The definition of derivative says how to find the instantaneous rate of change of a quantity that varies with (tell) time, calculate how its value changes over a short time interval, and divide by the time concerned. Then let that interval become arbitrarily small. It provides a rigorous basis for calculus and the main way scientists model the natural world. It led to the calculation of tangents and areas, formulas for volumes of solids and lengths of curves, Newton’s laws of motion, differential equations, the laws of conservation of energy, and momentum.

## The Formula to Get 42 Billion Digits of π

While writing "7 Utterly Well-written Math Books About Pi," I found a very interesting math formula that will give you 42 consecutive digits of π accurately but is still wrong.