The golden ratio is a mathematical proportion defined by a particular division of a segment: the ratio of the whole to the larger part equals that of the larger part to the smaller. Its value is approximately 1.6180339. Greek mathematicians studied this “division in extreme and mean ratio,” which is found in the regular pentagon. Modern occultism places it at the heart of many compositions described as sacred. Its real significance is considerable, but it does not justify automatically finding the same proportion in every work of art, body, or monument.
| Notation | φ (phi) |
|---|---|
| Value | (1 + √5) / 2 ≈ 1,618034 |
| Ancient definition | Division in extreme and mean ratio |
| Geometry | Pentagon and golden rectangle |
| Caution | Claims about monuments must be measured and supported by sources |
How exactly is the golden ratio defined?
If a segment of length a+b is divided into two portions, with a greater than b, the golden ratio appears when (a+b)/a = a/b. This equality leads to φ² = φ + 1, hence φ = (1+√5)/2.
The proportion does not depend on any religious tradition to exist. It is an exact geometric relationship, studied particularly in problems involving the construction of regular figures.
Why did the Greeks know about this proportion?
Euclid's Elements define division in extreme and mean ratio and use it in the geometry of the pentagon, decagon, and certain polyhedra.
The construction is found notably in the dodecahedron and the icosahedron. This gives the golden ratio a genuine place in the history of regular solids.
Why is the pentagram linked to the golden ratio?
In a regular pentagon, the ratio of a diagonal to a side is φ. The pentagram, formed by the diagonals of a pentagon, reveals segments that are again divided according to this proportion.
The connection is geometric and measurable. It explains part of the pentagram’s appeal in mathematical and occult traditions, without imposing a common interpretation on all its uses.
Do the Parthenon and the pyramids follow the golden ratio?
Modern composites frequently apply golden rectangles to photographs of Greek temples or pyramids. Several historical analyses show that the choice of measurement boundaries is then decisive.
There is no evidence that the golden ratio served as a universal blueprint for these monuments. The existence of a remarkable proportion should not replace archaeological study of construction methods.
Why does modern occultism attach so much importance to it?
φ’s ability to connect the pentagon, golden rectangle, and certain numerical sequences encourages an interpretation of harmony.
This fascination has its own cultural history, particularly since the 19th century. The golden ratio is a precise mathematical tool; considering it a “law of all beauty” remains an interpretation that should be discussed rather than assumed.
Sources and historical reference points
Wolfram MathWorld, “Golden Ratio” establishes the definition of φ. “The golden ratio—dispelling the myth” examines modern claims concerning the Parthenon and the pyramids.
