Surfaces43 of 113
Hyperbolic paraboloid
string model after Olivier, c. 1830
Lift two opposite corners of a square frame and lower the other two, then stretch threads between opposite sides. Every thread is straight, and together they make the curved saddle. Théodore Olivier built moving models like this to teach descriptive geometry.
z = xy
On mathcurve.com as Paraboloïde hyperbolique
Elsewhere
3Work the library cites and does not hold: in copyright, never released as a file, or not a file at all. The cited shelf
- 1937
Cherrywood and string. Moore named the string models in the Science Museum, London, as the source: straight threads strung between two frames to make a curved surface you can see through.
Not yet checkedSuggested by an AI model, 2026-10-08
An AI reviewer had doubts, 2026-10-09: The library's entry for the shape says "Every thread is straight, and together they make the curved saddle.", so the geometry fits a string sculpture. The record for the work gives only title, maker, year, kind and holder, so nothing there supports the cherrywood, the string, or Moore naming the Science Museum models, and the holder's page could not be read.
- 1954
For 61 players, first heard at Donaueschingen in 1955. Each string glissando is a straight line on Xenakis’s pitch and time graph, and together the lines sweep curved surfaces, which he later built in concrete.
Not yet checkedSuggested by an AI model, 2026-10-08
An AI reviewer had doubts, 2026-10-09: The holder's page says "(ou Metastasis) pour 60 musiciens", and its listed instruments also add up to 60, so the note's 61 players is wrong. The Donaueschingen premiere in 1955 is borne out, but nothing in the evidence links the work to the hyperbolic paraboloid or to concrete.
- 1958
Philips Pavilion, Expo 58, Brussels
A tent of hyperbolic paraboloid shells. Xenakis said he had built the ideas of Metastaseis in it: the straight lines of the glissandi became the straight lines of the shells.
Not yet checkedSuggested by an AI model, 2026-10-08
An AI reviewer agreed, 2026-10-09: The holder's page says the engineer's plan was "dividing the hyperbolic paraboloids of the pavilion in numerous prefabricated concrete slabs", so the shape is in the building. The page also says Xenakis underlined the likeness between the Metastaseis glissandi lines and the shell, which fits the note's point.