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Journal articles on the topic 'Geometrical knowledge'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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1

Anderson, James A. D. W. "Representing geometrical knowledge." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 352, no. 1358 (August 29, 1997): 1129–39. http://dx.doi.org/10.1098/rstb.1997.0096.

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This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space–time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top–down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space–time. It can be used to match a prototype shape to an image, even in so called ‘accidental’ views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

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Dehaene, Stanislas, Véronique Izard, Pierre Pica, and Elizabeth Spelke. "Core Knowledge of Geometry in an Amazonian Indigene Group." Science 311, no. 5759 (January 20, 2006): 381–84. http://dx.doi.org/10.1126/science.1121739.

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Does geometry constitute a core set of intuitions present in all humans, regardless of their language or schooling? We used two nonverbal tests to probe the conceptual primitives of geometry in the Mundurukú, an isolated Amazonian indigene group. Mundurukú children and adults spontaneously made use of basic geometric concepts such as points, lines, parallelism, or right angles to detect intruders in simple pictures, and they used distance, angle, and sense relationships in geometrical maps to locate hidden objects. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.

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Jayawardana, Chandana. "Geometrical Knowledge in Early Sri Lanka." History of Science in South Asia 10 (July 31, 2022): 44–67. http://dx.doi.org/10.18732/hssa69.

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This article addresses on history of mathematics (specially one of its specific branch, geometry) in Sri Lanka. Despite the large amount of research on the history of mathematics in India, China and the Middle East, that on Sri Lanka still remains limited. Sri Lanka had close relations with all these regions from ancient times and knowldge on mathematics should not be an alien subject there. This article tries to address the paucity of research on the history of mathematics in Sri Lanka while emphasizing the local character of that ancient knowldge.

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Tièche, François, and Heinz Hügli. "From Topological Knowledge to Geometrical Map." IFAC Proceedings Volumes 31, no. 3 (March 1998): 81–86. http://dx.doi.org/10.1016/s1474-6670(17)44065-1.

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5

Werner, Markus, and Hans Stein. "Knowledge-based Engineering of Geometrical Data." ATZproduktion worldwide eMagazine 4, no. 1 (March 2011): 30–35. http://dx.doi.org/10.1365/s38312-011-0007-y.

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Tièche, François, and Heinz Hügli. "From topological knowledge to geometrical map." Control Engineering Practice 7, no. 6 (June 1999): 797–802. http://dx.doi.org/10.1016/s0967-0661(99)00026-x.

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7

Dal Magro, Tamires, and Manuel J. García-Perez. "On Euclidean diagrams and geometrical knowledge." THEORIA. An International Journal for Theory, History and Foundations of Science 34, no. 2 (September 25, 2019): 255. http://dx.doi.org/10.1387/theoria.20026.

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We argue against the claim that the employment of diagrams in Euclidean geometry gives rise to gaps in the proofs. First, we argue that it is a mistake to evaluate its merits through the lenses of Hilbert’s formal reconstruction. Second, we elucidate the abilities employed in diagram-based inferences in the Elements and show that diagrams are mathematically reputable tools. Finally, we complement our analysis with a review of recent experimental results purporting to show that, not only is the Euclidean diagram-based practice strictly regimented, it is rooted in cognitive abilities that are universally shared.

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Plotkin, T., and B. Plotkin. "Geometrical aspect of databases and knowledge bases." Algebra Universalis 46, no. 1 (June 2001): 131–61. http://dx.doi.org/10.1007/pl00000333.

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Salkov, Nikolay, and N. Kadikova. "Reforming of geometrical and graphic knowledge estimates." Геометрия и графика 1, no. 1 (June 14, 2013): 52–53. http://dx.doi.org/10.12737/475.

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10

Chen-Morris, Raz. "Geometry and the Making of Utopian Knowledge in Early Modern Europe." Nuncius 35, no. 2 (September 10, 2020): 387–412. http://dx.doi.org/10.1163/18253911-03502011.

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Abstract In his Della Pittura, Leon Battista Alberti initiated what I call a “utopian moment,” a philosophical and practical disposition fusing human ingenuity, geometry, and political harmony. This paper follows these notions as they evolved over the course of the sixteenth century and were embraced by the new science of Johannes Kepler and René Descartes, who reshaped these utopian dispositions with their new geometrical analyses of sight and light. In his Dioptrice, Kepler suggests a new science of refractions produced and manipulated artificially through lenses, their physical properties analyzed geometrically; in analyzing the rainbow, Descartes artificially reproduces it, initially through a glass flask filled with water, and then through a prism, thus giving a geometrical causal account of its colors. In both cases these analyses are entwined with subtle political metaphors, transforming the technical scientific issues into key features of a “utopian moment.”

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11

Costreie, Sorin. "The geometrical basis of arithmetical knowledge: Frege & Dehaene." THEORIA. An International Journal for Theory, History and Foundations of Science 33, no. 2 (June 20, 2018): 361. http://dx.doi.org/10.1387/theoria.18089.

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Frege writes in Numbers and Arithmetic about kindergarten-numbers and “an a priori mode of cognition” that they may have “a geometrical source.” This resembles recent findings on arithmetical cognition. In my paper, I explore this resemblance between Gottlob Frege’s later position concerning the geometrical source of arithmetical knowledge, and some current positions in the literature dedicated to arithmetical cognition, especially that of Stanislas Dehaene. In my analysis, I shall try to mainly see to what extent (Frege’s) logicism is compatible with (Dehaene’s) intuitionism.

