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Journal articles on the topic 'Geometrı́a moderna'
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LORENAT, JEMMA. "CERTAIN MODERN IDEAS AND METHODS: “GEOMETRIC REALITY” IN THE MATHEMATICS OF CHARLOTTE ANGAS SCOTT." Review of Symbolic Logic 13, no. 4 (2019): 681–719. http://dx.doi.org/10.1017/s1755020319000066.
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AbstractCharlotte Angas Scott (1858–1932) was an internationally renowned geometer, the first British woman to earn a doctorate in mathematics, and the chair of the Bryn Mawr mathematics department for forty years. There she helped shape the burgeoning mathematics community in the United States. Scott often motivated her research as providing a “geometric treatment” of results that had previously been derived algebraically. The adjective “geometric” likely entailed many things for Scott, from her careful illustration of diagrams to her choice of references and citations. This article will focus on Scott’s striking and consistent use of geometric to describe a reality of dynamic points, lines, planes, and spaces that could be manipulated analogously to physical objects. By providing geometric interpretations of algebraic derivations, Scott committed to an early-nineteenth-century aesthetic vision of a “whole” analytical geometry that she adapted to modern research areas.
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García Olea, Alberto José, and Óscar López Zaldívar. "La geometría moderna de Boullée frente a la geometría clásica de Kahn: Una contradicción aparente = Boullée's modern geometry versus Kahn's classical geometry: An apparent contradiction." Anales de Edificación 6, no. 1 (2020): 1. http://dx.doi.org/10.20868/ade.2020.4449.
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Arifjonovich, Isakov Jasurbek. "MODERN REQUIREMENTS FOR TEACHING DESCRIPTIVE GEOMETRY AND PERSPECTIVES." International Journal of Pedagogics 4, no. 12 (2024): 55–61. https://doi.org/10.37547/ijp/volume04issue12-11.
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In this article, it can be seen from the fields of professional activity that currently there is not a single industry that computer technology has not penetrated. So, in order to produce a creatively thinking specialist who meets the requirements of the time, we first of all set one of the most urgent tasks for teachers -the formation of the ability of a mature expert in his field to apply computer technology on all fronts of his activity. Teaching geometry and perspective drawing highlights the advantages of computer-generated drawings, along with quality, accuracy and ease of use in the production process.
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Gîrban, Alexandru, and Bogdan D. Suceavǎ. "Power of a point: from Jakob Steiner to modern applications." Mathematical Gazette 106, no. 565 (2022): 41–53. http://dx.doi.org/10.1017/mag.2022.8.
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"What should we use?" seems to be the question when one approaches a plane geometry problem. In many ways, Euclidean geometry is a laboratory in the realm of logic, an ideal place where one can see how alternative methods can be employed to solve problems. What detail might represent a hint? And from among many choices, what method could one consider? Does the geometric structure suggest a certain type of approach?
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Tulkinovna, Ismoilova Mahmuda. "METHODS OF CONSTRUCTION AND DESIGN OF MODERN BUILDINGS USING THE HAYTEK METHOD." European International Journal of Multidisciplinary Research and Management Studies 02, no. 04 (2022): 216–22. http://dx.doi.org/10.55640/eijmrms-02-04-39.
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A variety of high technologies for the organization of accommodation allow you to build a house that combines original decoration and high functionality. Modern cottages in a high-tech style are distinguished by strict and unique geometry, laconic decor and an abundance of sunlight. Classic high-tech summer house: a combination of solid geometric shapes and large windows with a flat roof. High-tech style house - this opportunity allows you to create a comfortable and economical home.
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Posamentier, Alfred S. "Delving Deeper: Trisecting the Circle: A Case for Euclidean Geometry." Mathematics Teacher 99, no. 6 (2006): 414–18. http://dx.doi.org/10.5951/mt.99.6.0414.
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As an undergraduate mathematics major, a prospective teacher usually takes at least one geometry course. Typically, these courses focus on non–Euclidean geometry (sometimes presented as Modern Geometry), or vectors, transformations, or topology. Instead, we at the City College of New York offer a course on more advanced Euclidean geometry in which prospective teachers investigate a plethora of geometric theorems (or relationships) that enrich their understanding of Euclidean geometry and, consequently, their teaching of it.
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Magis Weinberg, Carolina. "Vicente Rojo, un diluvio geométrico." Intervención 2, no. 26 (2023): 222–43. http://dx.doi.org/10.30763/intervencion.275.v2n26.54.2022.
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La exposición en el Museo de Arte Moderno (MAM) Vicente Rojo: la destrucción del orden es un homenaje a la trayectoria del artista. En ella se presentan sus sistemas de trabajo a lo largo de seis décadas desde el mundo del arte en la dimensión pictórica, escultórica, del libro y de la acción. Destaca la presentación de su obra en series, lo que subraya en su manera de crear, proponiendo una subestructura geométrica que permite una visión del orden dentro de las múltiples facetas de este gran artista. _____________ The exhibition Vicente Rojo: la destrucción del orden (Vicente Rojo: the destruction of order) at the Modern Art Museum’s exhibition (MAM, Museo de Arte Moderno) is a tribute to the artist’s trajectory. The exhibition presents his work systems throughout six decades in the world of art within the dimensions of images, sculptures, books and action. One highlight of the exhibition is presenting his work in series, which underlines his way of creating by proposing a geometric substructure that allows a knowledge within the multiple sides of this great artist.
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Maißer, P. "Multi-body dynamics and electromechanics: From a differential-geometric point of view." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 219, no. 2 (2005): 147–58. http://dx.doi.org/10.1243/146441905x34135.
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Mechanics is the origin of physics. Almost any physical theory like electrodynamics stems from mechanical explanations. The mathematical-geometric considerations in mechanics serve as a prototype for other physical theories. Consequently, developments in modern physics in turn have a feedback to mechanics in terms of its representation. The laws of nature can be expressed as differential equations. The fact that these equations can be solved by average computers has led most engineers and many mathematical physicists to neglect geometrical aspects for solving and better understanding their problems. The intimate relation between geometry and analysis led to the differential geometry, which is a valuable tool for a better understanding in many physical disciplines like classical mechanics, electrodynamics, and nowadays in mechatronics. It has been the development of the theory of relativity that revealed the paramount importance of the differential geometry. Many problems in research and development can be studied by differential-geometric methods. Modern non-linear control theories, for instance, are entirely based on the differential geometry. This paper addresses some aspects in mathematical modelling of multi-body and electromechanical systems. The motivation for this research arises from applications of linear induction machines in modern transport technologies.
