Seeing the Math in Design

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Photo Courtesy of KDH Residential Designs

Whether in nature, art , or building design, there are certain rules and ratios that can account for an aesthetically pleasing composition. Mathematicians have studied the “golden ratio” for thousands of years. This golden ratio appears everywhere and can be calculated with formulas, number sequences, and even displayed graphically. The formula for the golden ratio is  or 1.618.  Leonardo Fibonacci identified a sequence of numbers that also have golden ratio implications. The Fibonacci sequence adds the sum of the two numbers prior to find the next number. The Fibonacci sequence is 0,1,1,2,3,5,8,13,21,34,55,89,144, etc. By taking the relationship of the two numbers next to each other we will find the golden ratio. Example: 8/5=1.6, 89/55 = 1.618, 144/89 = 1.618.

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These golden ratio numbers can also be found by looking in the mirror or by looking around at nature during a walk in the park. The segments of a human finger are all 1.618 larger than the next segment. The human ear has a nautilus shell shape. This shape is created by what is called an equiangular spiral, or “golden spiral”—meaning the length of the chord in each arc is 1.618 larger than the next. The golden ratio is also seen in what’s known as a “golden triangle,” an isosceles triangle where one side is shorter than its two equal sides in that 1.618 proportion. When these triangles are nested inside of one another, it creates the “golden spiral” shape.

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The human body shows examples of the golden ratio all over it, from the spacing of facial features, to the relationship between someone’s height and arm span. Examples of the golden ratio are easy to spot in trees and plants, too, since both naturally grow to the golden ratio. Flower pedals, for example, naturally come in Fibonacci sequence numbers. A flower will normally only have 1,2,3,5,8 or 13 pedals—which is why those four-leaf clovers are so hard to find.  Even in music for instance, one octave on a piano contains 13 keys, 8 white keys and 5 black keys.

So, what does this all mean when it comes to home design? Often, when drawing and designing homes the artist will simply see the math unknowingly. When designing, it is very common to continue to draw until the home looks pleasing to the eye. The human eye will pick up on anything that falls outside of the golden ratio as disproportionate and displeasing. Graphically, designers can use regulating lines (bisecting angles) which will hit key points of the building to check their proportions.

So if something seems a little “off” in the design of your next home, it may be because some aspect is slightly outside of the golden ratio. Using regulating lines and Fibonacci numbers may well fix the problem. Try superimposing the golden spiral onto your computer generated elevations to check for proper proportions as in the examples shown here.

Being aware of the golden ratio, including the golden spiral and golden triangle, will undoubtedly improve your design.

Sometimes it simply helps to do the math.

Original article, written by Kevin Holdridge, was published in the Winter 2016 Issue of Best in American Living Magazine.

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