تعاریف، مسائل حل‌شده و حل‌نشده، حدس‌ها و قضایای نظریه اعداد و هندسه

A collection of definitions, questions, and theorems edited by M. L. Perez, such as Smarandache type conjectures, problems, numerical bases, T-numbers, progressions, series, functions, Non-Euclidean geometries, paradoxes (such as Smarandache Sorites Paradox that our visible world is composed by a totality of invisible particles), linguistic tautologies, Smarandache hypothesis that there is no speed barrier in the universe - which has been extended to SRM-theory. A collection of definitions, problems, theorems, and conjectures (edited by Minh Perez) on Smarandache functions, sequences, criteria of primality, constants and series, numerical bases, progressions, partitions, continued fractions, theorems in synthetical geometry, Smarandache non-euclidean geometries, paradoxes and tautologies. Many contributors to the study of Smarandache notions are cited: C. Ashbacher, H. Ibstedt, F. Luca, S. Tabirca, K. Atanassov, J. Sandor, E. Weisstein, R. Stefan, D. Talukdar. Many conjectures and problems have been cheched with computer programs. The last part of the book is dedicated to physics, presenting the Smarandache Sorites Paradox:''Our visible world is composed of a totality of invisible particles; a) An invisible particle does not form a visible object, nor do two invisible particles, three invisible particles, etc. However, at some point, the collection of invisible particles becomes large enough to form a visible object, but there is apparently no definite point where this occurs. b) b) A similar paradox is developed in an opposite direction. It is always possible to remove an atom from an object in such a way that what is left is still a visible object. However, repeating and repeating this process, at some point, the visible object is decomposed so that the left part becomes invisible, but there is no definite point where this occurs''. Also, the well-known Smarandache Hypothesis (1972) that: there is no speed limit in the universe, which is being developed in the Smarandache-Rodrigues-Maiorino theory and has a strong impact in the theory of communication (Leonardo F. D. da Motta).