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Journal articles on the topic 'Geometrical Construction'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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1

Tan, S. T., M. M. F. Yuen, and K. M. Yu. "Parameterized Object Design Using a Geometrical Construction Representation." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 207, no. 1 (February 1993): 21–30. http://dx.doi.org/10.1243/pime_proc_1993_207_058_02.

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This paper proposes a geometrical construction interpretation of variational geometry for achieving parameterized object definition. Vector geometry is used to represent the various kinds of geometrical entities while dimensions are defined to have directional sense. Geometrical constructions are then used to link up all geometrical entities and dimensions of a solid in a meaningful way, to represent the variational geometry properly. The geometrical construction scheme is implemented in a prototype modeller using polyhedral solids as examples.
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2

Patel, Himani. "Geometrical Construction of Solar Eclipse." International Journal for Research in Applied Science and Engineering Technology 8, no. 5 (May 31, 2020): 1150–56. http://dx.doi.org/10.22214/ijraset.2020.5182.

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3

Parameswara, Rajasekhar, and Parameswara Aiyer Nilakanta. "Conditions For Geometrical Construction of Polygons." International Journal of Mathematics Trends and Technology 67, no. 1 (January 25, 2021): 1–8. http://dx.doi.org/10.14445/22315373/ijmtt-v67i1p501.

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4

Saveljev, V. A. "Geometrical Shaping of Reticulated Shells." International Journal of Space Structures 7, no. 1 (March 1992): 11–24. http://dx.doi.org/10.1177/026635119200700102.

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The problem of geometrical shaping consists of the construction of an abstract mathematical model representing a geometrical diagram of the structure. The paper considers the methods of geometrical construction of single and double-layer reticulated surfaces with equilateral quadrangular and hexagonal cells.
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Touhami, Abderrahmane Ouazzani, Nadia Benjellouna, Mohamed Alamia, and Haddou Aounia. "Experimentation of Java Software of Geometrical Optics JSGO during the geometrical construction of the virtual image." INTERNATIONAL JOURNAL OF RESEARCH IN EDUCATION METHODOLOGY 5, no. 3 (December 30, 2014): 730–41. http://dx.doi.org/10.24297/ijrem.v5i3.3898.

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This work aims to study the impact of using Java Software of Geometrical Optics JSGO on the geometrical construction success of the virtual image among the pupils in the first year of Baccalaureate, option: Experimental Sciences (ES).To examine this impact, we realized an experiment towards the end of the school year 2012/2013 among a group of learner consisting of 43 pupils. These pupils took a pretest using the traditional method, followed by a formation on how to use JSGO and finally they set for a posttest using the mentioned software.The analysis of the results of our study “evolution of the nature of geometrical constructions produced” confirms that using JSGO does not induce, in any case, the pupils to make an error in the construction of the virtual image.By analyzing the results concerning “pupils’ conceptual difficulties” we have scored the presence of the conceptual difficulty associated with an incorrect status that about 32 % of learners attribute to the construction ray extension. The use of JSGO provides a useful tool to overcome this conceptual difficulty. This analysis also indicates that, despite the interactive character of JSGO, about 12 % of pupils still face the conceptual difficulty related to the correspondence image object (punctual and global) and also to the conceptual difficulty related to the minimum number of rays departing from the same point of the luminous object.Finally, the study of “pupils’ perceptions about using JSGO” showed that the participants are very satisfied with using this computer wizard.
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Bertrand, Christine, and Richard Kerner. "Geometrical construction of a generalized Skyrme Lagrangian." Letters in Mathematical Physics 18, no. 3 (October 1989): 193–99. http://dx.doi.org/10.1007/bf00399967.

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7

Fedosov, Boris V. "A simple geometrical construction of deformation quantization." Journal of Differential Geometry 40, no. 2 (1994): 213–38. http://dx.doi.org/10.4310/jdg/1214455536.

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8

Варепо, Л., L. Varepo, О. Трапезникова, O. Trapeznikova, К. Панчук, K. Panchuk, А. Ляшков, A. Lyashkov, А. Голунов, and A. Golunov. "Computer Visual Representation For the Color Gamut of Reproduction Systems For Multicolor Image." Geometry & Graphics 5, no. 3 (September 28, 2017): 86–91. http://dx.doi.org/10.12737/article_59bfa789185862.08033475.

