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Geodesies on typical convex surfaces

Peter Manfred Gruber (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Using Baire categories uniqueness of geodesic segments and existence of closed geodesics on typical convex surfaces are investigated.

Geometric and combinatorial structure of a class of spherical folding tessellations – I

Catarina P. Avelino, Altino F. Santos (2017)

Czechoslovak Mathematical Journal

A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tessellations of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle. Within two possible cases of adjacency, only one will be addressed....

Geometric probabilities for non convex lattices. II

Andrei Duma, Marius Stoka (2002)

Bollettino dell'Unione Matematica Italiana

We solve problems of Buffon type for a lattice with elementary tile a nonconvex polygon, using as test bodies a line sigment and a circle.

Geometric study of the beta-integers for a Perron number and mathematical quasicrystals

Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry (2004)

Journal de Théorie des Nombres de Bordeaux

We investigate in a geometrical way the point sets of     obtained by the   β -numeration that are the   β -integers   β [ β ]   where   β   is a Perron number. We show that there exist two canonical cut-and-project schemes associated with the   β -numeration, allowing to lift up the   β -integers to some points of the lattice   m   ( m =   degree of   β ) lying about the dominant eigenspace of the companion matrix of   β  . When   β   is in particular a Pisot number, this framework gives another proof of the fact that   β   is...

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