The question
When did a line-dividing ratio become “golden”?
The short answer
For most of its history the ratio was a tool of geometry. Its mystique is largely modern, built in the 19th and 20th centuries on top of real mathematics.
What science knows
Historical FactEuclid, around 300 BCE, defined the “extreme and mean ratio” and used it to construct the regular pentagon and dodecahedron.
In 1509 Luca Pacioli published De divina proportione, illustrated by Leonardo da Vinci with drawings of polyhedra. Johannes Kepler praised the ratio as one of geometry’s two great treasures, beside Pythagoras’ theorem, and noticed that ratios of Fibonacci numbers approach it.
The pattern
Established Mathematicsφ = (1 + √5) / 2 ≈ 1.618. The same number appears in the pentagon, the dodecahedron and the limit of Fibonacci ratios.
What is still uncertain
Mixed EvidenceThe name “golden section” first appears in the 1830s, and Adolf Zeising’s 1854 claim that it was a universal law of beauty launched many later assertions about ancient buildings and art. Most do not survive careful measurement.
Why humans find it interesting
Historical FactIn the 20th century, the architect Le Corbusier built his Modulor system of proportions on it, and Salvador Dalí painted The Sacrament of the Last Supper (1955) on a golden rectangle.
CUE perspective
CUE PerspectiveThe golden ratio’s story shows how a real mathematical fact can gather myth. The fact is still worth knowing.
CUE keeps the two apart: the geometry is established; the legend is history.