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12

Görög, Augustín, and Ingrid Görögová. "Current Concept of Geometrical Accuracy." Research Papers Faculty of Materials Science and Technology Slovak University of Technology 22, no. 34 (June 1, 2014): 43–49. http://dx.doi.org/10.2478/rput-2014-0026.

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Abstract Within the solving VEGA 1/0615/12 research project "Influence of 5-axis grinding parameters on the shank cutter´s geometric accuracy", the research team will measure and evaluate geometrical accuracy of the produced parts. They will use the contemporary measurement technology (for example the optical 3D scanners). During the past few years, significant changes have occurred in the field of geometrical accuracy. The objective of this contribution is to analyse the current standards in the field of geometric tolerance. It is necessary to bring an overview of the basic concepts and definitions in the field. It will prevent the use of outdated and invalidated terms and definitions in the field. The knowledge presented in the contribution will provide the new perspective of the measurement that will be evaluated according to the current standards.

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Lvov, M. "ABOUT ONE APPROACH OF TESTING GEOMETRICAL KNOWLEDGE SYSTEM BUILDING." Information Technologies in Education, no. 18 (April 30, 2014): 42–50. http://dx.doi.org/10.14308/ite000465.

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14

Bigelmaier, Anton. "Profile of a geometrical knowledge base for CAD-systems." Computers & Graphics 10, no. 4 (January 1986): 297–305. http://dx.doi.org/10.1016/0097-8493(86)90019-1.

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15

Skordialos, Emmanouil, and Georgios Baralis. "A teaching approach of geometric shapes’ properties with the use of online educational tools in Greek primary school." New Trends and Issues Proceedings on Humanities and Social Sciences 4, no. 9 (January 11, 2018): 101–9. http://dx.doi.org/10.18844/prosoc.v4i9.3044.

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A number of researchers have shown concern at the difficulties that primary school pupils cope with in learning geometry, and have tried to explain why this happens and what can be done to make the subject more understandable to young learners. Van Hiele’s theoretical model postulates five levels of geometric thinking as visualisation, analysis, abstraction, formal deduction and rigour. Each level uses its own language and symbols. Pupils pass through the levels ‘step by step’. This hierarchical order helps them to achieve better understanding and results. In this research the teacher taught geometry in the 2nd class in a primary Greek school with the use of information and communication technologies. The aim is to find out the level of geometrical thought of the pupils and how geometrical activities – based on online tools – concerning the geometrical shapes and their properties, help students improve their mathematical knowledge in the class. Keywords: Geometric thinking, online tools, shapes, geometrical activities

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16

Callanan, John J. "Kant on the Acquisition of Geometrical Concepts." Canadian Journal of Philosophy 44, no. 5-6 (December 2014): 580–604. http://dx.doi.org/10.1080/00455091.2014.982746.

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It is often maintained that one insight of Kant’s Critical philosophy is its recognition of the need to distinguish accounts of knowledge acquisition from knowledge justification. In particular, it is claimed that Kant held that the detailing of a concept’s acquisition conditions is insufficient to determine its legitimacy. I argue that this is not the case at least with regard to geometrical concepts. Considered in the light of his pre-Critical writings on the mathematical method, construction in the Critique can be seen to be a form of concept acquisition, one that is related to the modal phenomenology of geometrical judgement.

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Souza, Fábio Nicácio. "A SOLUÇÃO DAS QUADRÁTICAS E CÚBICAS NA HISTÓRIA." Ciência e Natura 37 (August 7, 2015): 555. http://dx.doi.org/10.5902/2179460x14595.

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http://dx.doi.org/10.5902/2179460X14595For a long time the search to solve equations pushed the brilliant minds in the human History. Arithmetical, geometric and algebraic mechanisms ere developed bringing advance to the mathematics knowledge. A lot of these resources were "simplified" and nowadays they're handled in the classroom overruling among them the algebraic manipulation. This article, gotten from chapter 1 of Math Master dissertation in the PROFMAT Program from UFRPE and named A Geometrical Approach to the cubic Equations shows as from the history of algebra a geometrical manner, not usual anymore, to find the solution to second and third degree equations.

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Мельник, Olga Melnyk, Буда, and Antonina Buda. "Zero Control as Integral Part of Geometrical and Graphic Disciplines’ Instruction Technique." Geometry & Graphics 2, no. 2 (June 10, 2014): 32–36. http://dx.doi.org/10.12737/5589.

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The interdependence between diagnostic function of first year students’ zero level knowledge control in geometry and technical drawing and instruction technique in geometrical and graphic academic profile is considered in this work. Methodical procedures and developments for traditional learning system adaptation to existing level of students training are offered by: using of learning tests connecting the basic geometric knowledge with teaching materials; graphical tasks’ full spectrum content personification; using of specific E-learning courses oriented to full-time students.

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Basso, Alberto, Yang Zhang, Jacob Kjeldahl Pløger, Jon Spangenberg, and Hans Nørgaard Hansen. "Analysing Powder Injection Moulding of a Helix Geometry Using Soft Tooling." Polymers 13, no. 23 (November 29, 2021): 4183. http://dx.doi.org/10.3390/polym13234183.