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Hawryluk, Marek, Marek Kuran, and Jacek Ziemba. "The use of replicas in the measurement of machine elements with use of contact coordinate measurements." Mechanik 91, no. 11 (2018): 958–60. http://dx.doi.org/10.17814/mechanik.2018.11.169.
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Modern technology allows to design and manufacture machine elements with complex geometry that makes it difficult or even impossible to use coordinate measuring machines for verification of them. The article presents the possibility of using replicas of product geometry to control geometric features using contact measurements on a coordinate machine.
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VACARU, SERGIU I. "FINSLER AND LAGRANGE GEOMETRIES IN EINSTEIN AND STRING GRAVITY." International Journal of Geometric Methods in Modern Physics 05, no. 04 (2008): 473–511. http://dx.doi.org/10.1142/s0219887808002898.
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We review the current status of Finsler–Lagrange geometry and generalizations. The goal is to aid non-experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Finsler and Kähler geometry and geometric mechanics how they could perform their results in order to be accepted by the community of "orthodox" physicists. Although the bulk of former models of Finsler–Lagrange spaces where elaborated on tangent bundles, the surprising result advocated in our works is that such locally anisotropic structures can be modeled equivalently on Riemann–Cartan spaces, even as exact solutions in Einstein and/or string gravity, if nonholonomic distributions and moving frames of references are introduced into consideration. We also propose a canonical scheme when geometrical objects on a (pseudo) Riemannian space are nonholonomically deformed into generalized Lagrange, or Finsler, configurations on the same manifold. Such canonical transforms are defined by the coefficients of a prime metric and generate target spaces as Lagrange structures, their models of almost Hermitian/Kähler, or nonholonomic Riemann spaces. Finally, we consider some classes of exact solutions in string and Einstein gravity modeling Lagrange–Finsler structures with solitonic pp-waves and speculate on their physical meaning.
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Tomiczková, Světlana, and Miroslav LáviČka. "Using Dynamic Geometry and Computer Algebra Systems in Problem Based Courses for Future Engineers." International Journal for Technology in Mathematics Education 22, no. 4 (2015): 147–53. http://dx.doi.org/10.1564/tme_v22.4.02.
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It is a modern trend today when formulating the curriculum of a geometric course at the technical universities to start from a real-life problem originated in technical praxis and subsequently to define which geometric theories and which skills are necessary for its solving. Nowadays, interactive and dynamic geometry software plays a more and more important role in this scenario as it helps to think algorithmically, enables to discuss the solvability of the whole class of geometric problems from different point of views and mainly serves as a first step to variational geometry needed later in geometric modelling. This makes the teaching and learning process more efficient and also more interesting for students. In our contribution, we present some particular examples of this approach.
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Kötzer, Stephan. "GEOMETRIC IDENTITIES IN STEREOLOGICAL PARTICLE ANALYSIS." Image Analysis & Stereology 25, no. 2 (2011): 63. http://dx.doi.org/10.5566/ias.v25.p63-74.
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The paper reviews recent findings about geometric identities in integral geometry and geometric tomography, and their statistical application to stereological particle analysis. Open questions are discussed. This survey can also serve as an introduction to modern stereological particle analysis for readers who are interested in the mathematical background of the new methods.
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Abu Elwan, Reda. "The Effect of Teaching "Chaos Theory and Fractal Geometry" on Geometric Reasoning Skills of Secondary Students." INTERNATIONAL JOURNAL OF RESEARCH IN EDUCATION METHODOLOGY 6, no. 2 (2015): 804–15. http://dx.doi.org/10.24297/ijrem.v6i2.3876.
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Chaos theory and fractal geometry have begun to appear as an important issue in secondary school mathematics. Chaos theory is the qualitative study of unstable periods in deterministic nonlinear dynamical systems, chaos theory looks at how things evolve. Fractal geometry is a subject that has established connections with many areas of mathematics (including number theory, probability theory and dynamical systems). Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century; this paper investigate the concepts of chaos theory and fractal geometry as a conceptual transformation at secondary school level. This paper reports a study of the effects of teaching chaos theory and fractal geometry on geometric reasoning skills in geometry. Thirty of the tenth grade students of basic education participated in an experimental group, which was involved in working with chaos theory and fractal geometry activities, pre-treatment measures the geometric Reasoning skills. Teaching fractal geometry properties and examples were focused in the teaching activities. At the end of the teaching measures geometric reasoning skills were again obtained. Since the study was an exploration, the effectiveness of teaching chaos theory and fractal geometry, the exploratory data collected by the researcher was also considered to be an important part of the study.Â
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Banionis, Juozas. "Vaclovas Bliznikas (1930–1997) – creator of Lithuanian geometers' school." Lietuvos matematikos rinkinys 43 (December 22, 2003): 324–29. http://dx.doi.org/10.15388/lmr.2003.32434.
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Mathematician V. Bliznikas is a longevous professor of Vilnius pedagogical university, former Dean of Faculty of Mathematics, the Head of Geometry Department, one of creators of Lithuanian geometers' school. The main academic research activity embraced trends of modern geometry, theory of geometrical objects, geometry of differential equation, theory of non-holonomicity manifolds, geometry of supporting elements. He published over 95 scientific articles in the scientific publications in Lithuania and East Europe, prepared 11 Doctors of Sciences, wrote 10 coursebooks for the students of high mathematics.
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Kobryń, Andrzej, and Piotr Stachera. "S-Shaped Transition Curves as an Element of Reverse Curves in Road Design." Baltic Journal of Road and Bridge Engineering 14, no. 4 (2019): 484–503. http://dx.doi.org/10.7250/bjrbe.2019-14.454.
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A road designing involves horizontal and vertical alignment. The horizontal geometry is formed by straight and curvilinear sections that are traditionally formed using circular and transition curves (mainly the clothoid). Different geometric systems that are designed using circular and transition curves are between others circular curves with symmetrical or unsymmetrical clothoids, combined curves, oval curves and reverse curves. Designing these systems is quite complex. Therefore, so-called S-shaped transition curves are an alternative to traditional approaches. These curves are known from literature and are modern geometric tools for the shaping of reverse curves. The paper analyses the basic geometric properties of these curves as well as compare to the geometry of the appropriate geometric systems, which are formed with clothoid or using S-shaped transition curves. In addition, a procedure for designing reverse curves using S-shaped transition curves was proposed. Another research topic was the comparison of the analysed reverse curves (created using polynomial transition curves) with traditional curves (created using the clothoid). The results of the studies, despite the noticeable differences in the geometry of the compared components, confirm the practical usefulness of the S-shaped transition curves for designing the geometry of the route.
