compare with a single large circular open space, we equalize the total area of two circular
open space to the optimal amount of one circular open space as identified previously.
Subsequently, we examine four circular open space and alternate the total area.
Figure 5 shows distribution of two circular parks of open space in different
directions. As demonstrated by figure 6, in all three directions, the net social value of
open space and property tax increment increase first and then decrease with the distance
between open space. However, the turning points at which both net social value and tax
increment change from increasing to decreasing are different. When located along the
community diagonal, both net social value and tax increment reach their peaks when the
interdistance between open space is 2100m, while the peak-value interdistances are 600m
and 3000m respectively when located along x axis and y axis from community center. If
we compare these peak-value interdistances with the interdistance resulting from
geometrically even division, we will find the former is no less than the latter. As shown
by figure 6, after adjusting for the size of open space, the peak-value distance is 3628m
for diagonal, 1728m for x direction, and 4128m for y direction, while the interdistance
based on geometrically even division is 2981m for diagonal, 1333m for x direction, and
2666m for y direction, shorter than those peak-value interdistances. A possible
explanation is, the overlap of amenity on land located between open space tends to
increase the interdistance of open space to balance with land located outside of the
overlap of amenity. As a result, the comparison suggests that optimal location tends to
evenly distribute open space at least physically. This property is implicitly consistent
with the finding in the previous section, that is, a single open space should be located in
the center of a community, and two open space should be evenly distributed in the chosen
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