Ground Rules: The Golden Ratio and Golden Rectangle
My overactive left-brain was delighted to learn that math is important when designing a garden. If you’re right-brained, don’t panic! I’m just talking about some simple algebra. Furthermore, you won’t lose points if the math isn’t 100% correct to the second or third decimal point!
The Golden Ratio (1.618) and the related Golden Rectangle are design principles found in nature and used extensively in architecture, art, music, and physics. For example, both the Greek Parthenon and Salvador Dali’s The Sacrament of the Last Supper exhibit the Golden Ratio.
The Golden Rectangle
The Golden Rectangle, which is particularly helpful in establishing the most pleasing dimensions for everything from flowerbeds and lawns to terraces and arbors, is a rectangle where the ratio of the short side to the long side equals the ratio of the long side to the sum of both sides.
Written mathematically the Golden Rectangle is:
A = Short Side
B = Long Side
(A/B) = (B/(A+B))
The Golden Rectangle is why many flowerbeds are 5 feet wide by 8 feet long (1.5 by 2.4 metres):
(5/8) = (8/(5+8))
Ratio: 0.62 = 0.62
and for those more comfortable with the Metric system
(1.5/2.4) = (2.4/(1.5+2.4))
Ratio: 0.62 = 0.62
Figure 1. The Golden Rectangle.
The Golden Ratio
Alternatively if you know the length of the short side of the rectangle, simply multiply it by the Golden Ratio (1.618) to derive the appropriate length of the long side of the rectangle. For example, if the short side is 8 feet long (2.4 metres), the long side should be approximately 13 feet long (3.9 metres). Mathematically:
(8 feet x 1.618) = 12.9 feet
and
(2.4 metres x 1.618) = 3.9 metres
In order to check your math, the sum of the short and long sides should equal the length of the long side times 1.618:
(12.9 feet x 1.618) = 20.9 feet = (8 feet + 12.9 feet)
and
(3.9 metres x 1.618) = 6.3 metres = (2.4 metres + 3.9 metres)
See, there was no reason to fear the math.
Finally, the properties of the Golden Ratio and Golden Rectangle may apply to irregularly shaped designs. Simply draw a rectangle around the irregular shape as shown in the figure below. The formula and calculations work the same as with a rectangle.
Figure 2. Using the Golden Rectangle For Irregular Shapes.
While there are more mathematics-based design principles, if you can get your head around the Golden Ratio and Golden Rectangle, the others will be a piece of cake or pi, if you prefer.
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