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Figure 7.6 The large green hexagon contains the equivalent of three blue hexagons
(1 full one plus six 1/3 blue hexagons). Similarly, the intermediate-sized blue hexa-
gon contains the equivalent of six red hexagons. QR codes lead to animations.
Source: Arlinghaus, S. L. and W. C. Arlinghaus. 2005. Spatial Synthesis: Volume I,
Centrality and Hierarchy. Book 1. Ann Arbor: Institute of Mathematical Geography.
Spatial%20Synthesis2/singlek3bluenewcropped600.gif.
the equivalent of three red hexagons: One entire red hexagon is surrounded
by six copies of 1/3 of a red hexagon. Each green hexagon contains the equiv-
alent of three blue hexagons: One entire blue hexagon is surrounded by six
copies of 1/3 of a blue hexagon. The green hexagons contain the equivalent of
three blue hexagons and three-squared red hexagons. The next largest hexa-
gon, not shown in Figure 7.6, would contain three green hexagons, three-
squared blue hexagons, and three to the third power red hexagons. Powers of
3, fractions with 3, and the square root of three all come into play.
7.3.3.2 Transportation principle
Figure 7.7
shows the locations for the next nearest competitors, next beyond
those from the marketing principle above, to enter the system. Given that
they, too, will share the area evenly, a set of even larger hexagons emerges.
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