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Smarandache Theorem In Hyperbolic Geometry
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Book Synopsis Smarandache Theorem in Hyperbolic Geometry by : A.V. Kostin
Download or read book Smarandache Theorem in Hyperbolic Geometry written by A.V. Kostin and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper a hyperbolic version of the Smarandache pedal polygon theorem is considered.
Book Synopsis Smarandache Multi-Space Theory by : Linfan Mao
Download or read book Smarandache Multi-Space Theory written by Linfan Mao and published by Infinite Study. This book was released on 2006-01-01 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Smarandache multi-space is a union of n various spaces equipped with different structures for an integer n ¡Ý 2, which can be both used for discrete or connected spaces, particularly for geometries and space-times in theoretical physics. This monograph concentrates on characterizing various multi-spaces and includes three parts. The first part is on algebraic multi-spaces, with structures such as those of multi-groups, multi-rings, multi-vector spaces, multi-metric spaces, multi-operation systems and multi-manifolds, also multi-voltage graphs, multi-embedding of a graph in an n-manifold, etc. The second discusses Smarandache geometries, including those of map geometries, planar map geometries, and pseudo-plane geometries, in which the Finsler geometry, particularly the Riemann geometry appears as a special case of the Smarandache geometries. The third part of this book considers applications of multi-spaces to theoretical physics, including relativity theory, M-theory, and cosmology. Multi-space models for p-branes and cosmos are constructed and some questions in cosmology are clarified by multi-spaces. The first two parts are relatively independent for reading and in each part open problems are included for further research of interested readers.
Book Synopsis Analytic Hyperbolic Geometry in N Dimensions by : Abraham Albert Ungar
Download or read book Analytic Hyperbolic Geometry in N Dimensions written by Abraham Albert Ungar and published by CRC Press. This book was released on 2014-12-17 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author’s gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her book, and elsewhere, that the computation language of Einstein described in this book plays a universal computational role, which extends far beyond the domain of special relativity. This book will encourage researchers to use the author’s novel techniques to formulate their own results. The book provides new mathematical tools, such as hyperbolic simplexes, for the study of hyperbolic geometry in n dimensions. It also presents a new look at Einstein’s special relativity theory.
Book Synopsis Smarandache Geometries & Map Theories with Applications (I) [English and Chinese] by : Linfan Mao
Download or read book Smarandache Geometries & Map Theories with Applications (I) [English and Chinese] written by Linfan Mao and published by Infinite Study. This book was released on 2007 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 800x600 Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} Smarandache Geometries as generalizations of Finsler, Riemannian, Weyl, and Kahler Geometries. A Smarandache geometry (SG) is a geometry which has at least one smarandachely denied axiom (1969). An axiom is said smarandachely denied (S-denied) if in the same space the axiom behaves differently (i.e., validated and invalided; or only invalidated but in at least two distinct ways). Thus, as a particular case, Euclidean, Lobachevsky-Bolyai-Gauss, and Riemannian geometries may be united altogether, in the same space, by some SGs. These last geometries can be partially Euclidean and partially non-Euclidean. The novelty of the SG is the fact that they introduce for the first time the degree of negation in geometry, similarly to the degree of falsehood in fuzzy or neutrosophic logic. For example an axiom can be denied in percentage of 30 Also SG are defined on multispaces, i.e. unions of Euclidean and non-Euclidean subspaces, or unions of distinct non-Euclidean spaces. As an example of S-denying, a proposition , which is the conjunction of a set i of propositions, can be invalidated in many ways if it is minimally unsatisfiable, that is, such that the conjunction of any proper subset of the i is satisfied in a structure, but itself is not. Here it is an example of what it means for an axiom to be invalidated in multiple ways [2] : As a particular axiom let's take Euclid's Fifth Postulate. In Euclidean or parabolic geometry a line has one parallel only through a given point. In Lobacevskian or hyperbolic geometry a line has at least two parallels through a given point. In Riemannian or elliptic geometry a line has no parallel through a given point. Whereas in Smarandache geometries there are lines which have no parallels through a given point and other lines which have one or more parallels through a given point (the fifth postulate is invalidated in many ways). Therefore, the Euclid's Fifth Postulate (which asserts that there is only one parallel passing through an exterior point to a given line) can be invalidated in many ways, i.e. Smarandachely denied, as follows: - first invalidation: there is no parallel passing through an exterior point to a given line; - second invalidation: there is a finite number of parallels passing through an exterior point to a given line; - third invalidation: there are infinitely many parallels passing through an exterior point to a given line.
Book Synopsis Applications of NeutroGeometry and AntiGeometry in Real World by : Erick González-Caballero
Download or read book Applications of NeutroGeometry and AntiGeometry in Real World written by Erick González-Caballero and published by Infinite Study. This book was released on 2023-01-01 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: NeutroGeometries are those geometric structures where at least one definition, axiom, property, theorem, among others, is only partially satisfied. In AntiGeometries at least one of these concepts is never satisfied. Smarandache Geometry is a geometric structure where at least one axiom or theorem behaves differently in the same space, either partially true and partially false, or totally false but its negation done in many ways. This paper offers examples in images of nature, everyday objects, and celestial bodies where the existence of Smarandechean or NeutroGeometric structures in our universe is revealed. On the other hand, a practical study of surfaces with characteristics of NeutroGeometry is carried out, based on the properties or more specifically NeutroProperties of the famous quadrilaterals of Saccheri and Lambert on these surfaces. The article contributes to demonstrating the importance of building a theory such as NeutroGeometries or Smarandache Geometries because it would allow us to study geometric structures where the well-known Euclidean, Hyperbolic or Elliptic geometries are not enough to capture properties of elements that are part of the universe, but they have sense only within a NeutroGeometric framework. It also offers an axiomatic option to the Riemannian idea of Two-Dimensional Manifolds. In turn, we prove some properties of the NeutroGeometries and the materialization of the symmetric triad , , and .
