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Journal articles on the topic 'Analytical geometry'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 January 2023

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1

Chambers, Ll G., Howard Anton, and Albert Harr. "Calculus with Analytical Geometry." Mathematical Gazette 81, no. 490 (March 1997): 171. http://dx.doi.org/10.2307/3618820.

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2

Lord, Nick, and Howard Anton. "Calculus with Analytical Geometry." Mathematical Gazette 78, no. 481 (March 1994): 85. http://dx.doi.org/10.2307/3619461.

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3

Stepanov, M. E., and S. N. Voronina. "Tactile Models in Analytical Geometry." Моделирование и анализ данных 12, no. 2 (2022): 83–102. http://dx.doi.org/10.17759/mda.2022120204.

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The article discusses some of the problems that arise when working with students with visual defects. In particular, the authors discuss ways to improve the culture of mathematical thinking of students with visual defects. The authors rely on the experience of working at the Faculty of Information Technologies of Moscow State University of Psychology & Education.
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4

Ghosh, Debdas, and Debjani Chakraborty. "Analytical fuzzy plane geometry I." Fuzzy Sets and Systems 209 (December 2012): 66–83. http://dx.doi.org/10.1016/j.fss.2012.02.011.

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5

Chakraborty, Debjani, and Debdas Ghosh. "Analytical fuzzy plane geometry II." Fuzzy Sets and Systems 243 (May 2014): 84–109. http://dx.doi.org/10.1016/j.fss.2013.06.016.

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6

Ghosh, Debdas, and Debjani Chakraborty. "Analytical fuzzy plane geometry III." Fuzzy Sets and Systems 283 (January 2016): 83–107. http://dx.doi.org/10.1016/j.fss.2014.10.018.

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7

Pamungkas, Dasilvawati, and Eyus Sudihartinih. "ANALISIS KEBUTUHAN MAHASISWA CALON GURU MATEMATIKA TERHADAP APLIKASI GEOGEBRA PADA PEMBELAJARAN GEOMETRI ANALITIK." Jurnal Pendidikan Matematika Universitas Lampung 9, no. 2 (June 30, 2021): 223–32. http://dx.doi.org/10.23960/mtk/v9i2.pp223-232.

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The purpose of this study was to analyze the needs of the GeoGebra application in mathematics learning, especially the learning of analytic geometry for prospective mathematics teacher students. This research is descriptive quantitative research with a survey method. Participants in this study were prospective teacher students who had taken a course in analytic geometry at a university in Bandung, Indonesia. The sample of this research is student-teacher candidates in the sixth, fourth and second semesters. The total sample was 72 students with 20 males and 52 females. The data collection instruments used questionnaires and interviews. Based on the results of the study, it is known that when learning analytical geometry, most students have difficulty visualizing geometric shapes so that students feel they need GeoGebra as a learning medium in lectures on analytic geometry.
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8

Xu, Jingyan, and Benjamin M. W. Tsui. "An Analytical Geometric Calibration Method for Circular Cone-Beam Geometry." IEEE Transactions on Medical Imaging 32, no. 9 (September 2013): 1731–44. http://dx.doi.org/10.1109/tmi.2013.2266638.

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9

Todd, Philip. "A Symbolic Dynamic Geometry System Using the Analytical Geometry Method." Mathematics in Computer Science 14, no. 4 (June 25, 2020): 693–726. http://dx.doi.org/10.1007/s11786-020-00490-0.

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10

Liu, Qipeng, Kun Yang, Yuehua Gao, Fencheng Liu, Chunping Huang, and Liming Ke. "Analytical Study of Powder Stream Geometry in Laser-Based Direct Energy Deposition Process with a Continuous Coaxial Nozzle." Crystals 11, no. 11 (October 27, 2021): 1306. http://dx.doi.org/10.3390/cryst11111306.

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In the process of laser-based direct energy deposition, the particle concentration distribution and geometric characteristics of powder flow play an important role in laser–powder interaction and powder utilization, and they affect the forming quality and accuracy. In the current study, based on the geometry information of a powder nozzle and the divergence angles of a powder jet at the nozzle outlet, the geometric profile of a powder stream is analyzed. A set of formulas for calculating the geometric characteristics of the powder stream is derived based on an analytic geometry method. The influence of each parameter on the geometric characteristics of the powder stream is further studied using single-factor and sensitivity analyses. Validation is performed by comparing the results from the presented analytical expressions with those from experiments and/or simulations in published papers. The analytical formulas provided in this paper are simple and practical, providing a theoretical foundation for the control of powder flow and related processes in the forming process.
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11

Yusupova, Anora K., and Nafisa I. Tokhtasinova. "TYPICAL MISTAKES OF STUDENTS IN ANALYTICAL GEOMETRY AND DIAGNOSTICS OF THE CAUSES OF ERRORS." CURRENT RESEARCH JOURNAL OF PEDAGOGICS 03, no. 01 (January 1, 2022): 1–8. http://dx.doi.org/10.37547/pedagogics-crjp-03-01-01.