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Zeeman, Christopher. "Three-dimensional theorems for schools." Mathematical Gazette 89, S1 (2005): 1–92. http://dx.doi.org/10.1017/s0025557200590421.
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Geometry is gradually coming back into the school syllabus, but so far only 2-dimensional geometry. I would like to make a case for including some 3-dimensional geometry as well, because the latter is vital for describing the world throughout science, engineering and architecture. Higher-dimensional geometry also comprises a major part of modern research within mathematics itself. Also 3-dimensional geometry fosters both our intuitive understanding and our geometric imagination. It teaches us to see things in the round. It also trains us to see all sides of an argument simultaneously, as opposed to algebra and computing which emphasise thinking sequentially.
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Beisenbayeva, Galiya, Akan Mubarakov, Zoya Seylova, Larissa Zhadrayeva, and Botagoz Artymbayeva. "Visualisation of educational material in geometry using digital technologies on the Unity 3D platform." Scientific Herald of Uzhhorod University Series Physics, no. 56 (May 28, 2024): 2098–105. http://dx.doi.org/10.54919/physics/56.2024.209bi8.
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Relevance. Digital technologies are progressively being incorporated into the educational framework. Training with the use of digital technologies corresponds to the modern way of life, which is inextricably linked with access to, receipt, and use of information. This entails the modernization of not only the content of education, but also the forms, methods, and means of teaching. Purpose. This study aims to investigate the impact of augmented reality on the spatial abilities and academic performance of students. It involves the development and testing of an educational application for geometry classes to provide interactive material and improve learning efficiency. Methodology. The study used pedagogical experiments, observations, and assessments. The Geometria mobile application with augmented reality for visualizing spatial geometry problems was developed for a tenth-grade geometry textbook. Results. The study involved 40 tenth-graders studying the section "Parallelism in Space". Following the experiment, all participants except for four demonstrated improvements in their prior test outcomes, with ten out of nineteen participants achieving outstanding grades. According to the study results, teachers and students noted the originality of this product and the fact that its use increased the visibility and understanding of the geometric material. Conclusions. A positive experience of using augmented reality technology in the study of stereometry has been obtained. The study highlights the effectiveness of augmented reality in enhancing students' spatial abilities and academic performance in geometry. The results suggest that incorporating digital technologies like augmented reality can significantly improve learning outcomes and engagement in educational settings. Keywords: secondary education system; geometry; spatial thinking; stereometry
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Kemelbekova, E. A., and G. O. Syzdykova. "METAPHORICAL WAY OF FORMING APPLIED GEOMETRY TERMS IN THE MODERN KAZAKH LANGUAGE." Bulletin of Shokan Ualikhanov Kokshetau University. Philological Series 2023, no. 4 (2023): 18–27. http://dx.doi.org/10.59102/kufil/2023/iss4pp18-27.
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The present article is devoted to the presentation of the results of the study of one of the possible ways of appearance of terms in the field of applied geometry, namely metaphorization in the terminology of the Kazakh language. Despite the fact that there are enough works on metaphor, but there are no works on the study of metaphorical nomination in the terminology of applied geometry in the Kazakh language. This determines the novelty of this work. The purpose of this research is to study productive metaphorical models used in the formation of terms of applied geometry in the Kazakh language. For this purpose, the essence of metaphor and metaphorical transfer is considered, the ways of formation of terms of applied geometry by metaphorization are analyzed. The analysis of the sphere- the source of metaphorical transfer and the definition of the functions of geometric metaphor is carried out. The study presents the types of metaphor formation, as well as a detailed analysis of their models. The definitions of the studied terms of applied geometry are considered in the article, and the lexical meanings of the source words and their semantic components involved in the transfer of meaning are highlighted. The most common types of metaphors are identified. It has been revealed that anthropomorphic metaphorization is one of the most effective ways of forming terms of applied geometry in Kazakh terminology. Key words: term-metaphor, scientific metaphor, applied geometry, metaphorization, metaphorical models
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Rýparová, Lenka, Irena Hinterleitner, Sergey Stepanov, and Irina Tsyganok. "Infinitesimal Transformations of Riemannian Manifolds—The Geometric Dynamics Point of View." Mathematics 11, no. 5 (2023): 1114. http://dx.doi.org/10.3390/math11051114.
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In the present paper, we study the geometry of infinitesimal conformal, affine, projective, and harmonic transformations of complete Riemannian manifolds using the concepts of geometric dynamics and the methods of the modern version of the Bochner technique.
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Малаховская and V. Malakhovskaya. "To the question of educational process organization on graphic disciplines in Belarusian high educational institutions." Geometry & Graphics 1, no. 2 (2013): 38–41. http://dx.doi.org/10.12737/786.
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The analysis of the main trends related to descriptive geometry teaching methods in Belarusian engineering education system has been performed in this paper. The traditional structure has been characterized, from whence the need for adjustment the «Descriptive Geometry» section content of «Engineering Graphics» course in accordance with evolving the computer assisted design systems’ trends has been revealed. The organizational and methodological aspects related to descriptive geometry teaching on mechanical engineering faculties with regard to geometric computer simulation as modern design direction have been considered. The curricula change questions are proved, and also the actions for «Descriptive geometry» section teaching technique improvement are offered.
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Nazarova, Olga. "Modern Problems of “Applied Geometry and Engineering Graphics” Course Teaching For Exploitative Specialties of an Aviation High Educational Institution." Geometry & Graphics 8, no. 2 (2020): 58–65. http://dx.doi.org/10.12737/2308-4898-2020-58-65.
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In an aviation high educational institution, when getting students education in exploitative specialties it must be taken into account that it must be conducted in accordance with necessary requirements to the formedness level of professional competences in a specialized area. The planned results of “Applied Geometry and Engineering Graphics” learning include knowledge of methods for applied engineering and geometric problems solving, the ability to use the main elements of applied geometry and engineering graphics in professional activities, and solving of specific applied problems related to geometric modeling.
 The results of “Applied Geometry and Engineering Graphics” study are to gain experience and skills for solution of cognitive, organizational and other problems by themselves related to students’ future professional activities.
 In this paper are considered the main problems and tasks to be solved to achieve the necessary level for compliance of a student studying in one of the exploitative specialties at the Ulyanovsk Institute of Civil Aviation named after Chief Marshal of Aviation B.P. Bugaev, with professional competencies and modern educational standards. Issues related to the organization of “Applied Geometry and Engineering Graphics” discipline study, such as computerization of the educational process, use of distance learning technologies in the educational process, formation of students’ cognitive interest and spatial imagination.
