How to Use the Golden Mean Ratio in Architecture

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Since 500 BCE, the golden ratio has played an important part in the production of architecture. This ratio is found throughout nature and can be successfully transposed onto the proportioning systems of any man made objects.The golden ratio is the proportion of one length and a second, longer length that is equal to the proportion of the second, longer length and the sum of the two lengths. There are only two numbers, both transcendental, that meet this relationship: the approximation of 1.618 and its reciprocal 0.618. These two numbers are exactly the same except the integer at the beginning of the number. Furthermore, they are accurately rendered to any decimal point using the formula: the absolute value of one plus the square root of five divided by two.

Things You'll Need

  • Calculator
  • Paper
  • Pencil
  • Schematic architectural project drawings
  • Andrea Palladio's book, "The Four Books of Architecture"
  • Review the schematic drawings. Find the proposed length, width and height of the spaces in the schematic drawings.

  • Adjust your width and length of the architectural spaces to equal the ratio of 1 to 1.618 or the inverse, 0.618 to 1. All of the spaces do not need to be dimensionally equal, however the proportion should be the same for each space. For simplicity, some architect's use ratios that approximate the golden ratio, such as three to four, two to three and one to the square root of two. Palladio discusses these approximate ratios in his book, "The Four Books of Architecture."

    Again the dimensions of the space do not need to be equal, but the length and width must be able to be divided by a common denominator and the resulting proportion should equal or approximate the golden ratio.

  • Adjust the height of the spaces to the golden ratio, relative to either the length or width of the room. The result will produce spaces that Palladio describes as harmonically proportional. That is, the ratio of the length minus the width to the width minus the height is equal to the ratio of the length to the height of the space.

  • Break down the surfaces of the spaces, including the ceiling, floor and all of the walls, into modules that are equal to the golden ratio. This is accomplished by drawing a diagonal from one corner of the surface to its opposite. Any rectangle with a diagonal drawn perpendicular to the initial diagonal on the surface is a module equal to the golden ratio. In this way, a surface can be broken into golden modules. Because of the nature of the golden ratio, a fraction of the surface will not be able to be divided wholly into the modules. This creates interesting variation or modular complexity in the architectural design. However, approximations of the golden ratio, such as one to the square root of two can be divided wholly, and this is one reason why some architects choose to use the approximate ratios.

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References

  • Photo Credit Jupiterimages/Photos.com/Getty Images
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