×

Universal natural shapes. (English) Zbl 1120.53300

Starting from curves of Lamé, the authors give a presentation of the curves, surfaces and transformations of Gielis which turned out to describe an enormous variety of shapes of forms (which, from a purely geometrical view, satisfy some natural conditions on their curvatures and which naturally occur in physics, chemistry, biology), and more generally by changing exponents of coefficients in basically just one formula. It is also shown that the physical space-time of Friedmann and Lemaitre are determined by essentially similar geometrical formulae.

MSC:

53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
PDFBibTeX XMLCite