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Freeform injection moulding is a novel technology for powder injection moulding where a sacrificial 3D printed mould (i.e., a soft tooling) is used as an insert in the injection process. The use of 3D printed moulds enable a higher geometrical design flexibility as compared to the conventional injection moulding process. However, there is still very limited knowledge on how the sacrificial soft tooling material and powder suspension handles the increased geometrical complexity during the process. In this study, a stainless steel powder suspension is injected into a geometrically challenging sacrificial mould (viz. a helix structure) that is produced by vat photopolymerization additive manufacturing. Computed tomography is used to quantify the geometrical precision of the mould both before and after injection. In addition, a new numerical model that considers the suspension feedstock is developed to investigate the powder injection moulding process. The numerical results are found to be in qualitative good agreement with the experimental findings in terms of pinpointing critical areas of the structure, thereby highlighting a new pathway for evaluating sacrificial inserts for powder injection moulding with a high geometrical complexity.

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20

Demey, Lorenz, and Hans Smessaert. "Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation." Symmetry 9, no. 10 (September 29, 2017): 204. http://dx.doi.org/10.3390/sym9100204.

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21

Huang, Jian, Yong Chen, Zhinan Zhang, and Youbai Xie. "An affordance-integrated approach for design knowledge reuse." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 10 (April 6, 2015): 1569–85. http://dx.doi.org/10.1177/0954406215578702.

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Design knowledge reuse is regarded as an effective strategy for design organizations to develop products with shorter time and less effort. However, existing design reuse approaches primarily focus on reusing the geometrical information of similar parts, with a wealth of contextual knowledge behind detailed design results lost. This paper presents an affordance-integrated approach for the reuse of detailed design knowledge, which can be employed to help designers determine the values of geometrical design parameters. First, this paper introduces an affordance-integrated model, called the structure-behavior-affordance, to represent the detailed design information. Then an affordance-based approach is proposed to help designers reuse the detailed design knowledge, which is also integrated with commercial CAD tools. Finally, the proposed approach is implemented as a detailed design knowledge reuse system and a turbocharger shell fixture is adopted as an example to illustrate the proposed design knowledge reuse approach.

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22

Saeed, Anwar, Ayoub Al-Hamadi, Robert Niese, and Moftah Elzobi. "Frame-Based Facial Expression Recognition Using Geometrical Features." Advances in Human-Computer Interaction 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/408953.

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To improve the human-computer interaction (HCI) to be as good as human-human interaction, building an efficient approach for human emotion recognition is required. These emotions could be fused from several modalities such as facial expression, hand gesture, acoustic data, and biophysiological data. In this paper, we address the frame-based perception of the universal human facial expressions (happiness, surprise, anger, disgust, fear, and sadness), with the help of several geometrical features. Unlike many other geometry-based approaches, the frame-based method does not rely on prior knowledge of a person-specific neutral expression; this knowledge is gained through human intervention and not available in real scenarios. Additionally, we provide a method to investigate the performance of the geometry-based approaches under various facial point localization errors. From an evaluation on two public benchmark datasets, we have found that using eight facial points, we can achieve the state-of-the-art recognition rate. However, this state-of-the-art geometry-based approach exploits features derived from 68 facial points and requires prior knowledge of the person-specific neutral expression. The expression recognition rate using geometrical features is adversely affected by the errors in the facial point localization, especially for the expressions with subtle facial deformations.

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Bunawan, Wawan, and Agus Setiawan. "ANALYZE THE KNOWLEDGE INQUIRY SCIENCE PHYSICS TEACHER CANDIDATES WITH ESSENCE INQUIRY SCIENCE TEST INSTRUMENT OPTIKA GEOMETRY." Jurnal Pendidikan Fisika 2, no. 1 (June 1, 2013): 59. http://dx.doi.org/10.22611/jpf.v2i1.4338.

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The objective in this research to explore the relationship between ability of the knowledge essential features inquiry science and their reasons underlying sense of scientific inquiry for physics teacher candidates on content geometrical optics. The essential features of inquiry science are components that should arise during the learning process subject matter of geometrical optics reflectance of light on a flat mirror, the reflection of light on curved mirrors and refraction of light at the lens. Five of essential features inquiry science adopted from assessment system developed by the National Research Council. Content geometrical optics developed from an analysis of a college syllabus material. Based on the study of the essential features of inquiry and content develop the multiple choice diagnostic test three tier. Data were taken from the students who are taking courses in optics and wave from one the LPTK in North Sumatra totaled 38 students. Instruments showed Cronbach alpha reliability of 0.67 to test the essential features of inquiry science and 0.61 to there as on geometrical optics science inquiry.

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Cai, Yan, and Liang Zhi Li. "On Surface Continuity in the Procession of Product Design." Applied Mechanics and Materials 620 (August 2014): 60–64. http://dx.doi.org/10.4028/www.scientific.net/amm.620.60.

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The purpose of this paper was to verify the way in which CAD systems and their tools for visual surfaces analysis interact with morphological knowledge in the determination of continuity in product design procession. Geometrical knowledge is necessary but not enough for working with this attribute of form in everyday objects, where cultural factors are involved. Geometry establishes a progressive range of surface continuity that involves the concepts of position, tangency and curvature. In product design different degrees of continuity that not necessarily follow this idea of increment. What is understood as discontinuous in products in most cases is geometrically continuous.