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Methods of surfaces’ geometric simulation are widely used for construction of different solid figures. Colours at the XYZ color system are located at the same distance stated geometrically. It doesn't generate a complete visual presentation for the color gamut of reproduction system for multicolor image. The computer visualization of correspondent pictures at multicolor image’s reproduction accuracy estimation is one of priority tasks. In this paper have been presented results related to practical implementation of geometrical model and software for evaluation of printing system’s color reproduction, construction of color gamut bodies, and a projection representation of reproducible colors’ geometric models for different playback systems: additive and autotype synthesis of color. The color gamut construction is performed over CIE L*a*b* color space. The color is presented as the one lightness coordinate and two color-difference coordinates of chromaticity. A color gamut body volume calculation has been performed in automated mode using software tools. Calculation of the playback system’s color gamut is carried out with Qhull (Quickhull) algorithm realised in the Matlab software. The practical algorithm realisation has been considered on example of ink jet printing based on Epson 3880. The color gamut bodies’ surfaces projections construction was performing in light tones (lightness L = 80), middle tones (L = 50), and shadow tones (L = 20). Has been performed a section of the color gamut bodies’ constructed surfaces. Have been demonstrated the results of computer visualization for geometrical models interpreting the multicolor image’s reproduction accuracy relative to the original.
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Semerich, Yuriy. "ANALYTICAL MODELLING OF PERFORATED GEOMETRICAL DOMAINS BY THE R-FUNCTIONS." Mathematical Modelling and Analysis 25, no. 3 (July 8, 2020): 490–504. http://dx.doi.org/10.3846/mma.2020.11174.

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This paper deals with the construction of boundary equations for geometric domains with perforation. Different types of perforated geometric domains are considered. The R-functions method for analytical modelling of perforated geometrical domains is used. For all constructed equations, function plots are obtained.
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10

Vallo, Dušan. "Methodology of Geometrical Construction Tasks in DGS' Environment." Acta Mathematica Nitriensia 2, no. 1 (2016): 13–18. http://dx.doi.org/10.17846/amn.2016.2.1.13-18.

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Drábeková, Janka, and Martina Grófová. "Methodology of Geometrical Construction Tasks in DGS' Environment." Acta Mathematica Nitriensia 2, no. 2 (October 2016): 19–27. http://dx.doi.org/10.17846/amn.2016.2.2.19-27.

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Chytrý, Vlastimil, Roman Kroufek, and Jindřich Polák. "Methodology of Geometrical Construction Tasks in DGS' Environment." Acta Mathematica Nitriensia 3, no. 2 (October 2017): 15–23. http://dx.doi.org/10.17846/amn.2017.3.2.15-23.

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13

Mahmoudi, M. G. "102.33 A geometrical construction involving two intersecting circles." Mathematical Gazette 102, no. 554 (June 18, 2018): 335–39. http://dx.doi.org/10.1017/mag.2018.75.

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14

Brinkhuis, Jan. "On a geometrical construction of the multipler rule." Indagationes Mathematicae 11, no. 4 (December 2000): 517–24. http://dx.doi.org/10.1016/s0019-3577(00)80020-8.

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15

Kolwicz, Paweł, and Karol Leśnik. "Topological and geometrical structure of Calderón-Lozanovskiĭ construction." Mathematical Inequalities & Applications, no. 1 (2010): 175–96. http://dx.doi.org/10.7153/mia-13-14.

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16

Eiseman, Peter R. "The geometrical construction of pointwise distributions on curves." Applied Mathematics and Computation 21, no. 3 (February 1987): 233–75. http://dx.doi.org/10.1016/0096-3003(87)90004-x.

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17

Runčochář, M., J. Drahos, and J. Vrba. "Fuzzy number as a product of geometrical construction." Fuzzy Sets and Systems 83, no. 1 (October 1996): 43–49. http://dx.doi.org/10.1016/0165-0114(95)00328-2.

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18

Sidoli, Nathan, and Ken Saito. "The Role of Geometrical Construction in Theodosius’s Spherics." Archive for History of Exact Sciences 63, no. 6 (August 11, 2009): 581–609. http://dx.doi.org/10.1007/s00407-009-0045-2.