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12

Susanto, Hari Purnomo, Nely Indra Meifiani, and Taufik Hidayat. "ANALISIS HUBUNGAN HASIL BELAJAR GEOMETRI BIDANG DENGAN KEMAMPUAN ANALITIS MAHASISWA PADA MATA KULIAH GEOMETRI ANALITIK BIDANG." Media Pendidikan Matematika 5, no. 2 (December 30, 2017): 84. http://dx.doi.org/10.33394/mpm.v5i2.1472.

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This article is a result of research that aims to determine the correlation between students' geometry learning outcomes with analytical ability in the eyes of analytic geometry. This research is a correlational research. the study was conducted at STKIP PGRI Pacitan, where the population is a mathematics education students who is taking analytical geometry courses. Data were taken from 21 students, with test technique, documentation and interview. Data analysis was done by using simple linear regression analysis concept and its calculation using SPSS 16. Based on data analysis, it was found that the result of geometry of field study had positive correlation with students' analytical thinking ability. The relationship falls into the medium category, and the learning outcomes have a predictor contribution to students' analytical ability of 22.5%.
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13

Сенченкова, L. Senchenkova, Иванов, G. Ivanov, Серегин, V. Seregin, Боровиков, and Ivan Borovikov. "Geometric Transformations in Descriptive Geometry And Engineering Graphics." Geometry & Graphics 3, no. 2 (June 10, 2015): 23–28. http://dx.doi.org/10.12737/12165.

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The publication is devoted to the analysis and justification of questions of teaching one of the most important sections of the course "Descriptive geometry" "Geometrical transformations". On the basis of critical analysis suggestions are made for improvement of a presentation technique of this section in the classroom and in academic literature, as well as for extension of application of geometrical transformations for the solution of position and metric tasks, surfaces modelling, and also for design of complex engineering forms that meets certain preassigned conditions.It is offered to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. Some conclusions are made, and the appropriate proposals on feasibility of coordination of movementtransformationteachingin the courses of analytical and descriptive geometry are made. It will provide interdisciplinary communications and allow students to be convinced in usefulness and expediency of a combination of analytical and graphic ways of geometric tasks solution. Implementation of these suggestions contained in the article will contribute to a real transformation of engineering and geometrical training and as a consequence, the quality of training specialists.
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14

Pugina, L. V., and G. I. Mihalyov. "A ROUND OF APPLAUSE FOR ANALYTICAL GEOMETRY." World of Transport and Transportation 16, no. 4 (August 28, 2018): 248–52. http://dx.doi.org/10.30932/1992-3252-2018-16-4-20.

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ABSTRACT The article is devoted to the well-known Russian mathematician Boleslav Mlodzeevsky (10.07.1858- 18.01.1923), who from 1896 to 1913 worked at Moscow Institute of Railway Engineers, now - RUT (MIIT), and was the first head of the Institute’s department of mathematics. Scientific works of the scientist refer to differential and algebraic geometry and its applications. They are of interest to future mathematicians today as well. He was the first to organize such a form of training as a mathematical seminar, read the first course on the theory of functions of real variable and set theory. He developed the Russian terminology of set theory. This year marks the 160th anniversary of a remarkable mathematician and a man who has left an excellent mark in history. Keywords: mathematics, history, differential and algebraic geometry, engineering education, Boleslav Mlodzeevsky, mathematical seminar, set theory, scientific societies.
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15

Woodhouse, N. M. J. "METHODS OF DIFFERENTIAL GEOMETRY IN ANALYTICAL MECHANICS." Bulletin of the London Mathematical Society 23, no. 1 (January 1991): 105–6. http://dx.doi.org/10.1112/blms/23.1.105.

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16

Boothby, William M. "Book Review: Symplectic geometry and analytical mechanics." Bulletin of the American Mathematical Society 20, no. 1 (January 1, 1989): 89–95. http://dx.doi.org/10.1090/s0273-0979-1989-15708-x.

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17

Bains, R. "Methods of differential geometry in analytical mechanics." Engineering Analysis with Boundary Elements 9, no. 4 (January 1992): 367. http://dx.doi.org/10.1016/0955-7997(92)90031-2.

