Cut a shaft with sixteen shallow flutes or facets, give it a square abacus and a low round base: the “proto-Doric” column of the Middle Kingdom rock tombs at Beni Hasan.
Rules · Proportion · Theory
Measure before you believe
Treat claims that a building embodies the golden section with suspicion unless the designer’s own writings or drawings say so and careful measurement agrees; a ratio near 1.6 is found somewhere in almost anything.
The Parthenon, the Great Pyramid, Gothic cathedrals and Renaissance façades have all been “shown” to follow φ, usually by drawing rectangles on small photographs and choosing which edges to measure. No ancient or Renaissance architectural text prescribes it: Vitruvius never mentions it, and even Pacioli, its great admirer, recommended the simple ratios of Vitruvius for buildings. Ratios such as 3 : 5 (1.667) and 5 : 8 (1.6), which were in ordinary use, lie within the error of most measurements.
The golden section becomes a real design tool only in the twentieth century, when architects and painters adopted it consciously, Le Corbusier above all (The Modulor). The honest position is that φ is a beautiful piece of geometry that some designers have chosen to use, not a hidden law of all beauty.
Related rules
An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.
H ≈ w·s² ⁄ 8f (uniform load w per metre, span s, rise f)
To find how thick the pier of an arch must be, divide the intrados into three equal parts; draw a line from the springing through the first division, and produce it beyond the springing by its own length. A vertical through the end of that line marks the outer face of the pier.
pier ≈ ¼ span (semicircle) · ≈ 0.23 span (equilateral) · less for a lancet
Give the flight of steps before a temple an odd number, so that one who starts with the right foot will also set the right foot first on the top.
Make the corner columns thicker than the rest by a fiftieth of their diameter, because, seen against the open sky, they look thinner than they are.
D corner = D × (1 + 1⁄50); Parthenon: 1.95 m against 1.905 m
To end the frieze with a triglyph at the corner and keep every metope square, move the corner column inward: make the last intercolumniation narrower than the others by the amount the corner triglyph is displaced.
contraction c = e − t⁄2; Parthenon: 4.29 m normal, 3.68 m at the corners (c ≈ 0.61 m)
Cite this page Chris Paton, “Measure before you believe”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/golden-section-scepticism. Text, drawings and models licensed under CC BY-NC 4.0.