 Has been presented the proposed structure of “Applied Geometry and Engineering Graphics” course for the exploitative specialties of Ulyanovsk Institute of Civil Aviation; the need to develop a task book for classroom and home works, taking into account their applied value for formation of professional competencies, has been justified.
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Lelyukhin, Vladimir Egorovich, and Olga Valeryevna Kolesnikova. "Geometry of real objects in shipbuilding and ship repair." Vestnik of Astrakhan State Technical University. Series: Marine engineering and technologies 2020, no. 1 (2020): 31–44. http://dx.doi.org/10.24143/2073-1574-2020-1-31-44.
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The article considers the modern engineering practice of designing and manufacturing that uses various analytical and graphic forms representing geometric objects. Both of these forms are characterized by the presence of two problems in terms of production practice: 1 - tools of modern geometry cannot operate with non-ideal forms and configurations of material objects; 2 - lack of methods and tools for describing patterns of generating geometric objects, from production lines to the structure that characterizes the relative location of surfaces. The generalized provisions of the geometry of non-ideal objects theoretically justified for formal synthesis and their elements have been presented, which avoids problems of geometric configuration in the practice of designing and developing manufacturing technologies in shipbuilding and ship repair. A special toolkit based on discrete mathematics is proposed for the formal description of the geometric configuration of non-ideal objects. The principles of geometry of real objects describe the structural-parametric representation of objects in a six-dimensional space that is defined by linear and angular vectors. The concepts of linear and angular vectors are analyzed. It has been stated that the presence of an angular vector simplifies the perception and makes easier calculating the processes of geometric transformations. A geometrical object refers to a closed subspace bounded by a single surface, a set of mating or intersecting surfaces. The examples of the real plane deviations from its reference, location of the planes for creating the ideal geometric configuration, variants of real images, forming the basis for six-dimensional space, structure of geometric configurations have been illustrated. It has been found that any specific part acting as a geometric object can be represented by a set of surfaces and the structure of their relationships, which contributes to the correctness of its manufacture. The use of six-dimensional space allows to describe the spatial geometric configurations of parts of various mechanisms with mathematical accuracy.
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Sal'kov, N. "Building the Perspective of a Straight Line Along The Picture Trail and the Vanishing Point." Geometry & Graphics 11, no. 4 (2024): 32–42. http://dx.doi.org/10.12737/2308-4898-2024-11-4-32-42.
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The article recalls the essence of academic subjects: descriptive geometry, drawing, engineering graphics, computer graphics and what each of these subjects is intended for. It is said about the compulsory study of geometry by students, especially those students who study in technical fields of study, about the role of descriptive geometry in the learning process and later in practical activities. Therefore, the existence of departments of geometric and graphic profile for each technical university is unconditionally necessary. It is explained that the modern disdainful attitude of the university leadership towards the departments of the geometric direction should not lead to the disappearance of these departments, since an engineer without knowledge of geometry is a fundamental underachiever, and at best an amateur. The reasons that led to the insufficiency of highly qualified specialists in the geometric and graphic profile in universities are given and, in this regard, some steps are proposed to improve the quality of engineering education. The situation of the educational process in the supposedly leading technical universities of the country, which have already got rid of the departments of the geometric direction or are on the road to this "great" achievement, is given as a negative example, as a result of which various information has been received for quite a long time about the not very favorable situation in these universities. Some measures are proposed to improve geometric education in Russian universities.
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Gevorkyan, M. N., A. V. Korol’kova, D. S. Kulyabov, and L. A. Sevast’yanov. "Implementation of analytic projective geometry for computer graphics." Программирование, no. 2 (April 15, 2024): 51–65. http://dx.doi.org/10.31857/s0132347424020089.
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In their research, the authors actively exploit different branches of geometry. For geometric constructions, computer algebra approaches and systems are used. Currently, we are interested in computer geometry, more specifically, the implementation of computer graphics. The use of the projective space and homogeneous coordinates has actually become a standard in modern computer graphics. In other words, the problem is reduced to the application of analytic projective geometry. The authors failed to find a computer algebra system that could implement projective geometry in its entirety. Therefore, it was decided to partially implement computer algebra for visualization of algebraic relations. For this purpose, the Asymptote system was employed.
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Åžener, Fatma, and Meltem Erdogan. "Neo-Geo and Fashion Interaction." New Trends and Issues Proceedings on Humanities and Social Sciences 2, no. 1 (2016): 595–601. http://dx.doi.org/10.18844/prosoc.v2i1.909.
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Neo-geo, which appeared as an abstract and modern art movement towards the end of 20th century, has had its impact in 21st century as well. New geometry painting perception known as neo-geo is the works where materials and geometric forms are used in any environment. The effects of geometric forms are observed in fashion as in architecture and painting. Fashion designers are the people with an open perception who are able to manage to develop their artistic experience and knowledge using the current time and their abilities in a correct way. The purpose of the current study was to investigate the new geometry as an abstract and modern art movement and fashion interaction and determine its effect on fashion. In this research, the related literature was reviewed and the collections of the fashion designers who were impressed by this art movement was examined and some samples were given. Due to the fact that the art movement of neo-geo appeared towards late 1980s, clothing styles of 80s and its relation with the fashion in those days were given.Keywords: Fashion, neo-geo (new geometry), art.Â
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Darmawan, Arya Rizki, and Ida Barkiah. "Optimalisasi Kapasitas Lentur Balok Kombinasi Castellated dan Tapered Menggunakan Simulasi ANSYS." Jurnal Konstruksi 23, no. 1 (2025): 108–15. https://doi.org/10.33364/konstruksi/v.23-1.2361.
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Penelitian ini bertujuan menganalisis kapasitas lentur balok kombinasi Castellated dan Tapered menggunakan simulasi numerik ANSYS. Balok diuji dengan dua sistem tumpuan: sendi–rol dan kantilever, menggunakan variasi geometri WF, Castella, dan Tapered Castella. Hasil menunjukkan bahwa kombinasi taper dapat meningkatkan kapasitas lentur hingga 34–35% dibandingkan balok WF konvensional dan 16-21% dibandingkan dengan balok Castella prismatis. Hal ini dikarenakan geometry balok taper dapat meningkatkan inersia profil, terutama pada posisi momen maksimum. Kontribusi penelitian ini adalah pembuktian efisiensi struktur melalui distribusi geometri sesuai momen maksimum pada setiap sistem tumpuan. Penelitian ini menunjukkan potensi aplikasi sistem ini dalam penggunaan elemen struktur bangunan modern.
