Developable Surfaces: Their History and Application

Abstract

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Discrete Geodesic Nets for Modeling Developable Surfaces

“…The theory of surfaces formed by local C 2 isometries of the plane is covered in the differential geometry literature [do Carmo 1976;Spivak 1999] and traces back to the works of Euler and Monge in the eighteenth century [Lawrence 2011]. Gauss' Theorema Egregium coupled with Minding's theorem shows that C 2 developable surfaces are surfaces with zero Gaussian curvature.…”

Fabricate 2017

“…This makes the edge-layout amenable for realisation using standard hollow sections of aluminium. Developable surfaces retain a variety of applications in sheet-and plate-based industries including architecture because they can be isometrically mapped onto a plane (Lawrence, 2011). The chosen method of forming sheet material is kerf-cutting and bending for the node covers and cell walls.…”

“…Additionally, use of 'off-the-shelf' sheet and hollow sections compatible with ubiquitous 2-axis cutting technologies eliminated time-intensive milling techniques from design consideration (Scheurer, 2013), constraining the domain of geometric possibility to developable surfaces (Lawrence, 2011). Subsequently, all parts in the prototype were cut using 2-axis cutting methods, predominantly by laser.…”

Realizing Architecture’s Disruptive Potential

“…Mathematically these surfaces have been known for centuries but its in depth study gained traction after the invention of calculus and is widely credited to French mathematician Gaspard Monge. 21 As mentioned in the introduction, such in-depth mathematical knowledge was abstracted and captured as drawing machines and construction manuals during the nineteenth century. 22 These inventions, in turn, made them widely accessible and their materialization in stone and timber significantly more feasible.…”