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Vallortigara, Giorgio, Valeria Anna Sovrano, and Cinzia Chiandetti. "Doing Socrates experiment right: controlled rearing studies of geometrical knowledge in animals." Current Opinion in Neurobiology 19, no. 1 (February 2009): 20–26. http://dx.doi.org/10.1016/j.conb.2009.02.002.

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26

Xu, Yuanping, Paul J. Scott, and Jiaoling Zheng. "Novel Research on a Fibration Knowledge-Based Solution for Engineered Surface Tolerances within the Modern GPS Context." International Journal of Software Engineering and Knowledge Engineering 26, no. 05 (June 2016): 845–95. http://dx.doi.org/10.1142/s0218194016500297.

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Geometrical product specification and verification (GPS) is the only worldwide tolerancing specification language available for unambiguously communicating functional requirements and precisely expressing geometrical tolerances of workpieces on technical drawings. Although the understanding and application of GPS are of vital importance for modern manufacturing industry, the latest GPS standards contain huge amounts of data, information and knowledge that are obscurely linked together, so they are very difficult for designers, engineers and metrologists to understand, remember and comprehensively use them. This is especially true for surface texture that is one of the most complicated geometrical characteristics in GPS domain. To overcome the implementation barrier of GPS surface texture, a novel knowledge-based solution supported formally by a unified knowledge modeling of the complete GPS surface texture standard chain has been researched. This knowledge model can serve as a formal basis for developing more intelligent and reliable tolerance design and measurement systems. This paper starts with an introduction on how to build up a formal knowledge model based on category theory, called categorical fibration model, to unified acquisition and representation of all surface texture knowledge. It then moves on to define a recursive knowledge refinement process for the devised model to enable the recursive multi-level GPS knowledge transformations and refinements. This knowledge model is validated naturally by checking rules identified from category theoretic notions. Finally, this paper presents a general framework for applying the modeled GPS knowledge in practice, from the aspects of the integrated and complete modeling of all surface texture knowledge, detailed knowledge acquisition and modeling examples for four sub-knowledge bases of the proposed software solution, core functional features of this software, and a comprehensive case study for testing its validity and usability. This knowledge-based solution facilitates life cycle collaboration and integration of the complete GPS surface texture chain to reduce product development cost and lead time, and to ensure functional requirements of geometrical workpieces.

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Straka, Luboslav, and Gabriel Dittrich. "Improving of geometric precision in the manufacture of circular holes using technology WEDM." International Journal of Engineering and Management Sciences 4, no. 1 (March 3, 2019): 238–45. http://dx.doi.org/10.21791/ijems.2019.1.30.

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WEDM technology is among the final technology. It is characterized by the high quality of the machined surface. Therefore, a small geometric deviation from the desired shape, position, orientation or run out may have a significant impact on the functionality of the finished component. Its range is largely influenced by the accuracy of the applied electroerosion device, the precision of the workpiece and tool setting, the machining method, but also the combination of each other and the adjustment of all process parameters. They result in the final quality of the machined surface not only in terms of roughness parameters but also in terms of geometric precision of the machined surface. The aim of the paper was to describe the possibilities of improving the geometrical accuracy of WEDM with thin brass electrodes. At the same time, it contributes to an existing database of knowledge that defines the influence of selected aspects on the geometrical accuracy of the machined area in the production of circular openings.

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Montero, Joaquin, Sebastian Weber, Christoph Petroll, Stefan Brenner, Matthias Bleckmann, Kristin Paetzold, and Vesna Nedeljkovic-Groha. "GEOMETRICAL BENCHMARKING OF LASER POWDER BED FUSION SYSTEMS BASED ON DESIGNER NEEDS." Proceedings of the Design Society 1 (July 27, 2021): 1657–66. http://dx.doi.org/10.1017/pds.2021.427.

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AbstractCommercially available metal Laser Powder Bed Fusion (L-PBF) systems are steadily evolving. Thus, design limitations narrow and the diversity of achievable geometries widens. This progress leads researchers to create innovative benchmarks to understand the new system capabilities. Thereby, designers can update their knowledge base in design for additive manufacturing (DfAM). To date, there are plenty of geometrical benchmarks that seek to develop generic test artefacts. Still, they are often complex to measure, and the information they deliver may not be relevant to some designers. This article proposes a geometrical benchmarking approach for metal L-PBF systems based on the designer needs. Furthermore, Geometric Dimensioning and Tolerancing (GD&T) characteristics enhance the approach. A practical use-case is presented, consisting of developing, manufacturing, and measuring a meaningful and straightforward geometric test artefact. Moreover, optical measuring systems are used to create a tailored uncertainty map for benchmarking two different L-PBF systems.

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Panagiota Argyri. "Geometry and digital cultural heritage as unique linking for development students’ knowledge, skills and attitudes." IUL Research 1, no. 2 (December 1, 2020): 40–60. http://dx.doi.org/10.57568/iulres.v1i2.71.

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This paper presents the fruitful connection between geometry and cultural heritage as innovative teaching and learning approach and examines the way that students learn geometrical concepts and in which way they construct and transform geometrical concepts and students’ engagement to get familiar with cultural heritage. This pilot research based on implementation of learning scenario by Europeana DSI-4 project and results provided by qualitative and quantitative evaluation could motivate educational community for implementation interdisciplinary learning scenarios with geometry for developments students 21st century skills through cultural heritage.

