Pi and Friends

When the irrational number π appears to be particularly attracted to numerical buddies like e, i, and 𝜙 whenever they are indulged in some extra-mathematical activities together, as revealed by their intimate liaisons.

Don’t the following numerical relationships prove that pi and friends have an affinity for one another?
π ≈ 6/5 𝜙²
π ≈ (9 – e)
iⁱ = e^(-π/2)
e^(iπ) + 1 = 0

(- )! = √π
eⁱˣ = cos x + i sin x

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