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19

Alpatov, Vadim. "Building constructions modelling problems in modern cae-systems." E3S Web of Conferences 135 (2019): 03066. http://dx.doi.org/10.1051/e3sconf/201913503066.

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This article is about choosing building structure analysis model question. Construction analysis model type choice affects result of counting. Result accuracy and reliability depends on analysis scheme choice. Using modern computers, there is a lot of alternative abilities of creation construction analysis model. This article is made to understand these analysis models features and their influence on result. An example of counting beam in six independent CAD systems is shown. Engineering simulation and design software, which base on finite elements method, were chosen for analysis. These counting models differ from each other only by geometrical scheme. Beam geometry modeling is performed using beam elements, shell elements and solid elements. The comparison of beam calculation results with its beam, shell and solid elements analysis scheme modelling was performed. The analysis of single factor (geometric scheme) influence on the results of beam calculation is shown. It was defined, that the choice of calculation complex does not affect the calculation result, if the geometrical counting models are completely identical. It was defined, that in case creating construction with various types finite elements there are differences in the calculation results. Difference in calculation results, using different geometrical models, is seen in using the same complex and in comparison of different complexes. It was defined, that difference in calculating internal forces and moments in beam for different geometrical models can be more than 10%.
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20

Wang, Xuan, and Xiao Peng Duan. "Geometry in Ethnic Garment Construction." Advanced Materials Research 175-176 (January 2011): 884–89. http://dx.doi.org/10.4028/www.scientific.net/amr.175-176.884.

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Ethnic garment construction was investigated from the perspective of geometry. Basic characteristics of ethnic garment construction of different regions and nationalities were analyzed and summarized. Features of silk and the decisive role playing in the forming of geometrical garment structure of Chinese ethnic costumes which have great impact on the style features of oriental ethnic costumes were mainly discussed. The aesthetic features and philosophic ideas silk endows Chinese traditional garment were also discussed. By exploring the wisdom and skills of ethnic garment construction design, the geometric characteristics of ethnic garment construction, the basic rule of changes in ethnic garment construction and the essence of the construction structure variation were revealed. Inspiration from the techniques of ethnic garment construction design will be valuable for us to explore innovative ideas for today’s fashion design.
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21

Siripongsakul, Thamrongsin, Panya Wiman, Phichai Saranyachot, and Somrerk Chandra-Ambhorn. "Geometrical Construction of Auxiliary Axes in an Ellingham Diagram." Key Engineering Materials 856 (August 2020): 1–7. http://dx.doi.org/10.4028/www.scientific.net/kem.856.1.

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To facilitate the assessment of the oxide stability in H2-H2O or CO-CO2 atmospheres, auxiliary axes are constructed in the Ellingham diagram. Based on A. Ghosh’s approach, the geometrical interpretation of the diagram is proposed for the reaction 2X + O2 = 2Y, where X and Y could be originated from H2 and H2O or CO and CO2. Two cases are considered when oxygen partial pressures are lower and higher than one bar. By a geometrical method, it is proved that with an appropriate set-up of values relating to the auxiliary axes, the axes representing the ratio between the equilibrium partial pressure of hydrogen and that of water vapour, as well as the ratio between the equilibrium partial pressure of carbon monoxide and that of carbon dioxide, can be constructed. The geometrical method on the construction of axes using thermodynamic derivation is explained in the paper.
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22

Coll, Bartolomé, Joan J. Ferrando, and Juan A. Morales-Lladosa. "Emission and null coordinates: geometrical properties and physical construction." Journal of Physics: Conference Series 314 (September 22, 2011): 012105. http://dx.doi.org/10.1088/1742-6596/314/1/012105.

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23

Fujiwara, Y. "Geometrical construction of holonomy in three-dimensional hyperbolic manifold." Classical and Quantum Gravity 10, no. 2 (February 1, 1993): 219–32. http://dx.doi.org/10.1088/0264-9381/10/2/005.

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24

SUGIYAMA, Fumiko, and Taketoshi NOJIMA. "817 Geometrical Construction of Curved Folding and Its Applications." Proceedings of the Dynamics & Design Conference 2012 (2012): _817–1_—_817–9_. http://dx.doi.org/10.1299/jsmedmc.2012._817-1_.

