1. Introduction
The golden ratio φ ≈ 1.618 is one of the most famous numbers in mathematics. It is also one of the most misunderstood. Between its real mathematical properties and the pseudoscientific claims attributed to it, there is a considerable gap that this article attempts to bridge.
2. Mathematical Definition
φ is defined as the ratio a/b such that (a+b)/a = a/b. Its exact value is (1+√5)/2 ≈ 1.6180339887... It is an irrational number, root of the polynomial x² - x - 1 = 0. It is linked to the Fibonacci sequence: the ratio of two consecutive terms converges to φ.
3. Real Evidence
The golden ratio genuinely appears in phyllotaxis (golden angle = 360°/φ²), in continued fractions (φ = 1 + 1/(1 + 1/(1 + ...))), in regular pentagons (diagonal/side = φ), and in certain quasicrystals. These appearances are mathematically demonstrable and reproducible.
4. Myths and Pseudoscience
Many claims about the golden ratio do not withstand scrutiny. The Parthenon facade does not follow φ precisely — measurements vary depending on the chosen starting point. The human body does not follow φ systematically — proportions vary between individuals and according to measurement method. The nautilus shell spiral is not a logarithmic spiral with ratio φ — its ratio is generally between 1.24 and 1.43.
5. Art and Architecture
Some artists deliberately used φ in their compositions: Dalí in "The Sacrament of the Last Supper", Le Corbusier in his Modulor. But the retrospective attribution of φ to ancient works (Leonardo da Vinci, the Egyptian pyramids) is generally the result of biased selection of measurements.
6. Conclusion
The golden ratio has genuinely remarkable mathematical properties. Its supposed omnipresence in nature, art and the human body is largely exaggerated. Distinguishing real appearances from pseudoscientific projections is essential for an honest understanding of this fascinating number.