Concept
e, the number
The number whose exponential curve has slope equal to its own height everywhere, near enough 2.71828.
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
The curve that is its own slope
There is exactly one shape of exponential curve whose steepness at every point equals its height at that point. The number that produces it is 2.71828…, and it was not chosen for elegance.
Nobody gets their own hat
Hand back a pile of hats at random and ask for the chance that not one person gets their own. The answer barely moves as the crowd grows — it is a third and a bit at four people, and a third and a bit at four thousand.
Named alongside it
The objects these essays reach for when they reach for this one.
Alternating seriesApproximationComplementary countingCompound interestContinuityCounting argumentCounting two waysDerangementDerivativeLimitLogarithmNatural logarithm