Make the flat roof a garden and terrace, returning to the house the ground that the building has occupied.
Concrete made the flat roof reliable, and soil and planting kept its waterproofing from cracking in the heat. At the Villa Savoye a hanging garden open to the sky is cut into the main floor itself, and a sun terrace with curved screens crowns the roof. At the Unité d’habitation the roof becomes a public place with a gymnasium, a nursery, a running track and a paddling pool.
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)
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.
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.
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).
Cite this page Chris Paton, “The roof garden”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/roof-garden. Text, drawings and models licensed under CC BY-NC 4.0.