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25

ANAZAWA, MASAHIRO, and ATUSHI ISHIKAWA. "GEOMETRICAL CONSTRUCTION OF HETEROGENEOUS LOOP AMPLITUDES IN 2D GRAVITY." International Journal of Modern Physics A 17, no. 28 (November 10, 2002): 4069–80. http://dx.doi.org/10.1142/s0217751x02011448.

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We study a disk amplitude which has a complicated heterogeneous matter configuration on the boundary in a system of the (3,4) conformal matter coupled to two-dimensional gravity. It is analyzed using the two-matrix chain model in the large N limit. We show that the disk amplitude calculated by Schwinger–Dyson equations can be completely reproduced through purely geometrical consideration. From this result, we speculate that all heterogeneous loop amplitudes can be derived from the geometrical consideration and the consistency among relevant amplitudes.
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26

Heydari, Hoshang. "Selective Phase Rotation Quantum Gate Entangler." Open Systems & Information Dynamics 16, no. 04 (December 2009): 407–12. http://dx.doi.org/10.1142/s1230161209000293.

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We construct a quantum gate entangler for multi-qubit states based on a selective phase rotation transform. In particular, we establish a relation between the quantum integral transform and the quantum gate entangler in terms of universal controlled gates for multi-qubit states. Our result gives an effective way of constructing topological and geometrical quantum gate entanglers for multipartite quantum systems, which could also lead to a construction of geometrical quantum algorithms.
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Balázs, L. "The geometrical background of inversion." Acta Geodaetica et Geophysica Hungarica 47, no. 2 (June 2012): 141–48. http://dx.doi.org/10.1556/ageod.47.2012.2.3.

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28

BENVEGNÙ, ALBERTO, and MAURO SPERA. "ON UNCERTAINTY, BRAIDING AND ENTANGLEMENT IN GEOMETRIC QUANTUM MECHANICS." Reviews in Mathematical Physics 18, no. 10 (November 2006): 1075–102. http://dx.doi.org/10.1142/s0129055x06002863.

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Acting within the framework of geometric quantum mechanics, an interpretation of quantum uncertainty is discussed in terms of Jacobi fields, and a connection with the theory of elliptic curves is outlined, via classical integrability of Schrödinger's dynamics and the cross-ratio interpretation of quantum transition probabilities. Furthermore, a thoroughly geometrical construction of all special unitary representations of the 3-strand braid group on the quantum 1-qubit space is given, and the connection of one of them with elliptic curves admitting complex multiplication automorphisms — the physically relevant one corresponding to the anharmonic ratio — is shown. Also, contact is made with the Temperley–Lieb algebra theoretic constructions of Kauffman and Lomonaco, and it is shown that the standard trace relative to one of the above representations computes the Jones polynomial for particular values of the parameter, for knots arising as closures of 3-strand braids. Subsequently, a geometric entanglement criterion (in terms of Segre embeddings) is discussed, together with a projective geometrical portrait for quantum 2-gates. Finally, Aravind's idea of describing quantum states via knot theory is critically analyzed, and a geometrical picture — involving a blend of SU(2)-representation theory, classical projective geometry, binary trees and Brunnian and Hopf links — is set up in order to describe successive measurements made upon generalized GHZ states, close in spirit to the quantum knot picture again devised by Kauffman and Lomonaco.
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Čučaković, Aleksandar, and Biljana Jović. "The advantages of using digital 3D animation in geometrical education." SAJ - Serbian Architectural Journal 9, no. 2 (2017): 65–82. http://dx.doi.org/10.5937/saj1701065q.

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New media technologies and interdisciplinary approach is used and represented in this paper. The aspects and research results are shown through the production methodology, multimedia learning tool and the final application in geometrical education. The method we used here is obtained from overlapping of multiple disciplines such as architecture, structural systems, descriptive geometry and computer animation. Geometrical construction is presented on visual dynamic educational device for students of technical and applied arts faculties. Multimedia DVD is named: "Geometrical education by using 3D animation principles and tools". Geometrical education enables development of the understanding and perception of space as well as the ability of spatial representation. Drawing is not the goal of geometrical education. Our aim is to simplify the perception of geometrical construction, and by the method is proposed in this paper it is quite possible.
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Clouet, Axel, Jérôme Vaillant, and David Alleysson. "Physical noise propagation in color image construction: a geometrical interpretation." Color and Imaging Conference 2019, no. 1 (October 21, 2019): 375–80. http://dx.doi.org/10.2352/issn.2169-2629.2019.27.67.