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Ruane, P. N., and John R. Silvester. "Geometry Ancient and Modern." Mathematical Gazette 86, no. 506 (2002): 363. http://dx.doi.org/10.2307/3621906.
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Izen, Stanley P. "Proof in Modern Geometry." Mathematics Teacher 91, no. 8 (1998): 718–20. http://dx.doi.org/10.5951/mt.91.8.0718.
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With the recent availability of such excellent geometry software as The Geometer's Sketchpad (Jackiw 1995). the geometry curriculum has been changed forever. In particular, the role of deductive proof in geometry is being thoroughly reevaluated. Some observers believe that deductive proof is no longer important, whereas others see it as a necessary part of mathematics education.
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Ratnasarira; Caecilia S. Wijayaputri, Dewanti. "THE APPLICATION OF GEOMETRIC PROPORTION AND COMPOSITION THEORY TO THE BNI 46 JAKARTA BUILDING BY SILABAN." Riset Arsitektur (RISA) 1, no. 04 (2017): 447–62. http://dx.doi.org/10.26593/risa.v1i04.2755.447-462.
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Abstract- In terms of history, proportion, composition and geometry have been applied as design elements since long ago, way before the era of modern architecture. The existence of these three elements enables numerous variations and produces freedom of expression. Unfortunately, in current design processes, these visual principles are often overlooked. In fact, they play a role as one of the indicators of aesthetics of a building, as well as exerting influence on human perception in capturing and perceiving a given space. The purpose of this research is to study the application of proportion and composition principles to one of the creations of the Indonesian modern architect Frederich Silaban. The BNI 46 Building design by Silaban acts as the research object, displaying a façade which is crammed with modern thoughts, different on each side but remaining harmonious and visually attractive. The theory of proportion, composition, geometry and structuring principles provide the basis for analyzing the existing object. This research uses the descriptive analytical method with the qualitative approach to data collection of the research object. The next step is the vertical and horizontal analysis of the building enclosure in relation to the implementation of geometric proportion and composition principles in the building. This research is expected to be beneficial in terms of enriching the knowledge and study of geometric proportion and proportion in architecture, adding to the consideration of implementing visual principles for professionals, as well as adding to the archive/portfolio concerning Silaban as one of Indonesia’s pioneering modern architects. Keywords: proportion, composition, Geometry, Silaban
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Son, Le Ngoc, Nguyen Khanh Chi, Ngo Duc Duy, et al. "Experiential Learning in Geometry: Integrating Virtual Reality for Deeper Understanding." Journal of Advances in Education and Philosophy 9, no. 03 (2025): 102–7. https://doi.org/10.36348/jaep.2025.v09i03.001.
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This paper investigates the integration of experiential learning and virtual reality (VR) technology in geometry instruction to enhance students' deeper understanding of geometric concepts. The study aims to evaluate the effectiveness of using VR in experiential learning activities in improving students' comprehension and application of knowledge in Mathematics. The research method combines an experimental model with two groups: one group engages in geometry lessons using VR, while the other follows traditional teaching methods. Data were collected through pre- and post-test assessments, student satisfaction surveys, and analysis of learning behaviors. Results indicate that the use of VR in geometry teaching helps students develop spatial thinking skills and fosters greater interaction during learning. The study also reveals that VR can enhance student engagement, improve memory retention, and deepen understanding of complex geometric concepts. These findings open new pathways for the application of modern educational technologies to improve Mathematics teaching quality in secondary schools.
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Kampczyk, Arkadiusz. "Measurement of the Geometric Center of a Turnout for the Safety of Railway Infrastructure Using MMS and Total Station." Sensors 20, no. 16 (2020): 4467. http://dx.doi.org/10.3390/s20164467.
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The turnouts in railway infrastructure constitute bottlenecks, limiting the capacity of the entire railway network. Due to their design and geometry, these turnouts force speed limits. The need to ensure the proper technical condition of turnouts has prompted ongoing scientific research and the use of modern technological solutions. Until now, there have been no tests for the correct location of the geometric center of a double and outside slip turnout with the related geometric relationships. Therefore, the main objective of this research was to demonstrate the position of the geometric centre of a double slip turnout and the geometric conditions of the curves of circular diverted tracks by measuring the horizontal versines and geometric irregularities of turnouts. The application of this surveying method, with reference to obtuse crossings and arising from geometric dependencies in the double and outside slip turnout, is defined and implemented (also known as a method for checking the correct location of the geometric center of a turnout—Surveying and Monitoring of the Geometric Center of a Double and Outside Slip Turnout (SMDOST)) via the Magnetic-Measuring Square (MMS) and electronic Total Station. This method also recommends measuring the horizontal versines of the diverted tracks. This paper presents the results of field measurements using the SMDOST and MMS methods, which were applied to carry out an analysis and evaluation of the turnout geometry conditions, thereby presenting the irregularities that cause turnout deformations. The validity of the SMDOST method using MMS and Total Station was thus confirmed. The observations from the conducted research indicate that neglecting measurements of the geometry of the turnouts resulted in additional irregularities in their conditions.
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Goncharova, Tatyana. "Bionics in architecture and geometric modelling of thin shell surfaces." E3S Web of Conferences 389 (2023): 06002. http://dx.doi.org/10.1051/e3sconf/202338906002.
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In the scientific problem of design and calculation of thin elastic shells in the modern world, certain advances have already been made in mathematical and technical theory, based on hypotheses, experimental data, calculation equations and engineering calculations. Only such shells, which are designed based on calculation and used in building and technical constructions, can be referred to a small number of geometric surfaces. When designing thin shells, surfaces of rotation (sphere, torus, paraboloid, ellipsoid of rotation) and transfer surfaces (hyperbolic and elliptic paraboloid, circular transfer surface) are used. Trends in construction and engineering seek to apply complex mathematical models in harmony with environmental policy and the environment. This leads to the necessity of studying the influence of parameters when modeling an object on the parameters and properties of the created construction. Possessing a more complex shape the shells are realized as a result of experiment. As a result of active introduction of information technologies it became possible to introduce cardinally new methods in the application of geometric thin-walled spatial structures for the design of building and technical constructions, a number of machine-building parts. Modern analytical calculation programs and computer-aided design systems (Compass, Autocad, Archicad, etc.) make it possible to create a geometric projection model of a structure on the basis of primitives, to perform structural and static calculations of a project in an elementary manner. The solution of such layout problems is made possible with the support of computer geometry based on descriptive and analytical geometry, linear and vector algebra, mathematical analysis, and differential geometry. Modern bionics and environmental policy relies on the latest methods of mathematical modeling of architectural projects with a wide choice of computational and graphical software for calculation and 3d visualization.
