Using Geometry in Gardens
For centuries, designers have used the golden rectangle in garden design, sometimes without even realizing it. If you’re wondering how this could be, take a look at your own garden. How many groups of 3, 5, and 8 do you see? You planted them that way because you found a grouping that size visually appealing without knowing that groups of this size are an integral part of the golden ratio. Many Japanese gardens are known for their soothing designs, which, of course, are designed in golden rectangles and ratios.
What is the Golden Rectangle?
A golden ratio garden begins with a rectangle of the appropriate dimensions. Determine the measurement of the short sides of a golden rectangle by multiplying the length of the long sides by .618. The result should be the length of your short sides. If you know the measurement of the short sides and need to determine the length of the long sides, multiply the known length by 1.618.
Creating a Golden Ratio Garden
Another aspect of the golden ratio is the Fibonacci sequence, which goes like this: 0, 1, 1, 2, 3, 5, 8… To get the next number in the sequence, add the last two numbers together or multiply the last number by 1.618 (Recognize that number?). Use these numbers to determine how many plants to place in each grouping. Coincidentally (or not), you’ll find many flower bulbs in catalogs and garden stores packaged in groups of 3, 5, 8 and so forth. You can also use the ratio to determine the heights of plants to grow together. A 6 foot (2 m.) tree, three 4 foot (1 m.) shrubs, and eight 2.5 foot (76 cm. ) perennials is a pattern repeated through the most compelling gardens. I’ve given you the multipliers that you can use to calculate the lengths of the sides of a golden rectangle, but if you enjoy the beauty and elegance of mathematics, you might enjoy deriving the dimensions with a little geometric exercise. When drawn on graph paper, you can use the drawing to calculate the dimensions by assigning a unit of measurement, such as feet or inches, to each square. Here’s how:
Draw a square. Draw a line to divide the square in half, so that you have an upper half and the lower half. Draw a diagonal line to divide the upper half of the square into two triangles. Measure the length of the diagonal line. This measurement will be the radius of the arc you are about to draw. Using a simple compass like you used in grade school, draw an ark with a radius that you determined in step 3. The arc should touch the lower left and upper left corners of the square. The highest point of the arc is the length of your golden rectangle.
