Christaller's Central Place Theory

Imagine a flat, featureless farming plain with people spread evenly across it. Every good or service a town offers needs two things to survive: a threshold, the minimum number of customers required to keep the business running, and a range, the maximum distance a customer will travel to buy it before the trip feels pointless. A town selling milk needs a small threshold and has a tiny range, since no one drives far for milk. A town with a hospital or a university needs a huge threshold and draws customers from far away. Towns space themselves apart so each one's market area holds enough people to meet its threshold, without so much overlap that neighboring towns steal each other's customers.

If every town served a circular market area, circles would either leave gaps uncovered or overlap and double-count customers who live in the overlapping slivers. Christaller fixed this by shrinking the circles until they just touch, then filling the gaps by drawing straight lines between the circles' intersection points. The result is hexagons, the only shape that tiles a flat surface completely with no gaps and no overlap, while staying as close to a circle as possible. Nest these hexagons inside each other at different sizes and you get a hierarchy: hamlets with tiny hexagons for low-threshold goods, sitting inside the larger hexagons of villages, which sit inside the still-larger hexagons of towns and cities offering high-threshold goods like specialty hospitals or universities.

Mountains, rivers, or highways break the clean geometry: they pull population and access unevenly, stretching hexagons toward transport corridors and shrinking them where terrain blocks movement. The model still matters because it isolates the underlying logic, threshold and range, that drives real spacing even when the actual map looks nothing like a honeycomb.