = 1/f_2(1) + 1/f_2(2) + 1/2f_2(3)+ …