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Zakharov, A. A., and Yu V. Zakharova. "The use of modern computer technologies in the study of the Geometric Modeling course." Journal of Physics: Conference Series 2308, no. 1 (2022): 012007. http://dx.doi.org/10.1088/1742-6596/2308/1/012007.
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Abstract The paper describes the educational discipline “Geometric modeling”, which is suitable for students of applied mathematics. The course covers spline representations and transfinite interpolation methods for modeling the shape of geometric objects, the methods for performing Boolean operations between objects and methods for visualizing the objects. Screenshots of some graphic windows of the developed visualization programs for supporting the implementation of individual assignments in the course are shown. The programs have web interfaces that use the WebGL graphics API in a browser, independent of an operating system, and are also available for smartphones and tablets. They provide graphical output for curves and surfaces in three-dimensional space, user interfaces for entering the initial data and interaction with geometric objects. Students only need to write their own calculation code for the programs in the JavaScript programming language. The interactive tools enable students to get practical skills in working with splines and visually analyze the impact of the input data on the final geometry. The individual assignments and programs are specially focused to stimulate students’ interests. The paper is addressed to teachers of the geometric modeling for mathematicians and computer scientists. It seems to be interesting to those who develop software interfaces for geometric modeling algorithms.
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TIESZEN, RICHARD. "Free Variation and the Intuition of Geometric Essences: Some Reflections on Phenomenology and Modern Geometry." Philosophy and Phenomenological Research 70, no. 1 (2005): 153–73. http://dx.doi.org/10.1111/j.1933-1592.2005.tb00509.x.
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Macintyre, Angus. "Model Theory: Geometrical and Set-Theoretic Aspects and Prospects." Bulletin of Symbolic Logic 9, no. 2 (2003): 197–212. http://dx.doi.org/10.2178/bsl/1052669289.
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I see model theory as becoming increasingly detached from set theory, and the Tarskian notion of set-theoretic model being no longer central to model theory. In much of modern mathematics, the set-theoretic component is of minor interest, and basic notions are geometric or category-theoretic. In algebraic geometry, schemes or algebraic spaces are the basic notions, with the older “sets of points in affine or projective space” no more than restrictive special cases. The basic notions may be given sheaf-theoretically, or functorially. To understand in depth the historically important affine cases, one does best to work with more general schemes. The resulting relativization and “transfer of structure” is incomparably more flexible and powerful than anything yet known in “set-theoretic model theory”.It seems to me now uncontroversial to see the fine structure of definitions as becoming the central concern of model theory, to the extent that one can easily imagine the subject being called “Definability Theory” in the near future.Tarski's set-theoretic foundational formulations are still favoured by the majority of model-theorists, and evolution towards a more suggestive language has been perplexingly slow. None of the main texts uses in any nontrivial way the language of category theory, far less sheaf theory or topos theory. Given that the most notable interactions of model theory with geometry are in areas of geometry where the language of sheaves is almost indispensable (to the geometers), this is a curious situation, and I find it hard to imagine that it will not change soon, and rapidly.
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Boykov, A., and Nina Kadykova. "Engineering Geometry as a Fundamental Core of Engineering Training of Specialists." Geometry & Graphics 12, no. 4 (2025): 15–37. https://doi.org/10.12737/2308-4898-2025-12-4-15-37.
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The article formulates the urgent problem of ensuring the required quality of engineering specialists and concludes that in order to solve this problem it is necessary to ensure the quality of basic engineering and geometric training in junior years during the study of the geometric and graphic course - Descriptive Geometry, Engineering and Computer Graphics. Definitions of engineering geometry, descriptive geometry, engineering graphics and computer graphics are given. It is noted that from the very first lesson on the geometric and graphic course, students study the basis of the engineering method - a constructive approach, according to which the solution of any problem consists of the stages of analyzing the conditions of the problem, synthesizing the solution (prototype production), validation, research. Examples of the application of engineering and geometric methods in various fields are given: in mechanical engineering and robotics, aircraft, shipbuilding and machine tool manufacturing; in instrument making, radio engineering and radio electronics; in thermal, nuclear, hydropower and electric power engineering; in geoinformation and space systems; in chemistry, chemical technology and biotechnology; in materials science and physical and chemical analysis; in medicine. Additionally, a special type of drawings is considered – nomograms. Examples of modern nomograms are given. Conclusions are made that all specialists in engineering specialties without exception must have knowledge, skills and abilities in working with geometric and graphic information. The fundamental basis for this is the basic geometric and graphic course. Improving the general level of engineering training is impossible without a corresponding increase in the level of basic engineering and geometric training of students. References are given to publications devoted to the analysis of the causes of weak engineering and geometric training, and publications that show ways to ensure the required quality of basic engineering and geometric training.
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Naidysh, Andrew, Ivan Baliuba, Viktor Vereshchaga, and Dmitro Spirintsev. "MELITOPOL SCHOOL OF APPLIED GEOMETRY. HISTORY AND WORK EXPERIENCE." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 100 (May 24, 2021): 13–17. http://dx.doi.org/10.32347/0131-579x.2021.100.13-17.
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The work examines the history of formation, development and the main scientific works of the Melitopol School of Applied Geometry. The materials give a general characteristic of the main scientific directions of the school: variable discrete geometric modeling (VDGM) and point calculus Balyub-Naidish (BN calculus). The materials cover the list and peculiarities of scientific and organizational measures carried out by scientists of the school. The scientific school of applied geometry was founded by Meer Moiseevich Yuditsky in the 60s of the last century. The active personal, scientific and organizational activities of M. M. Yuditsky, the participation of scientists of the department in conferences and seminars of various levels, the defense of dissertations that took place in subsequent years gave the basis for the formation of a regional scientific center for applied geometry on the basis of the department. In 1977, Vladimir Mikhailovich Naydysh became the head of the school, which was called the Melitopol Scientific School of Applied Geometry. One of the significant results of the work of the school and its head personally is the holding in Melitopol of the annual International Scientific and Practical Conference "Modern Problems of Geometric Modeling" (held since 1994). The main scientific direction of the school is the development of the theory and applied aspects of discrete applied geometry. Since 2007, Andrei Vladimirovich Naydysh, Doctor of Technical Sciences, took over the leadership of the scientific school. Today, the basic institution of higher education for the school is the Bogdan Khmelnitsky Melitopol State Pedagogical University. Materials The modern state of the school, the level of its scientific developments, the personal achievements of the school's specialists give reason to consider the Melitopol School of Applied Geometry as having all the features of a scientific school by type - a school as a research team.
