Fly over farmland almost anywhere and you will see them: perfect green circles, packed side by side inside square fields. They are not a design choice. They are the shape a machine makes when it turns.
A centre-pivot irrigator is a long pipe on wheels, anchored at one end to a well in the middle of the field. The pipe walks slowly around that pivot, watering everything it passes over. Frank Zybach patented the idea in the United States in 1952, and it changed the look of the countryside from the air within a generation.
The geometry is unforgiving. A pipe four hundred metres long waters a circle of radius four hundred metres. Set that circle inside the square plot that surrounds it, and about seventy-nine percent of the square is green. The remaining corners get nothing — roughly a fifth of the land, left to dry grass or planted with something that can live without the machine.
Not every pivot goes all the way round. A road, a canal or a neighbour's boundary can stop the pipe partway, and then the wet ground is a wedge instead of a disc. The rule for how much land is watered is the same in both cases: the wedge is the same share of the circle as its turn is of a full turn. A pipe that sweeps a quarter of the way round waters a quarter of the circle.
Farmers learn the numbers quickly, because the pump is paid for by the hour and the crop is paid for by the hectare.