A developable surface has the property that it can be made out of sheet metal, since such a surface must be obtainable by transformation from a plane (which has Gaussian
curvature 0) and every point on such a surface lies on at least one straight
line.
Developable surfaces occur in architectural and machine-building applications where smooth surfaces formed from flat sheet materials are useful (Glaeser and Gruber 2007,
Bock Hyeng et al. 2025).
Bock Hyeng, C. A.; Krivoshapko, S. N.; Kouamou Nguessi, A.; Yamb Bell, E.; and Bahel, B. "Application of Curvilinear Analytical
Surfaces in Forms of Architectural Objects and Machine Building Products." Int.
J. Archit. Arts Appl.11, 19-35, 2025. https://doi.org/10.11648/j.ijaaa.20251101.13.Glaeser,
G. and Gruber, F. "Developable Surfaces in Contemporary Architecture."
J. Math. Arts1, 59-71, 2007.Gray, A.; Abbena, E.; and
Salamon, S. Modern
Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. Boca
Raton, FL: CRC Press, pp. 398 and 437-438, 2006.Kuhnel, W. Differential
Geometry Curves--Surfaces--Manifolds. Providence, RI: Amer. Math. Soc., 2002.Snyder,
J. P. Map
Projections--A Working Manual. U. S. Geological Survey Professional
Paper 1395. Washington, DC: U. S. Government Printing Office, p. 5, 1987.
everywhere. Developable surfaces therefore include the cone,
cylinder, elliptic cone,
hyperbolic cylinder, and plane.
Other examples include the tangent developable,
generalized cone, and generalized
cylinder.
