The Ancient Roots of the Golden Ratio

Richard G. Geldard

The famed Greek Mathematician Euclid (c. 325–c. 265 BC) in his monumental treatise Elements provides the first known written definition of what is now called the golden ratio: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less." Euclid explains a construction for cutting (sectioning) a line "in extreme and mean ratio", i.e. the golden ratio. Throughout the Elements, several propositions and their proofs employ the golden ratio. Some of these propositions show that the golden ratio is an irrational number.

The Golden Ratio is a universal principle appearing in nature and throughout human history in philosophy, architecture, design and the arts. Its significance comes from its geometrical uniqueness. The ratio results when a line is divided into two unequal parts so that the shorter part is to the longer part as the longer part is to the whole. There is no other ratio of which this can be said. Numerically, this translates to a ratio of 1 : 1.61803398 . . . ad infinitum, or 1 : Phi.

It has not been quite a century since Egyptologists discovered that the Golden Ratio, or Phi, appears in the earliest monuments and even in the dimensions of the pyramids. From there, the ratio moved to Greece, appearing in temple design, in sculpture and the dimensions of amphoras. And when the study of Greco-Roman pottery, sculpture and architecture arrived in Italy to stimulate a renaissance, the Golden Ratio began to appear in painting, pottery, sculpture and architecture, cementing its influence to this day.

 

PARTHENON

THE SPEAR BEARER

CRETAN AMPHORA

 

When asked why this unique mathematical and geometric principle should be foundational in these early structures, the answer comes as something quite profound. It was Robert Lawlor, whose article also appears on this page, who articulated its philosophical and spiritual power. The way in which Phi operates in creating geometric forms, particularly its rectangle and spiral forms, articulates the human desire to return to the source, to the ground of being itself.

The way the rectangle and spiral are generated from unity (a point) expressed as Phi shows the way back to that point or in spiritual terms to return to the source of its creation. It is this unique characteristic that the ancients and even some contemporary artists have chosen to express. It shows us how multiplicity can return to unity, or how the One can create the Many without losing its integrity or wholeness.

Illustrations from the Power of Limits - © György Doczi