Neutrogeometry Antigeometry Are Alternatives And Generalizations Of The Non Euclidean Geometries Revisited

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NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries (revisited)

Florentin Smarandache
NeutroGeometry AntiGeometry are alternatives and generalizations of the Non Euclidean Geometries revisited Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 22 pages
File Size : 45,8 Mb
Release : 2021-10-01
Category : Mathematics
ISBN : 8210379456XXX

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NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries (revisited) by Florentin Smarandache Pdf

In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry. While the Non-Euclidean Geometries resulted from the total negation of one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom or even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.) and from any type of geometry such as (Euclidean, Projective, Finite, Affine, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.) Geometry, and the NeutroGeometry results from the partial negation of one or more axioms [and no total negation of no axiom] from any geometric axiomatic system and from any type of geometry. Generally, instead of a classical geometric Axiom, one may take any classical geometric Theorem from any axiomatic system and from any type of geometry, and transform it by NeutroSophication or AntiSophication into a NeutroTheorem or AntiTheorem respectively in order to construct a NeutroGeometry or AntiGeometry. Therefore, the NeutroGeometry and AntiGeometry are respectively alternatives and generalizations of the Non-Euclidean Geometries. In the second part, we recall the evolution from Paradoxism to Neutrosophy, then to NeutroAlgebra & AntiAlgebra, afterwards to NeutroGeometry & AntiGeometry, and in general to NeutroStructure & AntiStructure that naturally arise in any field of knowledge. At the end, we present applications of many NeutroStructures in our real world.

NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries

Florentin Smarandache
NeutroGeometry AntiGeometry are alternatives and generalizations of the Non Euclidean Geometries Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 47,9 Mb
Release : 2024-06-25
Category : Antiques & Collectibles
ISBN : 8210379456XXX

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NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries by Florentin Smarandache Pdf

In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric space, by founding the NeutroGeometry & AntiGeometry. While the Non-Euclidean Geometries resulted from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom and even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.), and the NeutroAxiom results from the partial negation of one or more axioms [and no total negation of no axiom] from any geometric axiomatic system. Therefore, the NeutroGeometry and AntiGeometry are respectively alternatives and generalizations of the Non-Euclidean Geometries. In the second part, we recall the evolution from Paradoxism to Neutrosophy, then to NeutroAlgebra & AntiAlgebra, afterwards to NeutroGeometry & AntiGeometry, and in general to NeutroStructure & AntiStructure that naturally arise in any field of knowledge. At the end, we present applications of many NeutroStructures in our real world.

Neutrosophic Sets and Systems, Vol. 46, 2021

Florentin Smarandache,Mohamed Abdel-Basser,Said Broumi
Neutrosophic Sets and Systems Vol 46 2021 Book PDF

Author : Florentin Smarandache,Mohamed Abdel-Basser,Said Broumi
Publisher : Infinite Study
Page : 487 pages
File Size : 41,5 Mb
Release : 2021-10-19
Category : Antiques & Collectibles
ISBN : 8210379456XXX

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Neutrosophic Sets and Systems, Vol. 46, 2021 by Florentin Smarandache,Mohamed Abdel-Basser,Said Broumi Pdf

Papers on neutrosophic programming, neutrosophic hypersoft set, neutrosophic topological spaces, NeutroAlgebra, NeutroGeometry, AntiGeometry, NeutroNearRings, neutrosophic differential equations, etc.

