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The contributions of Hilbert and Dehn to non-archimedean geometries and their impact on the italian school

Cinzia Cerroni (2007)

Revue d'histoire des mathématiques

In this paper we investigate the contribution of Dehn to the development of non-Archimedean geometries. We will see that it is possible to construct some models of non-Archimedean geometries in order to prove the independence of the continuity axiom and we will study the interrelations between Archimedes’ axiom and Legendre’s theorems. Some of these interrelations were also studied by Bonola, who was one of the very few Italian scholars to appreciate Dehn’s work. We will see that, if Archimedes’...

The difference matrices of the classes of a Sharma-Kaushik partition

Bhu Dev Sharma, Norris Sookoo (2004)

Archivum Mathematicum

Sharma-Kaushik partitions have been used to define distances between vectors with n -coordinates. In this paper, “difference matrices” for the partitioning classes have been introduced and investigated. It has been shown that the difference matrices are circulant and that the entries of a product of matrices is an extended intersection number of a distance scheme. The sum of the entries of each row or columns of the product matrix has been obtained. The algebra of matrices generated by the difference...

The distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous planar anisotropic STIT Tessellations

Christoph Thäle (2010)

Commentationes Mathematicae Universitatis Carolinae

A result about the distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous and isotropic random tessellations stable under iteration (STIT tessellations) is extended to the anisotropic case using recent findings from Schreiber/Thäle, Typical geometry, second-order properties and central limit theory for iteration stable tessellations, arXiv:1001.0990 [math.PR] (2010). Moreover a new expression for the values of this probability distribution is presented...

The Friendship Theorem

Karol Pąk (2012)

Formalized Mathematics

In this article we prove the friendship theorem according to the article [1], which states that if a group of people has the property that any pair of persons have exactly one common friend, then there is a universal friend, i.e. a person who is a friend of every other person in the group

The game of End-Nim.

Albert, Michael H., Nowakowski, Richard J. (2001)

The Electronic Journal of Combinatorics [electronic only]

The geometry of non-unit Pisot substitutions

Milton Minervino, Jörg Thuswaldner (2014)

Annales de l’institut Fourier

It is known that with a non-unit Pisot substitution σ one can associate certain fractal tiles, so-called Rauzy fractals. In our setting, these fractals are subsets of a certain open subring of the adèle ring of the associated Pisot number field. We present several approaches on how to define Rauzy fractals and discuss the relations between them. In particular, we consider Rauzy fractals as the natural geometric objects of certain numeration systems, in terms of the dual of the one-dimensional realization...

Currently displaying 961 – 980 of 1135