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Pi and Friends

When the irrational number ฯ€ appears to be particularly attracted to numerical buddies like e, i, and ๐œ™ whenever they are indulged in some extra-mathematical activities together, as revealed by their intimate liaisons.
Donโ€™t the following numerical relationships prove that pi and friends have an affinity for one another?
ฯ€ โ‰ˆ 6/5 ๐œ™ยฒ
ฯ€ โ‰ˆ (9 โ€“ e)
iโฑ = e^(-ฯ€/2)
e^(iฯ€) + 1 = 0

(- )! = โˆšฯ€
eโฑหฃ = cos x + i sin x
by MathPlus February 5, 2021
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