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With respect to the outside walls, one floor of The Pentagon in Arlington, VA has a perimeter efficiency of 92.995% [Eq 5]. There are 5 floors above grade. Hence k for the building as a whole is
[Eq. 2]2.
Suppose that, instead of renovating the obsolete and decaying 50 year old structure, the DOD officials decided to spend the same billion dollars on an entirely new complex of four 30-story towers, each in the shape of an octagon. What would be the increase in perimeter? k for an octagon = 97.368% [Eq. 5]; k for the complex of 120 floors would be 8.888% [Eq. 2].
Given the exact same gross floor area above grade -- and note that for purposes of comparing perimeter it is not necessary to know this exact floor area -- the four octagonal towers will have 41.59/8.89 = 4.7 times the amount of perimeter [Eq. 3], which means that nearly 5 times the number of people as at present could have a view of the outside world in the alternate complex described.
2If the inner courtyard of the Pentagon is considered legitimate view, the numbers change somewhat. The Pentagon and its inner courtyard have an area of 33.55 acres and an outer perimeter of 4608 feet (921.6 feet per side). The inner court has an area of 5 acres and perimeter of 1780 feet. Ignoring the more or less useless perimeter of the narrow interior alleys, k for one floor is then 61.83% and for the 5 floors is 27.65%. Thus even when the inner courtyard is counted, the complex of four octagonal towers would have more than 3x the perimeter as the existing antiquated building (27.65/8.89 = 3.11). [Top]
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