The Euler–Mascheroni constant
Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.
A sum whose terms vanish and whose total does not
Add a half, a third, a quarter, and keep going. The terms shrink to nothing and the total passes every number there is — but so slowly that no computation will ever watch it happen.
How long until every one turns up
Draw at random from six equally likely kinds until all six have appeared. The wait is not six draws, and it is not sixty; it is fourteen point seven, and the number is a harmonic sum wearing a hat.
The sum that steps over every whole number
The harmonic sum 1 + 1/2 + 1/3 + … passes 2 at the fourth term, 3 at the eleventh, 4 at the thirty-first, and eventually every whole number there is. It never lands on one. The proof is a single number in the list 1, 2, …, n that carries more factors of two than any other — and the same arithmetic makes the numerators divisible by squares of primes they have no business knowing about.
Named alongside it
The objects these essays reach for when they reach for this one.
Harmonic seriesApproximationBlock stackingCollisionConvergenceConvergence rateDivergenceDivisibilityExpectationFermats little theoremHarmonicsLcm