I was never much taken with mathematics and was left unmoved by mathematicians' delight in the logic of numbers and the “beautiful” solutions they offered. It wasn't until I started to study landscape architecture that I came to appreciate the true magic of numbers, which can be tied to real things and used to solve real problems. Who knew, for example, that an equation can tell you how high a retaining wall should be or that geometry can help generate a plan whose proportions positively sing?
The notion that beauty and geometry are one, each an expression of the other, is deeply rooted in human culture. Certain proportions and forms seem “right” and evoke in us a sense of harmony and serenity. Most notable among these are shapes generated from the so-called golden mean, or golden section, which was first expressed in mathematical form by the Greek geometer Pythagoras (560 to 480 B.C.), who showed it to be the basis for the proportions of the human figure. It is as simple as it is perfect. A single line is divided so that one section—the larger—has the same proportion to the whole as the smaller section has to the larger.
From the time of Pythagoras to the present, this golden mean has inspired forms in art, design and architecture [such as the Parthenon, shown here]. A Japanese gardening manual of the 15th century used it to relate rocks in landscape compositions; in 2003 the golden mean inspired the design of an award-winning garden at the Chelsea Flower Show in London, England. (For a step-by-step how-to of the golden mean, go to goldennumber.net.)
Faced with a sheet of paper marked with little more than the outlines of a plot of land and the house that sits in it, I thank Pythagoras and all who came after him. Using lines taken from the edges, doors and windows of the building, from the boundaries of the property, from the configuration of a stand of trees or anything else close at hand, I can generate shapes—circles, squares, rectangles, triangles—often using the principles of the golden section. These can be divided again and again and connected to each other in a mesh that supports my design.
The shapes don't necessarily appear as such in the final version, but they underpin it. They suggest the proportion of open space—which might be paving or lawn—to volume, such as massed trees, shrubs and perennials or garden structures. Points generated by intersecting lines can be connected into symmetrical or asymmetrical patterns or swooping curves.
Geometry also helps to keep the design coherent and organized, allowing me to align and bring all the bits together in an orderly way and to set up clean axial lines and focal points.
Amazingly, order on the page translates perfectly into order in the garden. There is beauty in balance, pleasure in proportion. Plato said, “Geometry existed before creation.” That must explain it.