Scale drawings are also used in other
engineering fields, such as surveying. For
example, distances measured in the field
can be translated to a smaller scale (such
as a drawing) in order to accurately
depict what was measured. The ratio
between the real distance and the drawn
distance is called the drawing scale. If the
measurement is 200 feet in the field, and
on paper the desired line is 8 inches long,
then 8 inches on the paper would equal
200 feet on the ground, and 1 inch would
be equal to 25 feet on the ground. This is
translated as a diagram with a scale of 1"
25' (1 inch equals 25 feet), or 1:25.
There is another way of approaching such
an illustration: If the longest distance
measured in the field was 300 feet and
the desired drawing scale is 1 inch 25
feet, then the minimum length of paper
needed would be 12 inches, or 300/25.How are the principles of ratio, proportion,and symmetryapplied to
architecture?
The definition of a ratiois a comparison by division of two quantities expressed as the
same unit measurement. For example, a building that is 200 feet wide and 100 feet tall
has a ratio of 2:1 (200:100) between its width and height; it is also seen as the fraction 1/2.
Such a relationship was understood as far back as ancient Greece and Rome, when people
used mathematics to give structure and aesthetics to buildings. This is especially impor-
tant in architecture, in which building design is based on complex mathematical ratios.
Proportionis an equation stating that two ratios are equal. Every proportion has
four terms, with the first and fourth terms being the extremes; the second and third
terms are called the means. In each proportion, the product of the means equals the
product of the extremes. The Greeks and Romans often used proportions in their
buildings and other structural designs. (The Roman architect Vitruvius was also
instrumental in praising the virtues of proportion and symmetry in architecture; for
more about Vitruvius, see above.) During the Renaissance, architects applied propor-
tion (and other mathematical formulas) to produce aesthetically pleasing buildings—
beauty that still holds true today.
Although there are other types of symmetry,the most common is line symmetry,
338 in which a line divides an object, line, or other structure into two equal halves (an
Gustave Eiffel used mathematical concepts to design
his famous Eiffel Tower in France in 1889. National
Geographic/Getty Images.