NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries (revisited) PDF Download
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Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 22
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Book Description
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.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 22
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Book Description
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.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Antiques & Collectibles
Languages : en
Pages :
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Book Description
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.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Antiques & Collectibles
Languages : en
Pages : 487
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Book Description
Papers on neutrosophic programming, neutrosophic hypersoft set, neutrosophic topological spaces, NeutroAlgebra, NeutroGeometry, AntiGeometry, NeutroNearRings, neutrosophic differential equations, etc.
Author: Erick Gonzalez-Caballero
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 19
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Book Description
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
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Author: Smarandache, Florentin
Publisher: IGI Global
ISBN: 1668447428
Category : Mathematics
Languages : en
Pages : 280
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Book Description
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.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 8
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Book Description
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.
Author: Smarandache, Florentin
Publisher: IGI Global
ISBN: 1668434970
Category : Mathematics
Languages : en
Pages : 333
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Book Description
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.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 1008
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Book Description
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.
Author: MIRCEA E. SELARIU
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 14
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Book Description
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.
Author: Florentin Smarandache