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To avoid false colors, classical color sensors cut infrared wavelengths for which silicon is sensitive (with the use of an infrared cutoff filter called IR-cut). However, in low light situation, noise can alter images. To increase the amount of photons received by the sensor, in other words, the sensor's sensitivity, it has been proposed to remove the IR-cut for low light applications. In this paper, we analyze if this methodology is beneficial from a signal to noise ratio point of view when the wanted result is a color image. For this aim we recall the formalism behind physical raw image acquisition and color reconstruction. A comparative study is carried out between one classical color sensor and one specific color sensor designed for low light conditions. Simulated results have been computed for both sensors under same exposure settings and show that raw signal to noise ratio is better for the low light sensor. However, its reconstructed color image appears more noisy. Our formalism illustrates geometrically the reasons of this degradation in the case of the low light sensor. It is due on one hand to the higher correlation between spectral channels and on the other hand to the near infrared part of the signal in the raw data which is not intrinsically useful for color.
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Jia, Xi Bin, and Mei Xia Zheng. "Video Based Visual Speech Feature Model Construction." Applied Mechanics and Materials 182-183 (June 2012): 1367–71. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1367.

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This paper aims to give a solutions for the construction of chinese visual speech feature model based on HMM. We propose and discuss three kind representation model of the visual speech which are lip geometrical features, lip motion features and lip texture features. The model combines the advantages of the local LBP and global DCT texture information together, which shows better performance than the single feature. Equally the model combines the advantages of the local LBP and geometrical information together is better than single feature. By computing the recognition rate of the visemes from the model, the paper shows the HMM which describing the dynamic of speech, coupled with the combined feature for describing the global and local texture is the best model.
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32

Rediske, Arthur Clair. "The Trisection of an Arbitrary Angle." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 2 (April 18, 2018): 7640–69. http://dx.doi.org/10.24297/jam.v14i2.7402.

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This paper presents an elegant classical geometric solution to the ancient Greek's problem of angle trisection. Its primary objective is to provide a provable construction for resolving the trisection of an arbitrary angle, based on the restrictions governing the problem. The angle trisection problem is believed to be unsolvable for compass-straightedge construction. As stated by Pierre Laurent Wantzel (1837), the solution of the angle trisection problem corresponds to an implicit solution of the cubic equation x cubed minus 3x minus 1 equals 0, which is algebraically irreducible, and so is the geometric solution of the angle trisection problem. The goal of the presented solution is to show the possibility to solve the trisection of an arbitrary angle using the traditional Greek's tools of geometry (a classical compass and straightedge) by changing the problem from the algebraic impossibility classification to a solvable plane geometrical problem. Fundamentally, this novel work is based on the fact that algebraic irrationality is not a geometrical impossibility. The exposed methods of proof have been reduced to the Euclidean postulates of classical geometry.
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Графский, O. Grafskiy, Пономарчук, and Yu Ponomarchuk. "On One Property of a Circle on the Coordinate Plane." Geometry & Graphics 5, no. 2 (July 4, 2017): 13–24. http://dx.doi.org/10.12737/article_5953f2af770c35.65774157.

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Descartes’ and Fermat's method allowed to define many geometrical forms, including circles, on the coordinate plane by means of the arithmetic equations and to make necessary analytical operations in order to solve many problems of theoretical and applied research in various scientific areas, for example. However, the equations of a circle and other conics in the majority of research topics are used in the subsequent analysis of applied problems, or for analytical confirmation of constructive solutions in geometrical research, according to Russian geometrician G. Monge and others, including. It is natural to consider a circle as a locus of points, equidistant from a given point — a center of the circle, with a constant distance R. There is another definition of a circle: a set of points from which a given segment is visible under constant directed angle. Besides, a circle is accepted to model the Euclid plane in the known scheme of non-Euclidean geometry of Cayley-Klein, it is the absolute which was given by A. Cayley for the first time in his memoirs. It is possible to list various applications of this geometrical form, especially for harmonism definition of the corresponding points, where the diametral opposite points of a circle are accepted as basic, and also for construction of involutive compliances. The construction of tangents to a circle can be considered as a classical example. Their constructive definition is simple, but also constructions on the basis of known projective geometry postulates are possible (a hexagon when modeling a series of the second order, Pascal's lines). These postulates can be applied to construction of tangents to a circle (to an ellipse and hyperboles to determination of imaginary points of intersection of a circle and a line. This paper considers the construction of tangents to a circle without the use of arches of auxiliary circles, which was applied in order to determine the imaginary points of intersection of a circle and a line (an axis of coordinates). Besides, various dependences of parameter p2, which is equal to the product of the values of the intersection points’ coordinates of a circle and coordinate axes, are analytically determined.
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Браилов and A. Brailov. "The Analysis of Measurement Systems for the Construction of Geometrical Models of the Product." Geometry & Graphics 4, no. 1 (March 17, 2016): 34–43. http://dx.doi.org/10.12737/18056.