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Douellou, Corentin, Xavier Balandraud, and Emmanuel Duc. "Assessment of geometrical defects caused by thermal distortions in laser-beam-melting additive manufacturing: a simulation approach." Rapid Prototyping Journal 25, no. 5 (June 10, 2019): 939–50. http://dx.doi.org/10.1108/rpj-01-2019-0016.

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Purpose The purpose of this paper is to develop a numerical approach inspired by Geometrical Product Specifications (GPS) standards for the assessment of geometrical defects appearing during Additive Manufacturing (AM) by Laser Beam Melting (LBM). Design/methodology/approach The study is based on finite element (FE) simulations of thermal distortions, then an assessment of flatness defects (warping induced by the high-residual stresses appearing during the manufacturing) from the deformed surfaces provided by simulation, and finally the correction of the calculated flatness defects from preliminary comparison between simulated and experimental data. Findings For an elementary geometrical feature (a wall), it was possible to identify the variation in the flatness defect as a function of the dimensions. For a complex geometry exhibiting a significant flatness defect, it was possible to improve the geometric quality using the numerical tool. Research limitations/implications To the best of the author’s knowledge, this work is the first attempt using a numerical approach inspired by GPS standards to identify variations in thermal distortions caused by LBM, which is an initial step toward optimization. This paper is mainly focused on flatness defect assessment, even though the approach is potentially applicable for all types of geometrical defects (shape, orientation or position defects). Practical implications The study opens prospects for the optimization of complex parts elaborated using LBM, based on the minimization of the geometric defects caused by thermal distortions. Social implications The prospects in terms of shape optimization will extend the potential to benefit from the new possibilities offered by LBM additive manufacturing. Originality/value Unlike the usual approach, the proposed methodology does not require any artifacts or comparisons with the computer-aided-design (CAD) model for geometrical distortion assessment. The present approach opens up the possibility of performing metrology from FE simulation results, which is particularly promising in the AM field.

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Hristova, Gergana. "VARIOUS PROBLEMS FOR TEACHING GEOMETRY TO THIRD GRADE STUDENTS." Knowledge International Journal 28, no. 3 (December 10, 2018): 997–1003. http://dx.doi.org/10.35120/kij2803997g.

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The knowledge on geometry are of great importance for the understanding of reality. Spatial notion and geometrical concepts, graphical skills and habits are an important part of the study of geometrical knowledge in elementary school as propedeutics of the system course on geometry in the next school levels. In the recent years, education in Bulgaria follows the trends imposed by the European Union related to the acquiring of some basic key competencies. They promote to the improvement of knowledge, skills, abilities and attitudes of students and their more successful social development. From the school year 2016/2017, the education in the Bulgarian schools is in accordance with the new Law on pre-school and school education. Under this law, students are teached under new curriculum and teaching kits for the corresponding class. According to the new curriculum, the general education of the students of I-IV grade, covers basic groups of key competencies. Here, much more attention is paid also to the results of international researches on the students’ performance in mathematics. Primary school students participate in international competitions and Olympiads, which lead to the need of working on more mathematical problems with geometric content of the relevant specific types. This allows to study and use author’s various mathematical problems for teaching geometry. Their purpose is to contribute to the expansion of space notions of the students, to develop their thinking and imagination. This article is dedicated to the application of author’s various mathematical problems and exercises for teaching students from the third grade through which the geometrical knowledge and skills of the students develop and build. The solving of the mathematical problems is realized on a rich visual-practical basis, providing conditions for inclusion of the students in various activities. The proposed various mathematical problems are developed by themes including fully geometric problems and exercises for teaching mathematics to third grade students. Teaching by using the various mathematical problems was held with 149 students from third grade, from five schools - three in Sofia and two in smaller towns, in the school year 2016/2017.

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32

Martinetti, Pierre. "Emergence of Time in Quantum Gravity: Is Time Necessarily Flowing?" Kronoscope 13, no. 1 (2013): 67–84. http://dx.doi.org/10.1163/15685241-12341259.

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Abstract We discuss the emergence of time in quantum gravity and ask whether time is always “something that flows.” We first recall that this is indeed the case in both relativity and quantum mechanics, although in very different manners: time flows geometrically in relativity (i.e., as a flow of proper time in the four dimensional space-time), time flows abstractly in quantum mechanics (i.e., as a flow in the space of observables of the system). We then ask the same question in quantum gravity in the light of the thermal time hypothesis of Connes and Rovelli. The latter proposes to answer the question of time in quantum gravity (or at least one of its many aspects) by postulating that time is a state-dependent notion. This means that one is able to make a notion of time as an abstract flow—that we call the thermal time—emerge from the knowledge of both: the algebra of observables of the physical system under investigation; a state of thermal equilibrium of this system. Formally, the thermal time is similar to the abstract flow of time in quantum mechanics, but we show in various examples that it may have a concrete implementation either as a geometrical flow or as a geometrical flow combined with a non-geometric action. This indicates that in quantum gravity, time may well still be “something that flows” at some abstract algebraic level, but this does not necessarily imply that time is always and only “something that flows” at the geometric level.

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Rodrigues, M. A., Y. E. Li, M. H. Lee, and J. J. Rowland. "Robotic grasping of complex shapes: is full geometrical knowledge of the shape really necessary?" Robotica 13, no. 5 (September 1995): 499–506. http://dx.doi.org/10.1017/s0263574700018336.

