@article{PMFA_2007_52_2_a4,
author = {Verstraelen, Leopold},
title = {Univerz\'aln{\'\i} p\v{r}{\'\i}rodn{\'\i} tvary},
journal = {Pokroky matematiky, fyziky a astronomie},
pages = {142--151},
year = {2007},
volume = {52},
number = {2},
zbl = {1265.53006},
language = {cs},
url = {http://geodesic.mathdoc.fr/item/PMFA_2007_52_2_a4/}
}
Verstraelen, Leopold. Univerzální přírodní tvary. Pokroky matematiky, fyziky a astronomie, Tome 52 (2007) no. 2, pp. 142-151. http://geodesic.mathdoc.fr/item/PMFA_2007_52_2_a4/
[1] Verstraelen, L.: The geometry of eye and brain. Soochow Journal of Mathematics 30 (2004) (volume in honour of Professor Bang-Yen Chen), 367–376. | MR | Zbl
[2] Coolidge, J. L.: A history of geometrical methods. Dover Publ., London (1963). | MR | Zbl
[3] Bronowski, J.: The ascent of man. Litte, Brown & Co, Boston 1973.
[4] Lejeune, A.: Euclide et Ptolémée, deux stades de l’optique géométrique grecque. Université de Louvain, Bureau du “Recueil” (1948). | MR | Zbl
[5] Montel, P.: Encyclopédie française, Tome 1. Larousse, Paris 1937.
[6] Dillen, F., Verstraelen, L.: Handbook of differential geometry. North-Holland, Amsterdam, Vol. 1 (2000) and Vol. 2 (2005). | MR | Zbl
[7] Chern, S. S., Chen, W. H., Laser, K. S.: Lectures on differential geometry. World Scientific, Singapore 1999. | MR
[8] Kühnel, W.: Differential geometry: curves-surfaces-manifolds. AMS-Student Math. Library, vol. 16 (2002). | MR | Zbl
[9] Penrose, R.: The geometry of the universe. In Mathematics Today (ed. Steen, L. A.), Vintage Books, New York 1980. | MR
[10] Penrose, R.: The emperor’s new mind, concerning computers, minds and the laws of physics. Oxford University Press, Oxford 1989. | MR
[11] Browder, F. E., Mac Lane, S.: The relevance of mathematics. In Mathematics Today (ed. Steen, L. A.), Vintage Books, New York 1980.
[12] Hilbert, D.: Mathematical problems (1900 – Paris – Lecture). AMS-Proceedings of Symposia in Pure Mathematics, Vol. 28 (1976).
[13] d’Arcy Thompson, W.: On growth and form. Cambridge University Press, Cambridge 1917. | MR
[14] Lamé, G.: Examen des différentes méthodes employées pour résoudre les problèmes de géométrie. Hermann, Paris 1818.
[15] Thompson, A. C.: Minkowski geometry. Encyclopedia of mathematics and its applications, Vol. 63, Cambridge University Press, Cambridge 1996. | MR | Zbl
[16] Chen, B.-Y.: What can we do with Nash’s embedding theorem?. Soochow Journal of Mathematics 30 (2004), 303–338. | MR | Zbl
[17] Chen, B.-Y.: Riemannian submanifolds. In [6, Vol. 1]. | Zbl
[18] Hildebrandt, S., Tromba, A.: Panoptimum. Spektrum, Heidelberg 1986. | MR
[19] Willmore, T. J.: A survey on Willmore immersions. In Geometry and Topology of submanifolds, Vol. IV, (eds. Dillen, F., Verstraelen, L.), World Scientific, Singapore 1992. | MR | Zbl
[20] Chen, B.-Y.: Total mean curvature and submanifolds of finite type. World Scientific, Singapore 1984. | MR | Zbl
[21] Barros, M.: The conformal total tension variational problem in Kaluza-Klein supergravity. Nuclear Physics B 535 (1998), 531–551. | DOI | MR | Zbl
[22] Barros, M.: Willmore-Chen branes and Hopf T-duality. Class. Quantum Grav. 17 (2000), 1979–1988. | DOI | MR | Zbl
[23] Gielis, J., Haesen, S., Verstraelen, L.: Universal natural shapes; from the supereggs of Piet Hein to the cosmic egg of Georges Lemaître. Kragujevac Journal of Mathematics 28 (2005), 57–68. | MR
[24] Gielis, J.: A generic transformation that unifies a large number of natural and abstract shapes. American Journal of Botamy 90 (2003), 333–338. | DOI
[25] Gielis, J.: Inventing the circle. Geniaal Press, Antwerpen (2003).
[26] Gielis, J., Gerats, T.: A botanical perspective on plant shape modeling. Proc. International Conference on Computing, Communications and Control Technologies, Vol. VI (2004), 265–272.
[27] Gielis, J.: Wiskundige supervormen bij bamboes. Newsletter Belgian Bamboo Society 13 (1996), 20–26.
[28] Gielis, J., Beirinckx, B., Bastiaens, E.: Superquadrics with rational and irrational symmetries. Proc. 8th ACM symposium on Solid Modeling and Applications (2003), 262–265.
[29] Gielis, J.: Variational superformula curves for 2D- and 3D graphic arts. Proc. World Multi-Conference on Systemics, Cybernetics and Informatics, Vol. V: Computer Science and Engineering (2004), 119–124.
[30] Haesen, S., Sebeković, A., Verstraelen, L.: Relations between intrinsic and extrinsic curvatures. Kragujevac J. Math. 25 (2003), 139–145. | MR | Zbl
[31] Dillen, F., Haesen, S., Petrović-Torgasev, M., Verstraelen, L.: An inequality between intrinsic and extrinsic scalar curvature invariants for codimension 2 embeddings. J. Geom. Phys. 52 (2004), 101–112. | DOI | MR | Zbl
[32] Haesen, S., Verstraelen, L.: Ideally embedded space-times. J. Math. Phys. 45 (2004), 1497–1510. | DOI | MR | Zbl
[33] Lemaître, G.: Un univers homogène de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extra-galactique. Annales Soc. Sc. Bruxelles 47 (1927), 49–59.
[34] O’Neill, B.: Semi-Riemannian geometry, with applications to relativity. Acad. Press, New York 1983. | MR
[35] Helmholtz, H. von: Ueber die Tatsachen welche der Geometrie zu Grunde liegen. In Abhandlungen zur Philosophie und Geometrie, Junghaus, Cuxhausen 1987.
[36] Riemann, B.: Ueber die Hypothesen welche der Geometrie zu Grunde liegen. In Gaussche Flächentheorie, Riemannsche Räume und Minkowski-Welt, Teubner, Leipzig 1984.