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18

Chen, XiaoAn, and Hong Chen. "Analytical geometry method of planetary gear trains." Science China Technological Sciences 55, no. 4 (February 6, 2012): 1007–21. http://dx.doi.org/10.1007/s11431-011-4736-y.

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19

Tirira, J., P. Trocellier, and J. P. Frontier. "Analytical capabilities of ERDA in transmission geometry." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 45, no. 1-4 (January 1990): 147–50. http://dx.doi.org/10.1016/0168-583x(90)90805-5.

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20

Brauer, Jesper. "Analytical geometry of straight conical involute gears." Mechanism and Machine Theory 37, no. 1 (January 2002): 127–41. http://dx.doi.org/10.1016/s0094-114x(01)00062-3.

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21

Hu, De, Zhe Chen, and Fuliang Yin. "Analytical Geometry Calibration for Acoustic Transceiver Arrays." IEEE Signal Processing Letters 27 (2020): 1979–83. http://dx.doi.org/10.1109/lsp.2020.3035956.

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22

Pilat, Adam. "Analytical modeling of active magnetic bearing geometry." Applied Mathematical Modelling 34, no. 12 (December 2010): 3805–16. http://dx.doi.org/10.1016/j.apm.2010.03.021.

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23

Bains, R. "Methods of differential geometry in analytical mechanics." Advances in Engineering Software 14, no. 3 (January 1992): 237. http://dx.doi.org/10.1016/0965-9978(92)90034-d.

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24

Grigorieva, V. B. "Use of information technologies in teaching course "Analytical geometry" in higher schools on example of software "ANALYTICAL GEOMETRY"." Information Technologies in Education, no. 3 (April 15, 2009): 216–24. http://dx.doi.org/10.14308/ite000076.

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25

Batalaev, A. V. "USING THE DUALITY PRINCIPLE WHEN CONSTRUCTING EXERCISES AT THE GEOMETRY LESSONS." Vektor nauki Tol'yattinskogo gosudarstvennogo universiteta. Seriya Pedagogika i psihologiya, no. 4 (2021): 7–16. http://dx.doi.org/10.18323/2221-5662-2021-4-7-16.

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Geometry is one of the complex disciplines where many facts are interconnected. It is possible to develop the idea of facts interrelations through correlation using the duality principle. The duality principle is known in projective geometry, mathematical logic. This principle is clearly pronounced in one of the theorems of new triangle geometry. The traditional analytical geometry course does not study the facts of new triangle geometry. To reinforce many topics of the analytical geometry course, for example, “The distance between two points”, “The symmetrical form of the equation of a line”, “The angle between two lines”, it is reasonable to consider some facts from the new triangle geometry in the Cartesian coordinate system. Thus, an element of novelty is introduced to the reviewed material. The guidebooks on triangle geometry solve tasks through classical approaches or applying barycentric coordinates not using analytical geometry formulas. The paper proposes the constructing technique for the couples of exercises using the duality principle in the plane geometry teaching methods. Tasks are constructed for the Cartesian coordinate system as this allows demonstrating the duality of points in the drawings. In the composed exercises, two drawings are constructed in parallel columns. In different cases, the points can be the triangle-apexes, an orthocenter, or a height base. The initial triangle sides are located on the axes of coordinates, and their side lengths set up Pythagorean triple for better understanding the task-solving algorithm by the students. The symmetrical form of the equation of a line shows the necessity of analytical study since it is difficult to check the distance from the orthocenter to the orthotriangle sides in the drawings due to the small value. For many such information units, the aggregation relationships (whole-part) are set up, reflecting the geometric embedding of components.
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26

Dibra, Sebhia Marie, and Ulrich Winter. "Pentagram Geometry." JOURNAL OF ADVANCES IN PHYSICS 13, no. 4 (August 1, 2017): 4852–57. http://dx.doi.org/10.24297/jap.v13i5.6051.

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The Natural Constant Phi is included in the geometrical figure of a Pentagram as many artists have found out. Michelangelo may be the most famous one, whose sketch was transported in the payload of the first sucessful mission to the moon. By deriving this natural constant from the geometrics of the Pentagram a new analytical expression is found for Phi.
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27

Wang, Zhi Jian, Shi Yun Dong, Bin Shi Xu, and Wei Xia. "Laser Clad Geometry: Experimental Observation and Geometric Modeling." Advanced Materials Research 148-149 (October 2010): 628–32. http://dx.doi.org/10.4028/www.scientific.net/amr.148-149.628.