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SummaryThis paper aims at contributing to a sub-symbolic, feedback-based “theory of robotic grasping” where no full geometrical knowledge of the shape is assumed. We describe experimental results on grasping 2D generic shapes without traditional geometrical processing. Grasping algorithms are used in conjunction with a vision system and a robot manipulator with a three-fingered gripper is used to grasp several different shapes. The altorithms are run on the shape as it appears on the computer screen (i.e. directly from a vision system). Simulated gripper ringer with virtual sensors are configured and positioned on the screen whose inputs are controlled by moving their position relative to the image until an equilibrium is reached among the control systems involved.

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Werner, Maike, Nicholas A. Kurniawan, and Carlijn V. C. Bouten. "Cellular Geometry Sensing at Different Length Scales and its Implications for Scaffold Design." Materials 13, no. 4 (February 21, 2020): 963. http://dx.doi.org/10.3390/ma13040963.

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Geometrical cues provided by the intrinsic architecture of tissues and implanted biomaterials have a high relevance in controlling cellular behavior. Knowledge of how cells sense and subsequently respond to complex geometrical cues of various sizes and origins is needed to understand the role of the architecture of the extracellular environment as a cell-instructive parameter. This is of particular interest in the field of tissue engineering, where the success of scaffold-guided tissue regeneration largely depends on the formation of new tissue in a native-like organization in order to ensure proper tissue function. A well-considered internal scaffold design (i.e., the inner architecture of the porous structure) can largely contribute to the desired cell and tissue organization. Advances in scaffold production techniques for tissue engineering purposes in the last years have provided the possibility to accurately create scaffolds with defined macroscale external and microscale internal architectures. Using the knowledge of how cells sense geometrical cues of different size ranges can drive the rational design of scaffolds that control cellular and tissue architecture. This concise review addresses the recently gained knowledge of the sensory mechanisms of cells towards geometrical cues of different sizes (from the nanometer to millimeter scale) and points out how this insight can contribute to informed architectural scaffold designs.

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Laborde, C. "Core Geometrical Knowledge for using the Modelling Power of Geometry with Cabri-Geometry." Teaching Mathematics and its Applications 18, no. 4 (December 1, 1999): 166–71. http://dx.doi.org/10.1093/teamat/18.4.166.

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Ugaglia, Monica. "Knowing by Doing: The Role of Geometrical Practice in Aristotle’s Theory of Knowledge." Elenchos 36, no. 1 (March 1, 2015): 45–88. http://dx.doi.org/10.1515/elen-2015-360103.

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Abstract Aristotle’s way of conceiving the relationship between mathematics and other branches of scientific knowledge is completely different from the way a contemporary scientist conceives it. This is one of the causes of the fact that we look at the mathematical passages we find in Aristotle’s works with the wrong expectation. We expect to find more or less stringent proofs, while for the most part Aristotle employs mere analogies. Indeed, this is the primary function of mathematics when employed in a philosophical context: not a demonstrative tool, but a purely analogical model. In the case of the geometrical examples discussed in this paper, the diagrams are not conceived as part of a formalized proof, but as a work in progress. Aristotle is not interested in the final diagram but in the construction viewed in its process of development; namely in the figure a geometer draws, and gradually modifies, when he tries to solve a problem. The way in which the geometer makes use of the elements of his diagram, and the relation between these elements and his inner state of knowledge is the real feature which interests Aristotle. His goal is to use analogy in order to give the reader an idea of the states of mind involved in a more general process of knowing.

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Mogari, David. "Developing geometrical knowledge outside school: The case of miniature wire toy car makers." African Journal of Research in Mathematics, Science and Technology Education 8, no. 2 (January 2004): 117–26. http://dx.doi.org/10.1080/10288457.2004.10740566.

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Xu, Yuanping, Zhijie Xu, Xiangqian Jiang, and Paul Scott. "Developing a knowledge-based system for complex geometrical product specification (GPS) data manipulation." Knowledge-Based Systems 24, no. 1 (February 2011): 10–22. http://dx.doi.org/10.1016/j.knosys.2010.05.002.

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Lee, Je An, Jong Hak Lee, and Won Kyung Kim. "A Study on Mathematics Teachers’ Mathematical Knowledge for Teaching in the Geometrical Probab." Korean Journal of Teacher Education 32, no. 1 (January 30, 2016): 187–220. http://dx.doi.org/10.14333/kjte.2016.32.1.187.

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Sauer, Tilman, and Tobias Schütz. "Einstein on involutions in projective geometry." Archive for History of Exact Sciences 75, no. 5 (January 8, 2021): 523–55. http://dx.doi.org/10.1007/s00407-020-00270-z.

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AbstractWe discuss Einstein’s knowledge of projective geometry. We show that two pages of Einstein’s Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his Princeton years. By this correspondence, we show that the sketches are all related to a common theme, the discussion of involution in a projective geometry setting with particular emphasis on the infinite point. We offer a conjecture as to the probable purpose of these geometric considerations.

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Anselmo, G., and A. Fandella. "Detubularization and/or reconfiguration." Urologia Journal 63, no. 4 (August 1996): 487–90. http://dx.doi.org/10.1177/039156039606300414.

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Technical variants of reservoir construction can develop from in-depth knowledge of the important physiopathological implications involved in the choice of whole intestinal segments and especially the aperture and reconfiguration of the segment. The physical geometrical and physiological principles applied to clinical practice are therefore described, represented by the configuration or geometrical capacity, the accommodation, the visco-elasticity or compliance and the contractility.

