Article PDF
Avoid common mistakes on your manuscript.
References
L. B. Alberti,On the Art of Building in Ten Books, J. Ryk-wert, N. Leach, and R. Tavernor, trans., Cambridge, Mass: MIT Press, 1988.
F. Clarke,Optimization and Nonsmooth Analysis, Centre de recherches mathématiques, Montreal, 1989.
T. Clausen, “Über die Form architektonischer Säulen,”Bull. cl. physico-math. Acad. St. Pétersbourg 9, 1851, pp. 369–380.
S. J. Cox and M. L. Overton, “On the optimal design of columns against buckling,”SIAM J. on Math. Anal. 23 (1992), to appear.
W. B. Dinsmoor, “The architecture of the Parthenon,” inThe Parthenon, V. J. Bruno, ed., New York: Norton, 1974, pp. 171–198.
L. Euler,Leonhardi Euleri Opera Omnia, Scientiarum Nat-uralium Helveticae edenda curvaverunt F. Rudio, A. Krazer, P. Stackel. Lipsiae et Berolini, Typis et in aedibus B. G. Teubneri, 1911-.
R. Hooke, “Lectures de Potentia Restitutiva, or of spring explaining the power of springing bodies,” London, John Martyn, 1678; reprinted, pp. 331–388 of R. T. Günther,Early Sciences in Oxford 8, Oxford, 1931.
J. Keller, “The shape of the strongest column,”Arch. Rat. Mech. Anal. 5 (1960), pp. 275–285.
J. L. Lagrange,Oeuvres de Lagrange, J. A. Serret, ed., Paris: Gauthier-Villars, 1867.
M. Laugier,An Essay on Architecture, W. and A. Herrmann, trans., Los Angeles, Hennessey & Ingalls, 1977.
E. Masur, “Optimal structural design under multiple eigenvalue constraints,”Int. J. Solids Struct. 20 (1984), pp. 211–231.
N. Olhoff and S. Rasmussen, “On single and bimodal optimum buckling loads of clamped columns,”Int. J. Solids Struct. 13 (1977), pp. 605–614.
F. Penrose,An investigation of the principles of Athenian architecture;or, The results of a survey conducted chiefly with reference to the optical refinements exhibited in the construction of the ancient buildings at Athens, Macmillan, London, 1888. Reprinted by McGrath, Washington, 1973.
A. Seiranian, “On a problem of Lagrange,”Inzhenernyi Zh., Mekhanika Tverdogo Tela, 19 (1984), pp. 101–111.Mechanics of Solids 19 (1984), pp. 100-111.
G. Stevens, “Entasis of Roman columns,”Mem. Amer. Acad. Rome IV, 24 (1924), pp. 121–139.
I. Tadjbakhsh and J. Keller, “Strongest columns and iso-perimetric inequalities for eigenvalues,”J. Appl. Mech. 29 (1962), pp. 159–164.
I. Todhunter and K. Pearson,A History of the Theory of Elasticity and of the Strength of Materials, Cambridge, 1886.
E. Viollet-Le-Duc,Dictionnaire Raisonné de l’Architecture Française du Xle au XVIe siècle, Paris: A. Morel, 1875.
P. Vitruvius,On Architecture, F. Granger, trans., London, W. Heinemann, Ltd.; New York: G. P. Putnam’s sons, 1931-34.
T. Young,Miscellaneous Works, vol. 2, G. Peacock, ed., John Murray, London, 1855. New York: Johnson Re- print, 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cox, S.J. The shape of the ideal column. The Mathematical Intelligencer 14, 16–24 (1992). https://doi.org/10.1007/BF03024137
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03024137