Math in Engineering

Mathematics and Architecture

What are scale drawings?

Scale drawings are drawings or illustrations that are proportional in scale to the real structures they represent. In order for a new building to be designed, an architect must convert his or her ideas to drawings. But since the drawings can’t be as large as the building, the architect uses scale drawings to depict the structure. These miniature versions of the actual structure show the sizes, shapes, and arrangements of rooms, along with structural parts, windows, doors, closets, and other important details of construction. The scale drawings of these buildings must be in exact proportion to the actual structure, with various scales used for this purpose. For example, 1/8 inch might be used to represent one foot; thus, an eight-foot-long building feature would be drawn as an inch long on paper. One of the most common scales used by architects is ¼ inch = 1 foot. (These measurements can also be translated into the metric scale.)

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.


The patterns on a butterfly’s wings demonstrate the concept of symmetry in nature.


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