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In the present work, on the basis of the analysis of existing systems of measurement for geometrical modeling, their components are defined. The system of measurement for geometrical modeling consists of three mutually perpendicular planes H-П1, F-П2, P-П3 and connected with them right three-dimensional system of coordinates OXYZ. The major features of such system related to ways of formation of the two-dimensional complex drawing of a geometrical image on the basis of laws of projective connections are revealed. As the first feature of systems of measurement for geometrical modeling it is possible to allocate a way of orientation (binding) of the right three-dimensional system of co-ordinates OXYZ concerning the set planes of projections H-П1, F-П2, P-П3. The second feature of systems of measurement for geometrical modeling is the way of conditional division of space on a part (semi spaces, quadrants, and octants). The third feature of systems of measurement for geometrical modeling is the way of numbering of the allocated parts of space (semi spaces, quadrants, and octants). Interrelations of elements of different systems of measurement with different projections of a geometrical image are defined. The relative location of projections of a geometrical image into the constructed two-dimensional complex drawings for various systems of measurement is determined. For the American system of measurement in the two-dimensional complex drawing of a geometrical image the horizontal projection is located above a frontal projection, and the profile projection is located to the right of a frontal projection. For the European system of measurement in the two-dimensional complex drawing of a geometrical image the horizontal projection is located below a frontal projection, and the profile projection is located to the right of a frontal projection. The logic behind a particular arrangement of views in the projective drawing of a product in the analyzed systems of measurement is explained. For the realized way of construction of the complex drawing in the American system of measurement the horizontal projection is the bottom view, and the profile projection is the left-side view. For the realized way of construction of the complex drawing in the European system of measurement the horizontal projection is the top view, and the profile projection is the left-side view.
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35

Klusák, Jan, and Zdeněk Knésl. "A Bi-Material Wedge – a Model for the Prediction of Failure Initiation at Shape and Material Discontinuities." Key Engineering Materials 324-325 (November 2006): 1305–8. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.1305.

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Geometrical and material discontinuities in constructions lead to singular stress concentrations and consequently to a crack initiation. The model of a bi-material wedge makes it possible to analyse such construction points to assess their stability. The presented approach is based on the knowledge of the strain energy density factor distribution in the concentrator vicinity.
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Lee, C. K. "Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 1: Construction of underlying geometrical model." International Journal for Numerical Methods in Engineering 56, no. 11 (2003): 1593–614. http://dx.doi.org/10.1002/nme.630.

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37

Kotov, Alexei, and Thomas Strobl. "Lie algebroids, gauge theories, and compatible geometrical structures." Reviews in Mathematical Physics 31, no. 04 (April 17, 2019): 1950015. http://dx.doi.org/10.1142/s0129055x19500156.

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The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge invariance of the construction, need to satisfy particular compatibility conditions. This paper is supposed to analyze these compatibilities from a mathematical perspective.In particular, we show that the compatibility of a connection with a Lie algebroid that one finds is the Cartan condition, introduced previously by A. Blaom. For the metric on the base [Formula: see text] of a Lie algebroid equipped with any connection, we show that the compatibility suggested from gauge theories implies that the foliation induced by the Lie algebroid becomes a Riemannian foliation. Building upon a result of del Hoyo and Fernandes, we prove, furthermore, that every Lie algebroid integrating to a proper Lie groupoid admits a compatible Riemannian base. We also consider the case where the base is equipped with a compatible symplectic or generalized Riemannian structure.
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38

Виситаева, М., and Maret Visitaeva. "Classification of Abilities of High School Students in the Geometry Study." Profession-Oriented School 6, no. 3 (July 18, 2018): 43–51. http://dx.doi.org/10.12737/article_5b2782842d7ec6.86271773.

