Universal natural shapes

Johan Gielis ; Stefan Haesen ; Leopold Verstraelen

Kragujevac Journal of Mathematics, Tome 28 (2005) no. 1.

Résumé

UNIVERSAL NATURAL SHAPESFrom the supereggs of Piet Hein to the cosmic egg of Georges LemaîtreJohan Gielis1, Stefan Haesen2 and Leopold Verstraelen21 Genicap Co. N.V., Lange Van Ruusbroeckstraat 116, B2018, Antwerpen, Belgium 2 K.U. Leuven Section Of Geometry, Celestijnenlaan 200B,B3001 Leuven (Heverlee), Belgium From the Introduction and the Epilogue of d'Arcy Thompson's ''On Growth and Form'' [7], respectively, we quote the following: ''The search for differences or fundamental contrasts between the phenomena of organic or inorganic, of animate or inanimate things, has occupied many men's minds, while the search for community of principles or essential similitudes has been pursued by few; ... things animate and inanimate, we dwellers in the world and this world wherein we dwell are bound alike by physical and mathematical law''.We aim to show that honeycombs and shells, crystals and galaxies, DNA-molecules and flowers, stems, tissues and pollen grains of plants, etc. and the relativistic space-time universe itself, in accordance with similar natural curvature conditions, all do assume shapes with similar geometrical formal descriptions.