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)
A thin curved shell carries load by the membrane forces in its surface, not by bending; so shape it to its loads and supports, and it can span great distances with a thickness of a few centimetres.
span ÷ thickness of a good shell ≈ 400–1000 (an egg: ≈ 100)
Span the whole depth of the building with the structure so that each floor is a single open plate, adaptable to uses that cannot be foreseen.
Pompidou: 48 m clear span between column lines, 13 bays of 12.8 m
In a framed building the columns and beams carry every load; the outer wall can be reduced to a light cladding hung on the frame, floor by floor, and need grow no thicker as the building rises.
load-bearing wall: thickness grows with height · frame: cladding thickness constant
The outward form of a building should arise from, and express, what the building does and how it is made, as the form of every living thing expresses its life.
Omit applied ornament from buildings and everyday objects: it wastes work, money and material, dates quickly, and adds nothing that fine material and exact workmanship cannot give.
Build the house as a standard skeleton of flat concrete slabs, a few columns set back from the slab edges, and a stair; everything else (walls, windows, partitions) is infill that can be placed freely.
3 slabs + 6 columns + 1 stair
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
Raise the main storey on slender columns so that the ground beneath flows under the building (for circulation, cars, gardens or public space) and the rooms are lifted into light, air and view.
Since columns carry the floors, partitions can be placed wherever the use requires, independent of the structure and different on every storey.
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.
Make the flat roof a garden and terrace, returning to the house the ground that the building has occupied.
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.
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)
House a whole community in one tall slab: stack duplex flats that run through the block with light on both sides, put shops and services on an interior street half-way up, and give the roof to everyone.
Open the corners, extend the roofs and terraces beyond the walls with cantilevers, and let the space of the house flow outward rather than being enclosed in rooms like boxes.
Train artists as craftsmen in workshops, and unite architecture, sculpture, painting and design in the common work of building.
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.
Reduce a building to the fewest, most exactly made elements (a regular structure, a clear enclosure, an open and adaptable space) and let their proportion and detail carry the whole effect.
Hang the outer wall from the edges of the floor slabs as a continuous skin of glass and metal, independent of the frame behind it, and express its grid of mullions.
skin = vision glass + spandrel panel per floor, on a module of ≈ 1.5 m
Understand every building as a combination of four elements (the hearth, the roof on its supports, the enclosure and the mound), each descended from a craft: ceramics, carpentry, weaving and masonry.
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)
Make the roof flat and use it: a garden and terrace that gives back to the building the ground it covers, drained inward and kept watertight by a continuous membrane.
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).
Concentrate the business centre in a few very tall towers set far apart on a regular grid, so that they cover only a small fraction of the ground and the rest can be park: density and open space at once.
twenty-four cruciform towers of about sixty storeys; a small fraction of the centre built on
Replace the street lined with buildings by roads for traffic alone, sorted by speed and on separate levels, crossing at a central interchange; give the ground between them to pedestrians and parkland.
House the population in continuous slabs raised on pilotis and folded back and forth round large open courts, so that every flat looks over the park and the ground runs unbroken beneath the buildings.
Analyse the city into four functions (dwelling, work, recreation and circulation) and plan a separate, appropriate place for each, joined by a network of roads classified by speed.
Where density is needed, build tall blocks widely spaced, so that every dwelling has sun, air and a view, and the ground freed between them becomes green space.
Run housing slabs in parallel rows, north to south so that the flats have morning and evening sun, and space them by a fixed angle of light: then the taller the rows, the more dwellings the same ground holds, or the more ground is left free for the same number.
gap = H ÷ tan α (α the chosen angle of light, e.g. 30°: gap ≈ 1.7 H)
Place industry and other large work places in their own zone, served by road and rail, near the housing but separated from it by a belt of green.