Applications of NeutroGeometry and AntiGeometry in Real World

Erick Gonzalez-Caballero
Applications of NeutroGeometry and AntiGeometry in Real World Book PDF

Author : Erick Gonzalez-Caballero
Publisher : Infinite Study
Page : 19 pages
File Size : 44,9 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 8210379456XXX

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Applications of NeutroGeometry and AntiGeometry in Real World by Erick Gonzalez-Caballero Pdf

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 ,

NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World

Smarandache, Florentin,Al Tahan, Madeline
NeutroGeometry NeutroAlgebra and SuperHyperAlgebra in Today s World Book PDF

Author : Smarandache, Florentin,Al Tahan, Madeline
Publisher : IGI Global
Page : 280 pages
File Size : 43,9 Mb
Release : 2023-05-15
Category : Mathematics
ISBN : 9781668447420

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NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World by Smarandache, Florentin,Al Tahan, Madeline Pdf

NeutroAlgebra and AntiAlgebra were extended to NeutroGeometry and AntiGeometry in order to catch the Non-Euclidean Geometries. In the real world, the spaces and the elements that populate them and the rules that apply to them are not perfect, uniform, homogeneous, or complete. They are fragmentary and disparate, with unclear and conflicting information, and they do not apply in the same degree to each element. Therefore, these partial, hybrid, and mixed structures are necessary. NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World presents applications of many NeutroStructures in our real world and considers NeutroGeometry and AntiGeometry as new fields of research that resemble everyday life. Covering key topics such as hyperbolic geometry, elliptic geometry, and AntiGeometry, this reference work is ideal for mathematicians, industry professionals, researchers, scholars, academicians, practitioners, instructors, and students.

Real Examples of NeutroGeometry & AntiGeometry

Florentin Smarandache
Real Examples of NeutroGeometry AntiGeometry Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 8 pages
File Size : 46,9 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 8210379456XXX

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Real Examples of NeutroGeometry & AntiGeometry by Florentin Smarandache Pdf

For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only partially true (and partially indeterminate, and partially false), and no item that is totally false. The AntiGeometry is a geometrical space that has some item that are totally (100%) false. While the Non-Euclidean Geometries [hyperbolic and elliptic geometries] resulted from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom [and in general: theorem, concept, idea etc.] and even of more axioms [theorem, concept, idea, etc.] and in general from any geometric axiomatic system (Euclid’s five postulates, Hilbert’s 20 axioms, etc.), and the NeutroAxiom results from the partial negation of any axiom (or concept, theorem, idea, etc.). Clearly, the AntiGeometry is a generalization of Non-Euclidean Geometries.

Neutrosophic Sets and Systems, vol. 52/2022

Florentin Smarandache,Mohamed Abdel-Basset,Maikel Leyva Vazquez,Said Broumi
Neutrosophic Sets and Systems vol 52 2022 Book PDF

Author : Florentin Smarandache,Mohamed Abdel-Basset,Maikel Leyva Vazquez,Said Broumi
Publisher : Infinite Study
Page : 420 pages
File Size : 55,8 Mb
Release : 2022-11-01
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Sets and Systems, vol. 52/2022 by Florentin Smarandache,Mohamed Abdel-Basset,Maikel Leyva Vazquez,Said Broumi Pdf

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).

Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras

Smarandache, Florentin,Al-Tahan, Madeline
Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras Book PDF

Author : Smarandache, Florentin,Al-Tahan, Madeline
Publisher : IGI Global
Page : 333 pages
File Size : 47,6 Mb
Release : 2022-04-15
Category : Mathematics
ISBN : 9781668434970

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Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras by Smarandache, Florentin,Al-Tahan, Madeline Pdf

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are well-defined, but this is a restrictive case because there are situations in science where a law of composition defined on a set may be only partially defined and partially undefined, which we call NeutroDefined, or totally undefined, which we call AntiDefined. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebra introduces NeutroAlgebra, an emerging field of research. This book provides a comprehensive collection of original work related to NeutroAlgebra and covers topics such as image retrieval, mathematical morphology, and NeutroAlgebraic structure. It is an essential resource for philosophers, mathematicians, researchers, educators and students of higher education, and academicians.