Book Synopsis Smarandache Notions, Vol. 14 by : W. B. Vasantha Kandasamy
Download or read book Smarandache Notions, Vol. 14 written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2004-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers concerning any of the Smarandache type functions, sequences, numbers, algorithms, inferior/superior f-parts, magic squares, palindromes, functional iterations, semantic paradoxes, Non-Euclidean geometries, manifolds, conjectures, open problems, algebraic structures, neutrosophy, neutrosophic logic/set/probability, hypothesis that there is no speed barrier in the universe, quantum paradoxes, etc. have been selected for this volume. Contributors are from Australia, China, England, Germany, India, Ireland, Israel, Italy, Japan, Malaysia, Morocco, Portugal, Romania, Spain, USA. Most of the papers are in English, a few of them are in Spanish, Portuguese, or German.
Book Synopsis Graduate Textbook of Mathematics: Smarandache Multi-Space Theory (second edition) by : Linfan Mao
Download or read book Graduate Textbook of Mathematics: Smarandache Multi-Space Theory (second edition) written by Linfan Mao and published by Infinite Study. This book was released on 2011-01-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Smarandache multi-space is a union of n different spaces equippedwith different structures for an integer n 2, which can be used for systems both innature or human beings. This textbook introduces Smarandache multi-spaces such asthose of algebraic multi-spaces, including graph multi-spaces, multi-groups, multi-rings,multi-fields, vector multi-spaces, geometrical multi-spaces, particularly map geometrywith or without boundary, pseudo-Euclidean geometry on Rn, combinatorial Euclideanspaces, combinatorial manifolds, topological groups and topological multi-groups, combinatorialmetric spaces, ¿ ¿ ¿, etc. and applications of Smarandache multi-spaces, particularlyto physics, economy and epidemiology. In fact, Smarandache multi-spacesunderlying graphs are an important systematically notion for scientific research in 21stcentury. This book can be applicable for graduate students in combinatorics, topologicalgraphs, Smarandache geometry, physics and macro-economy as a textbook.
Book Synopsis Smarandache Function Journal, vol. 14/2004 by : Sabin Tabirca
Download or read book Smarandache Function Journal, vol. 14/2004 written by Sabin Tabirca and published by Infinite Study. This book was released on with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
Book Synopsis Combinatorial Geometry with Applications to Field Theory, Second Edition, graduate textbook in mathematics by : Linfan Mao
Download or read book Combinatorial Geometry with Applications to Field Theory, Second Edition, graduate textbook in mathematics written by Linfan Mao and published by Infinite Study. This book was released on 2011 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Progress in Physics, vol. 1/2011 by : Dmitri Rabounski
Download or read book Progress in Physics, vol. 1/2011 written by Dmitri Rabounski and published by Infinite Study. This book was released on with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics
Book Synopsis International Journal of Mathematical Combinatorics, Volume 1, 2010 by : Linfan Mao
Download or read book International Journal of Mathematical Combinatorics, Volume 1, 2010 written by Linfan Mao and published by Infinite Study. This book was released on with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.
Book Synopsis Scientia Magna Vol. 6, No. 1, 2010 by : Zhang Wenpeng
Download or read book Scientia Magna Vol. 6, No. 1, 2010 written by Zhang Wenpeng and published by Infinite Study. This book was released on 2010 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on Smarandache¿s codification used in computer programming, smarandacheials, totient and congruence functions, sequences, irrational constants in number theory, multi-space and geometries.
Book Synopsis Progress in Physics, vol. 3/2010 by : Dmitri Rabounski
Download or read book Progress in Physics, vol. 3/2010 written by Dmitri Rabounski and published by Infinite Study. This book was released on with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics.
Book Synopsis Smarandache Manifolds by : Howard Iseri
Download or read book Smarandache Manifolds written by Howard Iseri and published by Infinite Study. This book was released on 2002 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Collected Papers. Volume V by : Florentin Smarandache
Download or read book Collected Papers. Volume V written by Florentin Smarandache and published by Infinite Study. This book was released on 2014-10-14 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volum includes 37 papers of mathematics or applied mathematics written by the author alone or in collaboration.They were written during the years 2010-2014, about the hyperbolic Menelaus theorem in the Poincare disc of hyperbolic geometry, and the Menelaus theorem for quadrilaterals inhyperbolic geometry, about some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles, etc.
Book Synopsis Essays in Mathematics and its Applications by : Themistocles M. Rassias
Download or read book Essays in Mathematics and its Applications written by Themistocles M. Rassias and published by Springer. This book was released on 2016-06-14 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a collection of research and survey papers written on a large spectrum of theories and problems that have been studied or introduced by Arnold himself. Emphasis is given to topics relating to dynamical systems, stability of integrable systems, algebraic and differential topology, global analysis, singularity theory and classical mechanics. A number of applications of Arnold’s groundbreaking work are presented. This publication will assist graduate students and research mathematicians in acquiring an in-depth understanding and insight into a wide domain of research of an interdisciplinary nature.
Book Synopsis Critics and alternative theories by : Nikolay Chavarga
Download or read book Critics and alternative theories written by Nikolay Chavarga and published by Infinite Study. This book was released on with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The word “dissident” is used in a broad sense. It includes scientists proposing not fully accepted ideas within the Relativity-Quantum Mechanics paradigm as well as opponents to some aspects of these theories.
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