A geometry problem solved with hexagons
Walter Christaller began his academic life trying and failing to get a doctorate in economics. No economist would take on his idea, so in the early 1930s he brought it to the University of Erlangen's geography department instead, finishing the dissertation in nine months. He framed the work as strictly deductive from the outset, writing that he started "not with descriptive statements" but "with a general and purely deductive theory," aiming to "find a general explanation for the sizes, number, and distribution of towns" through what he called "special economic geographical laws." The thesis was published in Jena in 1933 as Die zentralen Orte in Süddeutschland (Central Places in Southern Germany, translated into English in 1966).
It was a return, in a sense, to something Christaller had been doing since he was eight years old. In a 1972 memoir he described receiving an atlas as a Christmas present from a wealthy aunt and being instantly "bewitched" by its colored maps: "I didn't play ball or walk on stilts, but rather was only engrossed in the study of my atlas." He drew in new railroad lines, invented cities, redrew national borders along mountain ranges, and "designed new administrative divisions and calculated their populations." His doctoral thesis formalized the same impulse, and in his own account, seeing "six-sided figures (hexagons)" emerge from the map of southern Germany he was studying.
The hexagons follow from two simple constraints. Every good or service has a threshold, the minimum population needed to support it, and a range, the maximum distance a customer will travel to buy it. A circle drawn around a range either leaves gaps between market areas or overlaps its neighbors; a hexagon is the only regular shape that tiles a plane with no gaps and no overlap while still approximating a circle's efficiency. Christaller then nested three sizes of hexagon inside each other according to three separate logics. Under the marketing principle (K=3), a higher-order town captures exactly one-third of each of the six lower-order market areas around it, functioning as the equivalent of three lower-order towns combined. Under the transport principle (K=4), central places line up along the shortest possible road network connecting them. Under the administrative principle (K=7), each higher-order territory fully contains its subordinate places rather than splitting jurisdictions between them, the same all-or-nothing logic that let Inca administrators track an entire empire's census through knotted quipu cords rather than divided ones, just applied to hexagons instead of knots. The same kind of equidistant-point geometry shows up at planetary scale, too: Point Nemo, equidistant from three coastlines, is the single ocean spot farthest from any land on Earth, by the same geometric necessity that puts a hexagon's own center equidistant from its vertices.
Whether the hexagons actually show up on a map
Christaller's theory made a testable claim: real settlement patterns should approximate this hexagonal nesting. Geographer Brian Berry took up the test most thoroughly in his 1967 book Geography of Market Centers and Retail Distribution, using field surveys of southwestern Iowa as a central case study, a corn-belt landscape of dispersed farms and small market towns not unlike the southern Germany Christaller had originally mapped. Berry found that the basic mechanics, threshold and range, held up, and that the predicted hierarchy of settlement sizes was broadly confirmed in the data.
That result did not settle the argument. A 2017 evaluation of the theory in the Review of Urban & Regional Development Studies concluded that central place theory works well as a macro-scale account of trade-area geometry but does not easily accommodate the micro-scale reality of individual consumer choice, and that even where the spatial pattern of towns follows Christaller's transport logic, the actual nesting of trade areas often does not, because a central place's reputation and the information customers hold about it matter as much as travel distance. Modern retail-location analysis has mostly moved on to gravity models and GIS-based site selection, but the underlying insight, that a market has a threshold size below which it fails and a pull radius that widens with what it offers, is the same one Christaller derived from hexagons in 1933. A closely related urban model asks almost the mirror-image question: where central place theory asks how far a shopper will travel to reach a center, bid-rent theory asks how much a business or household will pay for land at each distance from one, and land use sorts itself into rings for much the same underlying reason.
The 1940 assignment: an atlas-obsessed child gets an actual map to redraw
Christaller's politics initially ran the opposite direction from where his career would take him. A member of the Social Democratic Party, he fled to France as a self-described political refugee in 1934, a year after the Nazis banned the SPD. He came back, and on 1 July 1940 he formally joined the Nazi Party. He went to work under Konrad Meyer in the Planning and Soil Department, a unit that operated under Heinrich Himmler's Reich Commission for the Strengthening of Germandom (Reichskommissariat für die Festigung deutschen Volkstums). His assignment was Warthegau, the region of western Poland annexed into the Third Reich after the September 1939 invasion.
The job was to apply his own dissertation to an actual, occupied landscape. In a 1941 planning document, Christaller wrote that regional planning's purpose was to replace "impractical, outdated and arbitrary urban forms" with "an ideal plan, which means in spatial terms a geometrical schema," specifying that "central places will be spaced an equal distance apart, so that they form equilateral triangles. These triangles will in turn form regular hexagons." He planned 36 new Hauptdorfs, main villages, for Warthegau, and the district of Kutno in the northeast was redesigned on paper according to his hexagonal system. A year earlier, describing the same assignment, he had written: "Because of the destruction of the Polish state... everything is again fluid... Our task will be to create in a short time all the spatial units, large and small, that normally develop slowly by themselves."
That fluidity had a specific, documented human cost. Historians Trevor Barnes and Claudio Minca, drawing on German federal archive research, put the Warthegau displacement figures at 560,000 Jews and 3.4 million Slavs, with only 1.1 million of the existing population judged "Germanized" enough to remain; the plan called for bringing in 3.4 million ethnic German settlers to replace them. Christaller himself described part of the purpose of the new hexagonal settlement pattern as a way "to give settlers roots so they can really feel at home." He was not the architect of the expulsions themselves, which were ordered above his position in the SS hierarchy, but the geometric layout those settlers moved into on paper was his.
The awards came in his seventies, and none of the citations mentioned this
Christaller's postwar political affiliations kept shifting: Nazi Party in 1940, Communist Party of Germany in 1945, and back to the Social Democrats by 1959. When his former supervisor Konrad Meyer stood trial at Nuremberg's RuSHA case, several of Meyer's former staff, Christaller among them, were called to provide character references for the Warthegau planning work; the trial ended with Meyer convicted only of Nazi Party membership and released for time already served.
Recognition for the underlying geographic theory came much later, and from an unrelated direction. From the mid-1950s, a group of American geographers building what they called the quantitative, law-seeking "new geography" adopted central place theory as a foundational reference point. Christaller received the Association of American Geographers' Outstanding Achievement Award in 1964, honorary doctorates from the University of Lund in Sweden and Ruhr University Bochum in Germany in 1968, and the Royal Geographical Society's Victoria Medal that same year, all in his seventies, more than three decades after the original dissertation. None of those citations mentioned his Nazi Party membership or his Warthegau planning work. He died on 9 March 1969 in Königstein im Taunus, West Germany, at age 75.
The theory Christaller drew as a child and then handed to occupying planners was not the only piece of 20th-century intellectual output whose original context got separated from the tool it produced; a phrase coined in 1962 explicitly as an insult toward Cold War nuclear strategy went on to become the literal doctrine governing it. What set Christaller's case apart was how long the separation lasted inside his own discipline. It was not until 2013, when historians Trevor Barnes and Claudio Minca published "Nazi Spatial Theory: The Dark Geographies of Carl Schmitt and Walter Christaller" in the Annals of the Association of American Geographers, the same association that had given Christaller its achievement award, that the field's flagship American journal laid out his wartime record in full for other geographers to read.