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Results for criterions: Parution: n° 174, Summer 2006 Modify search criterions 4 matches Title Azar game in the book of the dice of Alfonso X the learned. Its relation with the hazard games of Montmort, Cotton, Hoyle, De Moivre and Jacob Bernoulli Author BASULTO Jesùs, CAMUNEZ Jose-Antonio, ORTEGA Francisco-Javier Keywords Alfonso X The Learned, Craps Game of De Moivre, Game of "Azar", Hazard Game of Montmort Topics Game Theory, History of Mathematics, Probabilities Abstract A game called «Azar» is presented in the second part of the Book «The Book of Chess, Dice and Tables» by Alfonso X El Sabio (The Learned) (1221-1284). The rules of this Azar game depend on two events called «chance» and «azar». The winning probability in this Azar game implies an event whose probability depends on an infinite number of three-dice rolls. We intend to demonstrate here that this probability is of around 50 %. We associated this game with other games, like the Hazard game by Montmort, Cotton, Hoyle and De Moivre, and also with the Cinq et Neuf game of J. Bernoulli. Finally, we see that the first Hazard game of De Moivre is the famous Craps game. Number 174, Summer 2006 Language  English Read the article Title Henri-Auguste Delannoy, a biography [first part] Author SCHWER Sylviane, AUTEBERT Jean-Michel Keywords Biography, History of combinatorics Topics Arithmetic - Number Theory, Biography, Combinatorics, Game Theory, History of Mathematics Abstract The works of the mathematician Delannoy (1833-1915) which had sunk into oblivion have aroused a keen interest recently, because of the many objects which are counted by the sequences associated with his name. Indeed, these sequences emerged in works as varied as the representation and the space-time reasoning in data processing and linguistics, biology or theoretical physics. We propose here to pay tribute to this ignored mathematician. His carreer, although modest, informs us about the mathematical community at the end of the XIXth century. In this first article we present the known elements of his life, in particular of his activity as a mathematician. We provide in particular a complete review of his publications. In an appendix, the reader will find the description of the mathematical library bequeathed by Delannoy to the public library of Guéret and what has become of it. In a second article, we will analyse his major contribution thoroughly: the use of the arithmetic chess-boards in the resolution of combinatory and probabilistic problems and its current applications. Number 174, Summer 2006 Language   French Read the article Title Critical analysis of variable (semiotic and formal viewpoints) [second part] Author DESCLES Jean-Pierre, CHEONG Kye-Seop Keywords Algebra, Combinatory logic, Function, Quantification, Semiotics, Variable Topics Combinatorics, Linguistics, Logic, Semiology Abstract For B. Russell «The variable is perhaps the most distinctively mathematical of all notions ; it is certainly also one of the most difficult to understand» (The Principles of Mathematics, 1903). The aim of this paper is to highlight the meaning of variable in different fields of Mathematics: the expression of equations in Algebra with indeterminate entities; the analytical expression of functions in Analysis; the expression of quantification in Logic. We give a historical survey of this notion from Viète and Descartes to Frege's representations of a concept, viewed as a non numerical function, yielding to the modern theory of quantification in first order languages. On one hand, the Peirce's theory of signs, and on the other hand, with Church's functional types, l-calculus «with bound variables» and Curry's combinatory logic «without bound variables», are very useful tools for investigating different kinds of variables in Mathematics, in Logic and in theoretical Computer Sciences. For instance, it was showed that «bound variables» were not semiotic tools necessary to formulate quantification (in Frege's sense) in «classical» Logic. Indeed, a simple quantifier is an operator which applies to a predicate by building a proposition; restricted quantifiers are derived from simple quantifiers by formal combinations with logical connectors (conditional or conjunction operators). We propose to take into account and to formalize, inside the framework of Combinatory Logic with types, (i) the «old logical notions» of «extension / intension»; (ii) determination operations from Port Royal's Logic; (iii) the distinction from the anthropology and cognitive psychology between «typical» and «atypical» instances of a concept, which brings us to define new quantifiers, called «star quantifiers», conceived as determination operators acting on terms. These quantifiers are more adequate than the fregean quantifiers, for a natural languages processing. Thus, we are able to give a conceptual distinction between the meanings of «Whatever» and «Indeterminate», implicitly used in Gentzen's Natural Deduction; thanks to this distinction, we can clarify an apparent «paradox» emerging with the universal quantifier introduction rule. Number 174, Summer 2006 Language   French Read the article Title J.-H. Lambert, "Phénoménologie", trad. G. Fanfalone, Paris, Vrin, 2002, 221 p. Author MARTIN Thierry Keywords None Topics Book review, Epistemology, History of Mathematics, Logic, Probabilities Abstract Book review Number 174, Summer 2006 Language   French Read the article Users rights : The entire journal is licensed under a Creative Commons license