Rules · Proportion · Geometry · Façades
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.
Le Corbusier illustrated the tracés régulateurs on the façades of Notre-Dame, the Capitol in Rome and his own early villas: parallel or perpendicular diagonals show that windows, doors and the whole elevation are similar rectangles. He called them a guarantee against wilfulness, not a recipe. The Modulor of 1948 turned the same impulse into a scale of numbers: in the figure a Modulor wall of 366 × 226 cm is divided, square by square, into a golden spiral whose sides are all Modulor values.
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)
With a concrete frame, a house should stand on pilotis, have a free plan and a free façade, be lit by horizontal ribbon windows, and carry a garden on its flat roof.
pilotis · free plan · free façade · ribbon window · roof garden
Set the columns back from the edge of the slab, so that the outer wall carries nothing and can be opened, closed or glazed at will.
cantilever of slab beyond column line ≈ ⅕–⅓ of the bay
Run the windows in a continuous horizontal band from one end of the façade to the other, lighting the room evenly across its whole depth.
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)
Treat architecture as volume enclosed by thin planes rather than as solid mass; order it by the regular rhythm of the structure rather than by axial symmetry; and avoid applied decoration.
Cite this page Chris Paton, “Regulating lines”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/regulating-lines. Text, drawings and models licensed under CC BY-NC 4.0.