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The classifi cation of skills, which are the basis of mathematical abilities of students for basic and advanced levels are given: possession of basic techniques common training activities; possession of creative techniques and research training activities; image and the construction of geometrical figures; possession of the basic methods associated with the defi nition of the mutual position, properties and characteristics of geometric shapes and their components; handling trigonometric functions of an acute angle; based on real or mentally (vectors, geometric shapes and geometric quantities).
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Touhami, Abderrahmane Ouazzani, Nadia Benjellouna, Mohamed Alamia, and Haddou Aounia. "Virtual image and pupils’ conceptual difficulties in the first year of Baccalaureate Experimental Sciences." INTERNATIONAL JOURNAL OF RESEARCH IN EDUCATION METHODOLOGY 5, no. 3 (December 30, 2014): 721–29. http://dx.doi.org/10.24297/ijrem.v5i3.3897.

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This paper presents a research on the pupils’ conceptual difficulties in the first year of Baccalaureate Experimental Sciences (ES) during the geometrical construction of the virtual image.The experimentation realized in this research takes into account the reality of the teaching in the classroom. It was conducted towards the end of the school year 2012/2013 among a group of learners consisting of 54 pupils. These pupils must only use the traditional method paper, pencil, ruler and protractor for doing tests.By analyzing the conceptual difficulties proven in the false geometrical constructions produced by the pupils, we have marked that the first variant sub-tests do not allow the emergence of the conceptual difficulty associated with the tracing of the construction ray extension. The construction of the virtual image through the second variant sub-tests has shown that about 32 % of pupils face against this conceptual difficulty, which is related to an incorrect status that the pupil attributes to the construction ray extension.After checking the conceptual difficulty related to the correspondence image object (punctual and global) and the conceptual difficulty associated with the minimum number of rays departing from the same point of the luminous object and also the difficulty in tracing a construction ray, it seems that the both variants don’t allow the emergence of these conceptual difficulties.
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Gladkov, Aleksandr Vjacheslavovich, Yury Vjacheslavovich Sivets, and Ksenya Yuryevna Avdeeva. "NEW APPROACH TO APPLICATION OF MATHEMATICAL APPARATUS FOR THE CONSTRUCTION OF THREE-DIMENSIONAL SPINE MODEL." Hirurgiâ pozvonočnika, no. 1 (March 14, 2005): 100–104. http://dx.doi.org/10.14531/ss2005.1.100-104.

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The paper presents a mathematical model with graphic visualization, which describes spine geometric parameters and conditions of their changes in time and space. Reduction of data file size necessary for reproduction of vertebra shape and storage of this structure in a computer with the least losses is achieved with algorithm of geometrical interpolation and vertebral body shape reconstruction – with trigonometric interpolation sums (TIS). The developed spine model is based on three concepts. A spline interpolation is used for reproduction of the whole spine. The spline polynomial is built on data received by calculation of transition matrices. This requires the parameters of not each point, but only of three key ones (in the basic spine levels). Application of spline interpolation considerably reduces time expenses for transition matrices calculation. The developed model takes into account the geometrical features of human vertebra, and changes of its kinematic characteristics in space and time. The model will allow observation of deformation of the whole spine caused by change of one or several randomly chosen parameters. Thus the geometrical characteristics necessary to calculate matrix chain of the second model are the results of the first model calculations. Having a set of the statistical data, the given model can be used for observation of spine response to various disturbing factors. After assigning initial spine parameters a graphic interpretation of the model will enable to receive a three-dimensional spine image, to shift and rotate it, to assign a direction of load application, to trace the changes in the spine shape during physiological movements and walking.
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Fujita, Mitsutaka, Mitsuho Yoshida, and Eiji Osawa. "Geometrical Study for Fullerene Structures and Construction of New Carbon Forms." TANSO 1994, no. 162 (1994): 100–109. http://dx.doi.org/10.7209/tanso.1994.100.

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42

Kennaway, Kristian D. "A geometrical construction of rational boundary states in linear sigma models." Nuclear Physics B 647, no. 3 (December 2002): 471–511. http://dx.doi.org/10.1016/s0550-3213(02)00898-2.

