El problema de Dido, abelles, billars i principis de màxims i mínims
ISSN: 2014-7104, 1133-4282
Año de publicación: 2015
Número: 37
Páginas: 8-28
Tipo: Artículo
Otras publicaciones en: NouBiaix: revista de la FEEMCAT i la SCM
Resumen
Everyday life often presents us with the challenge of getting the most out of limited resources. There are many examples showing that Nature also follows some sort of economy principle, whereby it maximizes the utility of the materials at hand. Mathematically speaking, the right context for such questions are the so-called optimization problems or problems of maxima and minima. This article provides a brief overview of some famous problems of maxima and minima that share a remarkable geometrical flavour.
Referencias bibliográficas
- Batschelet, E. (1975). Matemáticas básicas para biocientíficos. Springer Verlag.
- Blåsjö, V. (2005). The Isoperimetric Problem. American Math. Monthly, vol. 112, 6, 526-566.
- Courant, R., Robins, H. (1979). Qué es la Matemática. Aguilar.
- De Temple, D., Robertson, J. (1981). A billiard path characterization of regular polygons. Mathematics Magazine, vol. 54, 2, 73-75.
- Fagnano, J.F. (1755; aparegut 1779). Acta Erud., 281-303.
- Fejes Tóth, L. (1964). What the bees know and what they do not know. Bull. Amer. Math. Soc., 70, 468-481.
- Gutkin, E. (1997). Two applications of Calculus to triangular billiards, vol. 104, 7, 618-622.
- Hales, T. (2001). The honeycomb conjecture. Discrete Comput. Geom., 25, 1-22.
- Heath, T. (1981). A history of greek mathematics. Dover
- Hildebrandt, S., Tromba, A. (1989). Matemática y formas óptimas. Biblioteca Scientific American. Premsa Científica.
- Huber, M. (2009). Mythematics. Princeton University Press.
- Nahin, P.J. (2007). When least is best. Princeton University Press.
- Pickover, C.A. (2009). El Libro de las Matemáticas. Librero.
- Polya, G. (1954). Mathematics and plausible reasoning. Princeton University Press.
- Rademacher, H., Toeplitz, O. (1994). The enjoyment of Mathematics. Princeton University Press. (Traduït de l’edició alemanya de 1933).
- Tabachnikov, S. (2005). Geometry and Billiards. American mathematical Society.
- Thompson, D. (1942). On growth and form, vol. II. Cambridge University Press.
- Varró, M.T. (1934). On Agriculture. Loeb Classical Library.
- Vorobets, Y.B., Galperin,G.A., Stepin,A.M. (1992).Periodicbilliard trajectoriesin polygons: generating mechanisms. Russian Math. Surveys, 47, 3, 5-80.