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Παπαδάμ, Μαρία, and Ιωάννης Αγαλιώτης. "Διερεύνηση γεωμετρικών γνώσεων μαθητών με ήπιες εκπαιδευτικές ανάγκες." Psychology: the Journal of the Hellenic Psychological Society 26, no. 1 (March 24, 2021): 135. http://dx.doi.org/10.12681/psy_hps.26234.

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Geometry is a structural component of mathematics, with increased spatial and design requirements that cannot be easily met by students with mild disabilities. Systematic investigation of the difficulties encountered by students with mild disabilities in their effort to learn Geometry is a prerequisite for the implementation of effective intervention programs. However, research on this issue is relatively scarce. The aim of the present study was to assess the geometric knowledge of 54 students with mild disabilities (learning disabilities or ADHD) who attended the two last classes of elementary school. Participants were asked to recognize, describe and categorize geometric shapes and solid bodies that were presented in tactile mode and through pictorial representations. Semi-structured clinical interviews were used for gathering the data in the context of Curriculum Based Assessment and the Van Hiele’s model of geometrical thinking. Participants of both categories of mild disabilities presented difficulties in distinguishing shapes and bodies, properly using the terminology, and formatting inductive geometrical reasoning. Participants with learning disabilities had higher achievement when dealing with haptic relative to pictorial representations of geometric shapes and bodies. Sixth graders performed better than fifth graders. Results are discussed in terms of the differences between the two categories of mild disabilities as well as with regard to the implementation of intervention programs.

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Błażejewski, Paweł, and Jakub Marcinowski. "Most adverse geometrical imperfections of steel spherical shells." Budownictwo i Architektura 13, no. 3 (September 11, 2014): 219–26. http://dx.doi.org/10.35784/bud-arch.1823.

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Steel, spherical shells subjected to an external pressure are exposed to the loss of stability and such a phenomenon determines the global resistance of such shells. Unavoidable, geometric imperfections present is this class of shells affect significantly global resistance of shells. The imperfection form corresponding to the first and second buckling modes, analysed in previous works of authors, do not cover all possible and observed in reality imperfection modes. The specification and comparison of other imperfections encountered in practice will allow to identify the most adverse ones. Additionally to the imperfection forms also their amplitudes were analysed. Consequently the ranges in which considered imperfection form is in fact the most adverse were determined. On the basis of this knowledge, the designer can choose the most adverse imperfection mode for given quality fabrication class of the shell.

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Soury-Lavergne, Sophie, and Michela Maschietto. "Articulation of spatial and geometrical knowledge in problem solving with technology at primary school." ZDM 47, no. 3 (May 22, 2015): 435–49. http://dx.doi.org/10.1007/s11858-015-0694-3.

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Di Stefano, F., A. Gorreja, E. S. Malinverni, and C. Mariotti. "KNOWLEDGE MODELING FOR HERITAGE CONSERVATION PROCESS: FROM SURVEY TO HBIM IMPLEMENTATION." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLIV-4/W1-2020 (September 3, 2020): 19–26. http://dx.doi.org/10.5194/isprs-archives-xliv-4-w1-2020-19-2020.

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Abstract. This paper aims to develop a strategy for architectural knowledge modeling in order to actively support the built heritage conservation process by fostering collaboration among stakeholders and interoperability between datasets. The integration of two modeling systems, one ontology-based and one in BIM environment, seems to be the right way to meet this objective: the former is rather exhaustive to represent the semantic contents of conservation activities, especially non-geometrical data, the latter is absolutely suitable to represent the logic of the construction, above all geometrical-constructive aspects typical of any architectural organism. Thus, this study proposes a side-by-side approach to synchronize these different ways of representing reality by managing the complexity of cultural heritage on the one hand and of technology tools, such as information systems, on the other. The proposed methodology was tested on the city walls of San Ginesio (Macerata, Italy) and included different steps considering the in-use technologies (notably geomatics and information technologies) as key enablers to acquire, hierarchically order, model and enrich the knowledge of that heritage site. The result is a knowledge-led strategy moving from survey to HBIM implementation, as a way to enhance representation and management in architectural heritage processes.

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Алексюк, А., and A. Aleksyuk. "Laboratory Practicum on Computer Graphics." Geometry & Graphics 5, no. 3 (September 28, 2017): 78–85. http://dx.doi.org/10.12737/article_59bfa72b151052.53229281.

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To master such important section of computer graphics as “Geometric Transformations of Coordinates” have been proposed laboratory works on discipline “Engineering and Computer Graphics” for MSUN students of specialties 27.03.04 “Management in Engineering Systems” and 09.03.01 “Informatics and Computer Engineering”. In contrast to existing laboratory works on computer graphics, demanding the knowledge of algorithmic languages and programming essentials, the presented tasks are performed in a MathCAD package, which allows represent results in the form of geometrical drawings without writing complicated computer programs. In this paper are considered elementary geometrical transformations and their compositions. Matrixes of object coordinates transformations at transfer, rotation and scaling on the plane and in space have been described. Constructions of orthogonal, axonometric and central projections on screen plane have been considered. Distinctions in algorithms for objects’ geometrical transformations above reference zero and arbitrary point have been noted. It has been showed that the end result of complex transformations depends on sequence of elementary transformations. A large number of examples covering the laboratory practicum’s content have been provided. Results have been presented in the form of numbers and drawings using MathCAD. In the first laboratory work have been considered the objects geometrical transformations (transfer, rotation and scaling) on the plane and in space; in the second one – construction of central, orthogonal and axonometric projections for three-dimensional objects on a computer screen (plane). Have been developed methodological instructive regulations for performance of laboratory and independent works which are used for students training on the MSUN’s descriptive geometry and graphics chair.

