Running a Closed Traverse

A plane table maps what it can see from a couple of stations. To survey a whole site — round a building, through woodland, along a boundary — you walk a chain of stations from one to the next, measuring the length of each leg and the angle at each corner, and finish back where you began. The reason it closes is the reason anyone trusts it. You know in advance what the angles of a closed polygon must add up to, and you know the trip must end at its own starting point. Both are checks nature provides for free, and the difference between what you measured and what must be true is your error — measured, not estimated. This rung is the arithmetic heart of surveying. It is also where a survey stops being a collection of readings and becomes a set of coordinates you can build from.