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Kumar, Mukesh. "New look at symmetries and conservation laws." RESEARCH REVIEW International Journal of Multidisciplinary 2, no. 6 (2017): 137–45. https://doi.org/10.5281/zenodo.5148409.
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Using the geometric language of modern differential geometry, we discuss different methods for obtaining symmetries and first integrals of Hamiltonian Poisson vector fields which are based on notion of pseudo symmetries, generalized Noether theorem, and Poisson brackets on tangent manifolds. The differential system which describes the two-dimensional isotropic harmonic oscillator is given as example.
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Kimuya, Alex M., and Stephen Mbugua Karanja. "Incompatibility between Euclidean Geometry and the Algebraic Solutions of Geometric Problems." European Journal of Mathematics and Statistics 4, no. 4 (2023): 14–23. http://dx.doi.org/10.24018/ejmath.2023.4.4.90.
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The transition from the “early-modern” mathematical and scientific norms of establishing conventional Euclidean geometric proofs has experienced quite mixed modes of reasoning. For instance, a careful investigation based on the continued attempts by different practitioners to resolve the geometric trisectability of a plane angle suggests serious hitches with the established algebraic angles non-trisectability proofs. These faults found the root for the difficult geometric question about having straightedge and compass proofs for either the trisectability or the non-trisectability of angles. One of the evident gaps regarding the norms for establishing the Euclidean geometric proofs concerns the incompatibility between the smugly asserted algebraic-geometric proofs and the desired inherent Euclidean geometric proofs. We consider an algebraically translated proof of the geometric angle trisection scheme proposed by [1]. We assert and prove that there is a complete incompatibility between the geometric and the algebraic methods of proofs, and hence the algebraic methods should not be used as authoritative means of proving Euclidean geometric problems. The paper culminates by employing the incompatibility proofs in justifying the independence of the Euclidean geometric system.
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Хейфец and Aleksandr Kheyfets. "Descriptive geometry course reorganization as the actual task of graphics chairs development." Geometry & Graphics 1, no. 2 (2013): 21–23. http://dx.doi.org/10.12737/781.
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The need of descriptive geometry (DG) course reorganization in the direction of reflecting in it the foundations of modern computer 3D geometric simulation techniques is shown. The full rate use of 3D methods calls on students a special theoretical training. New techniques require the knowledge of computer as modern 3D geometric simulation tool. A new theoretical course composed of three modules has been proposed. The basics of 3D are given initially. Then, in accordance with the FSES-3 requirements, the DG elements are given by the example of positional tasks, but they are also underpinned by 3D-methods. The proposed DG course reorganization on the basis of 3D computer geometric simulation will permit to equip the students with new methods of decisions related to graphic tasks, significantly increase their competitiveness on the labor market, as well as to raise the graphics chairs’ rating.
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Zorach, Rebecca. "Stones, Snowflakes, and Insect Eggs." Nuncius 35, no. 2 (2020): 341–63. http://dx.doi.org/10.1163/18253911-03502009.
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Abstract This paper takes as its broad context the evolution of the place of geometry in ways of thinking about nature and art in early modern Europe. Considering a set of questions about how Nature creates geometric forms, particularly in minerals but also in other kinds of natural beings, the paper explores the concept of “figure” as it appears in Conrad Gessner’s De rerum fossilium, where figure appears as a broad category that cuts across abstract geometry, artifactual images, and shape appearing within natural entities. Gessner is placed within changing ideas about the role of geometry as an intellectual pursuit or, rather, a mechanical property of nature conceived as inanimate and rule-bound.
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Nazimuddin, AKM, and Md Showkat Ali. "Riemannian Geometry and Modern Developments." GANIT: Journal of Bangladesh Mathematical Society 39 (November 19, 2019): 71–85. http://dx.doi.org/10.3329/ganit.v39i0.44159.
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In this paper, we compute the Christoffel Symbols of the first kind, Christoffel Symbols of the second kind, Geodesics, Riemann Christoffel tensor, Ricci tensor and Scalar curvature from a metric which plays a fundamental role in the Riemannian geometry and modern differential geometry, where we consider MATLAB as a software tool for this implementation method. Also we have shown that, locally, any Riemannian 3-dimensional metric can be deformed along a directioninto another metricthat is conformal to a metric of constant curvature
 GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 71-85
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Burn, Bob, Lars Kadison, and Matthias T. Kromann. "Projective Geometry and Modern Algebra." Mathematical Gazette 80, no. 488 (1996): 446. http://dx.doi.org/10.2307/3619609.
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Rustamyan, Vyacheslav, and I. Beglov. "Descriptive Geometry in Modern Education." Журнал технических исследований 2, no. 2 (2016): 2. http://dx.doi.org/10.12737/19440.
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Fedyaev, Alexander P., and Natalya V. Zaitseva. "Fractal geometry and modern science." Vestnik of Samara State Technical University. Series Philosophy 5, no. 2 (2023): 83–90. http://dx.doi.org/10.17673/vsgtu-phil.2023.2.9.
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The essence of fractal geometry is disclosed, the subject of study of which is the point as the self-similarity of Genesis. The essence of the torsion form of movement was analyzed. A new concept of space and time has been developed. The ideological and theoretical proximity of the provisions of modern science and ancient Eastern philosophy has been determined. G. Kantors axiom on continuity (1872), as well as K. Gdels incompleteness theorem, has been interpreted. The possibility of science entering the sphere of the nomen world has been proven. The theory of pulsating Chaos or Supersymmetry is based. It has been revealed that events occur not only in space and time, but that space and time themselves affect events.
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Kozlova, I., R. Slavin, and Boris Slavin. "Graphic Disciplines and Informatization of Engineering Education." Geometry & Graphics 10, no. 4 (2023): 35–45. http://dx.doi.org/10.12737/2308-4898-2022-10-4-35-45.
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The development of information technology has given a significant impetus and progress both for various industries and life, as well as for education. The national program "Digital Economy of the Russian Federation" provides for ensuring the introduction of digital technologies in the economy and social sphere, and is associated with the National Project "Education (2019-2024)", which includes the Federal Project "Digital Educational Environment" based on the introduction of the target model of modern digital technologies into educational programs. Innovative methods and forms of training create a strategy for the professional training of specialists, and computer visibility of the forms of the part gives an idea of the assembly technology, allows you to perform competent drawings. The purpose of the study is to analyze the methods of solving the problems of descriptive geometry and engineering graphics together with the use of methods of surface formation by geometric methods, as well as on the basis of basic CAD operations COMPASS-3D. 