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Purnomo, Yoppy Wahyu, Masitah Sharill, Olivia Pandansari, Rika Susanti, and Winarni Winarni. "Cognitive demands on geometrical tasks in Indonesian elementary school mathematics textbook." Jurnal Elemen 8, no. 2 (July 1, 2022): 466–79. http://dx.doi.org/10.29408/jel.v8i2.5235.

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Examples and exercises in mathematics textbooks have an essential role in directing teaching and learning to achieve the objectives of the mathematics curriculum. This study examines mathematical tasks, i.e., examples and exercises, for a grade 4 elementary school mathematics textbook published by the Indonesian Government in 2018. We focus on geometry tasks and categorize them based on the dimensions of cognitive processes and knowledge of the revised Bloom’s taxonomy. Textbook research is used to achieve the objectives of this study. The validity of the data was carried out by employing peer debriefing. The findings of this study indicate that only about 30% of the geometry tasks in this mathematics textbook require high-level mathematical thinking skills. This study also shows that procedural knowledge is more dominant and becomes an orientation in presenting geometry tasks. This finding becomes less relevant to the orientation of researchers and policymakers who want the direction of mathematics education to be forming students as problem solvers.

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Theodorakopoulos, Ilias, Foteini Fotopoulou, and George Economou. "Geometric Regularization of Local Activations for Knowledge Transfer in Convolutional Neural Networks." Information 12, no. 8 (August 19, 2021): 333. http://dx.doi.org/10.3390/info12080333.

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In this work, we propose a mechanism for knowledge transfer between Convolutional Neural Networks via the geometric regularization of local features produced by the activations of convolutional layers. We formulate appropriate loss functions, driving a “student” model to adapt such that its local features exhibit similar geometrical characteristics to those of an “instructor” model, at corresponding layers. The investigated functions, inspired by manifold-to-manifold distance measures, are designed to compare the neighboring information inside the feature space of the involved activations without any restrictions in the features’ dimensionality, thus enabling knowledge transfer between different architectures. Experimental evidence demonstrates that the proposed technique is effective in different settings, including knowledge-transfer to smaller models, transfer between different deep architectures and harnessing knowledge from external data, producing models with increased accuracy compared to a typical training. Furthermore, results indicate that the presented method can work synergistically with methods such as knowledge distillation, further increasing the accuracy of the trained models. Finally, experiments on training with limited data show that a combined regularization scheme can achieve the same generalization as a non-regularized training with 50% of the data in the CIFAR-10 classification task.

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Swafford, Jane O., Graham A. Jones, and Carol A. Thornton. "Increased Knowledge in Geometry and Instructional Practice." Journal for Research in Mathematics Education 28, no. 4 (July 1997): 467–83. http://dx.doi.org/10.5951/jresematheduc.28.4.0467.

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This study examined the effects on instruction of an intervention program designed to enhance teachers' knowledge of geometry and their knowledge of research on student cognition in geometry. Forty-nine middle-grade (4-8) teachers participated in a 4-week program consisting of a content course in geometry and a research seminar on van Hiele theory. The pretest and posttest results showed significant gains in content knowledge and in van Hiele level. The analysis of a lesson-plan task revealed a significant shift in goals and expectations to the next higher van Hiele level. Follow-up observations of 8 teachers found marked changes in what was taught, how it was taught, and the characteristics teachers displayed. Teachers attributed these changes to increased geometrical content knowledge and research-based knowledge of student cognition.

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Obaidat, Mohammed Taleb, Turki I. Al-Suleiman, and Khalid A. Ghuzlan. "A stereometric knowledge-based system for maintenance of street networks." Canadian Journal of Civil Engineering 25, no. 2 (April 1, 1998): 220–31. http://dx.doi.org/10.1139/l97-084.

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The main objective of this work was to investigate the potential of integrating a stereometric vision system, i.e., using digital stereo images, and a knowledge-based system for flexible pavement distress classification. Classification process includes distress type, severity level, and options for repair. A hybrid stereo vision and knowledge-based system (called K-PAVER) was developed. The system extracts distress measurements using a PC-based stereo vision system. Geometric surface measurements such as point locations, distances, areas, volumes, and surface areas could also be computed. The knowledge-based system developed utilizes a set of if...then rules from the PAVER system (a pavement maintenance management system for roads and streets) and related literatures. New parameters, including shape parameters, orientation, and some geometrical measurements, were introduced to the system in order to facilitate the distress classification process. A criterion for maintenance priorities based on four parameters was developed. These parameters are pavement condition index, average daily traffic, location of distressed pavement, and street class. Surface measurements and automatic classification decision-making were validated and tested for all distress types. The developed system gives accurate results in both the measurement mode and the decision-making phase. This result opens the door for a fully automated distress classification process without any human intervention.Key words: knowledge-based systems, vision systems, stereo measurements, flexible pavement distresses, maintenance priorities, pavement maintenance management systems.

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