Rules · Proportion · Modules · Geometry
Size everything from a single scale: a red series in which each measure is φ times the one before, anchored on a man 183 cm tall, and a blue series of its doubles, anchored on his raised hand at 226 cm.
red: … 27, 43, 70, 113, 183, 296 … (×1.618) · blue: … 53, 86, 140, 226, 366 … (= 2 × red)
The Modulor combines the golden ratio, the Fibonacci property (each term is the sum of the two before it) and human dimensions: 113 cm is the height of the navel, 183 cm the height of the man and 226 cm the reach of his raised hand, so that 183 : 113 and 113 : 70 are both close to φ. Le Corbusier offered it as a tool for designers and industry alike, in place of the unrelated systems of feet and metres.
The Unité d’habitation in Marseille was dimensioned with it throughout: its ceilings are 226 cm high, and a figure of the Modulor man is cast into its concrete.
A saddle surface in which two opposite corners are raised and two lowered is a hyperbolic paraboloid; it contains two families of straight lines, so it can be formed with straight boards and yet has double curvature.
y = k·x·z (or any bilinear patch through four points not in one plane)
Check the proportions of a façade with a few geometric lines (diagonals of similar rectangles, the golden section) so that its parts share one order and nothing is arbitrary.
To divide a line in extreme and mean ratio, make the whole stand to the larger part as the larger part to the smaller; the ratio is φ = (1 + √5)/2 ≈ 1.618. Construct the golden rectangle by swinging the line from the midpoint of a square’s side to its far corner.
φ = (1 + √5)/2 ≈ 1.618; φ² = φ + 1; 1/φ = φ − 1 ≈ 0.618
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.
Take the height of a man (183 cm) and of his raised hand (226 cm) and divide each by the golden section, again and again, to obtain two interlocking series of dimensions for every part of a building.
red series … 27 · 43 · 70 · 113 · 183 cm; blue series … 53 · 86 · 140 · 226 cm (each ≈ previous × φ)
Classify a roof by how its planes meet: one slope (shed), two meeting at a ridge (gable), four meeting at hips (hip, pyramid), a hip below a gable (hip-and-gable), two pitches each side (gambrel, mansard), or a curved surface (barrel, cone, dome).
Cite this page Chris Paton, “The Modulor: two golden series”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/modulor-series. Text, drawings and models licensed under CC BY-NC 4.0.