needed to know the pressure not only
along the entire structure, but also—and
especially—at its base. In general, the
pressure exerted by water equals the den-
sity times the depth, in which the density
of water is 62.4 pounds per cubic foot.
For Hoover Dam, this gives a pressure of
37,440 pounds per square foot, or 18.72
tons per square foot; the pressure calcu-
lated at half the height of the dam is 9.36
tons per square foot. This is why the base
width of the dam is 1,660 feet (201.2
meters)—it is thicker to compensate for
the increase in pressure at the bottom of
the dam—while the width of the crest of
the dam is only 45 feet (13.7 meters).How is mathematicsused to enable
buildings to withstand earthquakes?
It is not usually the quake that kills people, but the collapse of structures. In particu-
lar, the horizontal shaking during a quake is mostly responsible for causing building
or road damage and collapse. Most structures are designed to carry heavy loads, so
they are strong in the vertical direction. Designing structures to withstand the hori-
zontal earthquake shaking can save buildings and lives.
There may be other ways to mitigate the amount of structural collapse during
quakes—all include a healthy dose of simple and complex mathematics. One expensive
way would be to design all buildings to withstand the largest ground shaking an area
can expect. This could be done using mathematics familiar to designers and engineers;
the math involved analyzes how large quake frequency waves travel through an area.
Yet another, more practical, solution might be to design buildings to withstand the spe-
cific types of shaking expected in a region. Again, mathematics could be used to deter-
mine the frequency at which each building vibrates (or the number of times a building
sways per second) versus the potential type of quakes that roll through the area.MATHEMATICS AND ARCHITECTURE
What is architecture?
Simply put, architecture is the design of structures, mainly buildings, by architects.
But the definition does not end there. An architect not only builds the structures, he
332 or she also takes into consideration the form, symmetry, spaces, and beauty of the
Hoover Dam, an impressive structure on the Col-
orado River, could only have been made possible by
engineers designing it in such a way that the walls
were thick enough to withstand massive water pres-
sure. Stone/Getty Images.