Collected Papers. Volume IX

Florentin Smarandache
Collected Papers Volume IX Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 1008 pages
File Size : 41,7 Mb
Release : 2022-05-10
Category : Mathematics
ISBN : 8210379456XXX

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Collected Papers. Volume IX by Florentin Smarandache Pdf

This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, T. Gharibah, Hina Gulzar, Hashem Bordbar, Le Hoang Son, Emmanuel Ilojide, Tèmítópé Gbóláhàn Jaíyéolá, M. Karthika, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Huma Khan, Madad Khan, Mohsin Khan, Hee Sik Kim, Seon Jeong Kim, Valeri Kromov, R. M. Latif, Madeleine Al-Tahan, Mehmat Ali Ozturk, Minghao Hu, S. Mirvakili, Mohammad Abobala, Mohammad Hamidi, Mohammed Abdel-Sattar, Mohammed A. Al Shumrani, Mohamed Talea, Muhammad Akram, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Gulistan, Muhammad Shabir, G. Muhiuddin, Memudu Olaposi Olatinwo, Osman Anis, Choonkil Park, M. Parimala, Ping Li, K. Porselvi, D. Preethi, S. Rajareega, N. Rajesh, Udhayakumar Ramalingam, Riad K. Al-Hamido, Yaser Saber, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, A.A. Salama, Ganeshsree Selvachandran, Songtao Shao, Seok-Zun Song, Tahsin Oner, M. Mohseni Takallo, Binod Chandra Tripathy, Tugce Katican, J. Vimala, Xiaohong Zhang, Xiaoyan Mao, Xiaoying Wu, Xingliang Liang, Xin Zhou, Yingcang Ma, Young Bae Jun, Juanjuan Zhang.

CARDINAL FUNCTIONS AND INTEGRAL FUNCTIONS

MIRCEA E. SELARIU, FLORENTIN SMARANDACHE ,MARIAN NITU
CARDINAL FUNCTIONS AND INTEGRAL FUNCTIONS Book PDF

Author : MIRCEA E. SELARIU, FLORENTIN SMARANDACHE ,MARIAN NITU
Publisher : Infinite Study
Page : 14 pages
File Size : 42,7 Mb
Release : 2024-06-25
Category : Mathematics
ISBN : 8210379456XXX

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CARDINAL FUNCTIONS AND INTEGRAL FUNCTIONS by MIRCEA E. SELARIU, FLORENTIN SMARANDACHE ,MARIAN NITU Pdf

This paper presents the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics, or ordinary mathematics. Centric functions will also be presented in the introductory section, because they are, although widely used in undulatory physics, little known.

Introduction to the Division by Zero Calculus

SABUROU SAITOH
Introduction to the Division by Zero Calculus Book PDF

Author : SABUROU SAITOH
Publisher : Scientific Research Publishing, Inc. USA
Page : 203 pages
File Size : 43,8 Mb
Release : 2021-02-04
Category : Mathematics
ISBN : 9781649970893

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Introduction to the Division by Zero Calculus by SABUROU SAITOH Pdf

The common sense on the division by zero with the long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on differential coefficients we have a great missing since tan(π/2) = 0. Our mathematics is also wrong in elementary mathematics on the division by zero. In this book in a new and definite sense, we will show and give various applications of the division by zero 0/0 = 1/0 = z/0 = 0. In particular, we will introduce several fundamental concepts in calculus, Euclidean geometry, analytic geometry, complex analysis and differential equations. We will see new properties on the Laurent expansion, singularity, derivative, extension of solutions of differential equations beyond analytical and isolated singularities, and reduction problems of differential equations. On Euclidean geometry and analytic geometry, we will find new fields by the concept of the division by zero. We will collect many concrete properties in mathematical sciences from the viewpoint of the division by zero. We will know that the division by zero is our elementary and fundamental mathematics.

The History of Continua

Stewart Shapiro,Geoffrey Hellman
The History of Continua Book PDF

Author : Stewart Shapiro,Geoffrey Hellman
Publisher : Oxford University Press, USA
Page : 593 pages
File Size : 53,6 Mb
Release : 2021
Category : Mathematics
ISBN : 9780198809647

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The History of Continua by Stewart Shapiro,Geoffrey Hellman Pdf

Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.

