The Math Behind GPS

To pinpoint your location, your phone solves for four unknowns — x, y, z coordinates plus its own clock error — using signals from four satellites. Each signal gives one equation linking distance to travel time. Those equations aren't perfectly linear, so the receiver solves them by repeated linear approximation, refining the guess until it locks on.

This trick is centuries old. Chinese mathematicians in "The Nine Chapters on the Mathematical Art" (around 200 BC) described what we now call Gaussian elimination — the same method taught today, long before Gauss was born. The practical payoff is immediate: the same skill balances a budget, converts currencies, and splits a bill.