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43

Ramírez, José Luis, and Gustavo N. Rubiano. "A geometrical construction of inverse points with respect to an ellipse." International Journal of Mathematical Education in Science and Technology 45, no. 8 (May 7, 2014): 1254–59. http://dx.doi.org/10.1080/0020739x.2014.914255.

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44

Santana, Alejandro, Yohany Rodríguez, and Edgar A. Gómez. "Construction of ray diagrams in geometrical optics: a media-focused approach." Physics Education 47, no. 6 (October 22, 2012): 715–20. http://dx.doi.org/10.1088/0031-9120/47/6/715.

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Kennel, Matthew B., Reggie Brown, and Henry D. I. Abarbanel. "Determining embedding dimension for phase-space reconstruction using a geometrical construction." Physical Review A 45, no. 6 (March 1, 1992): 3403–11. http://dx.doi.org/10.1103/physreva.45.3403.

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Carrizosa, E., E. Conde, M. Mu�oz-Marquez, and J. Puerto. "Planar point-objective location problems with nonconvex constraints: A geometrical construction." Journal of Global Optimization 6, no. 1 (January 1995): 77–86. http://dx.doi.org/10.1007/bf01106606.

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47

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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Sabiniak, Henryk G., and Robert Cichowicz. "The Numerical Methods in Geometric Construction Mapping." Key Engineering Materials 490 (September 2011): 312–22. http://dx.doi.org/10.4028/www.scientific.net/kem.490.312.

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A dynamic development of numerical methods enables even so complicated geometrical modelling as modelling of hypoidal teeth, and in particular of worm teeth. Building on the basis of the finite element method of this type of geometrical mathematical model enables observing and analysing physical phenomena taking place in the teeth, e.g. changes of pressure distribution along the contact lines depending on the phase of meshing for particular cooperating pairs of teeth. Due to limited technical possibilities and mathematical apparatus such analyses were carried out only on the basis of the theory of plates with constant thickness. An unquestionable advantage of such numerical modelling is a short time needed to obtain final results, which enables profound analysis of the transmitted load. The knowledge of course of pressure distribution along the contact lines of particular pairs of intermeshing teeth in worm gears already in the design phase enables taking into consideration in adequate correction or even modification of the working surface of teeth, with the aim to equalise the distribution of pressure.
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Song, Weiju, Jun Xu, Xiaowei Wang, and Changjiang Liu. "Effect of Geometric Nonlinearity on Membrane Roof Stability in Air Flow." Shock and Vibration 2020 (April 9, 2020): 1–13. http://dx.doi.org/10.1155/2020/2305145.

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Membrane materials are widely used in construction engineering with small mass and high flexibility, which presents strong geometric nonlinearity in vibration. In this paper, an improved multiscale perturbation method is used to solve the aerostatics stability of membrane roofs on closed and open structures by quantifying the effect of geometric nonlinearity on the single-mode aeroelastic instability wind velocity. Results show that the critical wind velocities of two models are smaller when the geometrical nonlinearity of the membrane material is neglected. In addition, under normal wind load, the influence of geometrical nonlinearity of the membrane on the aerodynamic stability of the roof can be neglected. However, under strong wind load, when the roof deformation reaches 3% of the span, the influence of geometric nonlinearity should be considered and the influence increases with the decrease of transverse and downwind span of the membrane roof. The results obtained in this paper have an important theoretical reference value for the design membrane structures.
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Свентиков, Андрей. "Geometrically Nonlinear Calculation of Trailing rod designs. Part 1. Calculation of flexible threads." Construction and Architecture 1, no. 1 (May 1, 2013): 7–17. http://dx.doi.org/10.12737/335.

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Is treated geometrically nonlinear matrix calculation core construction with the use of flexible threads. The first part is devoted to the study the major calculation dependencies of flexible threads. It is established that the geometric nonlinearity of flexible rods depends on the cube of the ratio of the calculation in a zero-offsets end stabilize relations to its current value. Also found that the constructive nonlinearity is a special case of geometrical nonlinearity and depends on the degree of impact on the VDS of flexible thread load on its own weight. It is found that the preliminary adjustment of the length of flexible rods leads to the increase of the share of the stresses of constant load and, accordingly, to the approximation of the nature of the work of these elements into a linear model.
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