Concept
Power series
An infinite sum of powers of a variable, standing for a function wherever the sum settles.
Named by 2 essays across one field — 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.
The sum that fits in one square
Half, then a quarter, then an eighth, forever. Adding infinitely many things sounds like it should give infinity, and the picture that says otherwise is a square with a corner left uncut.
Named alongside it
The objects these essays reach for when they reach for this one.
LimitCompound interestContinuityConvergenceConvergence rateDerivativeDissectione, the numberGeometric seriesHarmonic seriesLogarithmMethod of exhaustion