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Euler's number (e)

The number where the curve y = eˣ has slope equal to its own value at every point.

Estimate e the Euler way

(1 + 1/n)n sneaks up on e as n grows.

n = 20 → (1 + 1/n)n = 2.65329771

e ≈ 2.71828182845…

Why e shows up everywhere

Anything that grows in proportion to itself — bacteria doubling, interest compounding, populations spreading — naturally lands on e. It's the number that growth picks for itself.

2.71828 18284 59045…

Like π, e is irrational and transcendental. Its decimal expansion never ends and never repeats.