 In modern high school, in most cases, drawing is not studied, or only the most general concepts and definitions are studied. The existing course of school computer science deals only with general issues and practically does not give skills in drawing and modeling. As a result, applicants for the most part come to a technical university unprepared for the normal perception of geometric and graphic disciplines. In this regard, two priority tasks of further informatization of engineering education at the technical university have been formulated. On the one hand, this is the improvement of the methodology for teaching geometro-graphic disciplines, including in distance learning. On the other hand, it is the involvement of schoolchildren in various Olympiads and competitions held on the basis of technical universities to develop the initial skills of drawing and modeling simple objects.
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IVANOVA, Katerina, and Oksana LIBA. "ORGANIZATION OF TEACHING ELEMENTS OF GEOMETRY FOR FUTURE PRIMARY SCHOOL TEACHERS." Cherkasy University Bulletin: Pedagogical Sciences, no. 2 (2024): 94–99. http://dx.doi.org/10.31651/2524-2660-2024-2-94-99.
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Introduction. The article deals with the problem of organizing the teaching of geometric figures to future primary school teachers. The study of this topic is a key aspect of the formation of professional competence of future teachers. The purpose of the study is to analyze the methods of teaching geometry used in the training of future teachers and to offer recommendations for their improvement. Theoretical and practical aspects of teach-ing, including the development of teaching materials, are considered. Modern approaches to teaching geometry that take into account pedagogical technologies and innova-tions in education are analyzed. The purpose. The study of different methods and ap-proaches to organizing geometry teaching for future pri-mary school teachers. Particular attention will be paid to practical tasks and real-life examples of applying geomet-ric knowledge The methods analysis and synthesis of scientific, pedagogical, methodological sources in order to identify the state of development of the problem; generalization of pedagogical experience in methods of teaching mathemat-ics; systematization and systematization and generaliza-tion to formulate conclusions. Results. The organization of teaching geometric shapes to future primary school teachers should include both theoretical and practical aspects. Students should learn not only to identify geometric shapes and study their properties, but also to develop teaching methods that will be accessible and engaging for primary school stu-dents. Originality. The relevance of the study of the organiza-tion of studying geometric shapes by future primary school teachers is due to the need to create correct ideas in younger students about volumetric and flat shapes, and for this purpose, the future primary school teacher needs to have a thorough knowledge of the elements of geometry in space and on the plane. Conclusion. The study of geometric shapes in the pro-cess of mathematical training of future primary school teachers is important for their professional competence. The study of geometric shapes not only enriches students' knowledge of shapes and their properties, but also pro-vides them with the necessary skills to effectively teach the elements of geometry to primary school students.
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Kumar, Nanda Kishor. "Symmetry in the context of the Almost Contact 3-Structure and Almost Quaternion Structure." Pragnya Sarathi प्रज्ञा-सारथि 23, no. 1 (2025): 141–46. https://doi.org/10.3126/ps.v23i1.77528.
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The aim of this paper is to explores the characteristics, relationships, and applications of nearly contact 3-structure and nearly quaternion structure in current mathematical study, as well as their foundations. The Interplay between almost contact 3-structure and almost quaternion structure and significance and future direction have also been described. The study of symmetry in Almost Contact 3-Structures and Almost Quaternion Structures provides deep insights into differential geometry and mathematical physics. These structures serve as a bridge between classical Riemannian geometry and modern physical theories, with ongoing research continuing to explore their rich algebraic and geometric properties.
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Kokesh, A. N., B. T. Kalimbetov, and N. K. Madiyarov. "Methods of teaching future mathematics teachers to depict geometric shapes using digital technologies." Gumilyov Journal of Pedagogy 150, no. 1 (2025): 248–66. https://doi.org/10.32523/3080-1710-2025-150-1-248-266.
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The article examines the methodological problems that arise in the process of depicting geometric shapes, studies effective methods for solving this problem in the context of digital transformation of education in Kazakhstan. The study involved an analysis of psychological, pedagogical, scientific and methodological literature on the image of geometric shapes and the preparation of future mathematics teachers to this task. Additionally, the article reviews the works of domestic and foreign authors devoted to research in the field of digital technologies. The article presents the results of a ascertaining experiment to identify problems in the image of geometric shapes, which outlines the causes of the problems that arise. Corrective experimental work has been carried out to solve the identified problems in terms of the opportunities provided by modern digital technologies. The prepared methods have been introduced into the educational process. Brief information is provided on the identified methodological problems and work to eliminate them by teaching future mathematics teachers the methods of “depicting geometric shapes” and 3D drawing models of visual learning in modern dynamic environments such as Geogebra, and Live Geometry. The experimental research works and their results carried out on the basis of the Department of Mathematics of the M. Auezov South Kazakhstan University were presented in order to determine the effectiveness of the use of digital technologies in teaching problems of constructing projections, images, and cross-sections of spatial figures in a school geometry course and training future mathematics teachers. During the pedagogical experiment, the methods of using digital technologies prepared by the authors were used in teaching students to depict geometric shapes to the experimental group, mathematical and statistical methods proved their positive effect on the quality of knowledge of future teachers. Specific methodological recommendations have been developed for teaching future mathematics teachers to depict geometric shapes.
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Ercolessi, Elisa. "A short course on quantum mechanics and methods of quantization." International Journal of Geometric Methods in Modern Physics 12, no. 08 (2015): 1560008. http://dx.doi.org/10.1142/s0219887815600087.
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These notes collect the lectures given by the author to the "XXIII International Workshop on Geometry and Physics" held in Granada (Spain) in September 2014. The first part of this paper aims at introducing a mathematical oriented reader to the realm of Quantum Mechanics (QM) and then to present the geometric structures that underline the mathematical formalism of QM which, contrary to what is usually done in Classical Mechanics (CM), are usually not taught in introductory courses. The mathematics related to Hilbert spaces and Differential Geometry are assumed to be known by the reader. In the second part, we concentrate on some quantization procedures, that are founded on the geometric structures of QM — as we have described them in the first part — and represent the ones that are more operatively used in modern theoretical physics. We will discuss first the so-called Coherent State Approach which, mainly complemented by "Feynman Path Integral Technique", is the method which is most widely used in quantum field theory. Finally, we will describe the "Weyl Quantization Approach" which is at the origin of modern tomographic techniques, originally used in optics and now in quantum information theory.