Golden Ratio in Landscaping. The golden ratio, or golden section, involves designing an element where the ratio of a small part to a bigger part is equal to the ratio of the bigger part to the whole. A golden rectangle has sides measured in the golden ratio. The golden ratio can and has been incorporated in landscape and garden design to achieve a unified design in balance with nature's proportions, which are often in the golden ratio.
Structures like the Parthenon and the Egyptian pyramids use the golden ratio, as do other classic and contemporary art and architectural works. Japanese garden design uses the golden ratio, particularly in how rocks placed in 15th-century gardens related to one another, though a contemporary researcher found the occurrence, and it's unclear if the original designers were aware of the ratio.
Create a golden section in your garden. Look for ways to divide a space into smaller sections expressing the 1.618 ratio. For instance, divide a space measuring 21 feet into two sections measuring 8 and 13 feet. You can do this repeatedly with larger areas, and putting a proportioned square at a 45-degree angle to a wall, house, fountain or other landscape structure can create a feeling of movement while keeping the ratio intact.
Look for ways to place plants near one another to mimic the golden ratio. Place a miniature 6-foot tree behind a group of 4-foot shrubs bordering a bed of perennials growing to 2 1/2 feet tall. You can create proportion within a single plant as well, pruning a tree so its flowering branches cover only the top third of the plant, giving a visual balance within the tree itself as well as in its proportion to surrounding plants and landscape structures.
Group plants according to the golden ratio. When you're deciding how many perennials, shrubs and trees to grow, use numbers that align with the golden ratio, also called the Fibonacci sequence after the mathematician who discovered them. Plant 8 perennials, 5 shrubs and 3 trees in the same area, for instance. Even if you're planting just one type of flower in a bed, use those numbers to guide how many you'll use. They end up looking visually balanced even when not set near other groups of plants in the proportional number.