Addis \cite{Addis2014} retraces the use of physical form-finding methods from Hooke via Poloni and Hübsch to Antoni Gaudí (1852-1926) who used the law of inversion not only on two-dimensional but also on three-dimensional networks of strings using sand bags as weights; and on to Heinz Isler (1926-2009) who, as the “last of the great concrete shell builders of the twentieth century” further expanded the law by using a sheet of cloth (rather than a chain) to make hanging models.
The characteristic feature of the method that each protagonist developed further, and which allowed them to use the law of inversion as a method for the design of full-scale structures in the first place, is that certain aspects of the structure, such as its static equilibrium and the funicular shape, are scale-independent and thus independent of materials involved. Therefore, they can be scaled up linearly to predict structural behaviour of compression structures such as funicular arches, vault and domes at full-scale (\citealt{Addis2014}, 34). This must obviously be seen in contrast to scale-dependent properties that cannot be scaled up linearly, such as the strength and elasticity of the material and the buckling behaviour of a column or thin shell (see Section 3.2).
Strikingly, both of Hooke’s laws of elasticity and of inversion are still in use today and constitute fundamental principles in the numerical methods for the design of contemporary form-found shell structures (see Section 3.3).