Varieties of Continua

Geoffrey Hellman,Stewart Shapiro
Varieties of Continua Book PDF

Author : Geoffrey Hellman,Stewart Shapiro
Publisher : Oxford University Press
Page : 224 pages
File Size : 53,8 Mb
Release : 2018-02-02
Category : Philosophy
ISBN : 9780191021350

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Varieties of Continua by Geoffrey Hellman,Stewart Shapiro Pdf

Varieties of Continua explores the development of the idea of the continuous. Hellman and Shapiro begin with two historical episodes. The first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view, that a true continuum cannot be composed of points, to the now standard, point-based frameworks for analysis and geometry found in modern mainstream mathematics (stemming from the work of Bolzano, Cauchy, Weierstrass, Dedekind, Cantor, et al.). The second is the mid-tolate-twentieth century revival of pre-limit methods in analysis and geometry using infinitesimals including non-standard analysis (due to Abraham Robinson), and the more radical smooth infinitesimal analysis that uses intuitionistic logic. Hellman and Shapiro present a systematic comparison of these and related alternatives (including constructivist and predicative conceptions), weighing various trade-offs, helping articulate a modern pluralist perspective, and articulate a modern pluralist perspective on continuity. The main creative work of the book is the development of rigorous regions-based theories of classical continua, including Euclidean and non-Euclidean geometries, that are mathematically equivalent (inter-reducible) to the currently standard, point-based accounts in mainstream mathematics.

Research in History and Philosophy of Mathematics

Maria Zack,Dirk Schlimm
Research in History and Philosophy of Mathematics Book PDF

Author : Maria Zack,Dirk Schlimm
Publisher : Birkhäuser
Page : 218 pages
File Size : 45,9 Mb
Release : 2017-12-18
Category : Mathematics
ISBN : 9783319645513

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Research in History and Philosophy of Mathematics by Maria Zack,Dirk Schlimm Pdf

This volume contains fourteen papers that were presented at the 2016 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held at the University of Calgary in Alberta, Canada. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics, this meeting also honored the life and work of the logician and philosopher of mathematics Aldo Antonelli (1962-2015). The first four papers in this book are part of that remembrance and have a philosophical focus. Included in these are a discussion of Bolzano’s objections to Kant’s philosophy of mathematics and an examination of the influence of rhetorical and poetic aesthetics on the development of symbols in the 16th and 17th Centuries. The remaining papers deal with the history of mathematics and cover such subjects as Early schemes for polar ordinates in the work of L’Hôpital, based on lessons given to him by Bernoulli A method devised by Euler for determining if a number is a sum of two squares Playfair’s Axiom and what it reveals about the history of 19th-Century mathematics education The modern library classification system for mathematical subjects An exploration of various examples of sundials throughout Paris Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.

Space, Number, and Geometry from Helmholtz to Cassirer

Francesca Biagioli
Space Number and Geometry from Helmholtz to Cassirer Book PDF

Author : Francesca Biagioli
Publisher : Springer
Page : 239 pages
File Size : 40,8 Mb
Release : 2016-08-22
Category : Philosophy
ISBN : 9783319317793

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Space, Number, and Geometry from Helmholtz to Cassirer by Francesca Biagioli Pdf

This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such later scientific developments as non-Euclidean geometries and Einstein’s general theory of relativity called into question the certainty of Euclidean geometry and posed the problem of reconsidering space as an open question for empirical research. The transformation of the concept of space from a source of knowledge to an object of research can be traced back to a tradition, which includes such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtz’s epistemological works. Although Helmholtz formulated compelling objections to Kant, the author reconsiders different strategies for a philosophical account of the same transformation from a neo-Kantian perspective, and especially Hermann Cohen’s account of the aprioricity of mathematics in terms of applicability and Ernst Cassirer’s reformulation of the a priori of space in terms of a system of hypotheses. This book is ideal for students, scholars and researchers who wish to broaden their knowledge of non-Euclidean geometry or neo-Kantianism.