Circular irrigation plots only irrigate 78.4% (pi/4) of a square patch of land. If properties were divided by hexagons, it would be better.
In contrast to "Fences make good neighbors", if there were no fences between adjacent properties, then coverage could be 100%, with the radius of the irrigator arm extending to the corner of the square instead of the edge. We need a way or coordinating arms so they don't collide, and shutting off the irrigation in the overlapped area (a variable length of the end of the arm) so it doesn't get watered twice.
These ideas could be easily deployed if a property owner owns a large swath of land. For the non-overlapping case, it is the classic geometric problem of packing circles into an area (perhaps a rectangle). Minimizing the cost of the irrigation equipment adds a twist. Perhaps a linear cost (by length of arm) and constant yield per irrigated land area.
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