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In this paper, a new analytical method of laser clad geometric simulation was developed. The effects of laser process parameters such as laser power, scanning speed, and powder feed rate on estimating clad geometry were investigated in this approach. A series of cladding was prepared by 1 kW diode pumping solid-state laser, to characterize the cross-section image of the clad by optical microscope. The clad profile was fitted by pitch arc and line in AutoCAD, with results displaying the arc-like upper profile of the clad. The theoretical results are discussed and compared with experimental data. The simulation based on the mass conservation is capable of predicting the clad width and depth with reasonable accuracy at medium powder feed rate.
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MASTROLIA, PAOLO, MARCO RIGOLI, and MICHELE RIMOLDI. "SOME GEOMETRIC ANALYSIS ON GENERIC RICCI SOLITONS." Communications in Contemporary Mathematics 15, no. 03 (May 19, 2013): 1250058. http://dx.doi.org/10.1142/s0219199712500587.

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Kholid, Muhammad Noor, Lingga Nico Pradana, Swasti Maharani, and Annisa Swastika. "GeoGebra in Project-Based Learning (Geo-PJBL): A dynamic tool for analytical geometry course." Journal of Technology and Science Education 12, no. 1 (February 10, 2022): 112. http://dx.doi.org/10.3926/jotse.1267.

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The integration of learning models and software is a trend in mathematics courses. However, no existing learning model for geometry courses involves the students in the making of a tool or media project. The researchers noticed the potential of the project-based learning (PjBL) model and GeoGebra in analytical geometry courses. This study revealed differences in the influence of the Geo-PjBL and PjBL models on students’ achievement. The subjects consisted of 137 prospective mathematics teachers. The Basic Geometry Instrument (BGI) was used to measure the subjects’ initial ability in basic geometry, and the Geometry Analytic Instrument (GAI) was used to evaluate the model and prospective teachers’ performance. The Geo-PjBL and PjBL classroom activities lasted for 15 weeks. Both classrooms received the same content; the difference between the Geo-PjBL and PjBL classrooms was the tools used to present the problems and the project results. An analysis of covariance (ANCOVA) was conducted to analyze the data (α = 0.01). The Geo-PjBL model is more effective in applying analytical geometry subjects that require precision and accurate visual illustrations. Meanwhile, in the range of algebraic operations, the Geo-PjBL model is as effective as the PjBL model.
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Dobrina, E. A. "POSSIBILITIES OF USING INTERDISCIPLINARY CONNECTIONS OF MATHEMATICAL ANALYSIS AND ANALYTICAL GEOMETRY IN MATHEMATICS CLASSES (FOR STUDENTS OF MATHEMATICAL SPECIALTIES OF SECONDARY PROFESSIONAL EDUCATION)." Educational Psychology in Polycultural Space 59, no. 3 (2022): 89–97. http://dx.doi.org/10.24888/2073-8439-2022-59-3-89-97.

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Motivation of students of mathematical specialties to study various sections of higher mathematics, in particular, mathematical analysis, has not increased in recent years. This undoubtedly leads to a gradual decrease in the level of mathematical training of students. The purpose of the article is to consider the possibilities of using interdisciplinary connections of mathematical analysis and analytical geometry in the educational process for students of mathematical specialties of the Institute of Secondary professional eduation. The article discusses the methods: 1) the implementation of interdisciplinary connections and 2) mathematical modeling. We believe that these methods will help to increase the level of motivation to study mathematical analysis among students. In particular, we consider the problems of calculating integrals using higher-order curves: ellipses, astroids, cardioids. In this regard, we use the following concepts in mathematical models from analytical geometry: Cartesian coordinate system, polar coordinate system, types of higher-order curves, their analytical expressions and images. Based on these facts, applications of certain integrals in geometric and physical problems can be carried out in the following sequence: a) first of all, students get acquainted with the curve, its analytical representation in the Cartesian and (or) polar coordinate system, its graph is constructed; b) historical information about this curve is given; c) specific tasks are proposed in which it is possible to trace the intersubject connections of analytical geometry and mathematical analysis. Main results of the work: 1) identification of intersubject connections of analytical geometry and mathematical analysis; 2) development of a methodology for the application of certain integrals in problems using higher-order curves. The theoretical significance of the study is to identify the possibilities of using intersubject connections of analytical geometry and mathematical analysis. The practical significance lies in the fact that the proposed methodology helps to increase the level of motivation of students to study mathematical analysis.
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31

Rahmatina, Desi. "PENGGUNAAN PERANGKAT PEMBELAJARAN GEOMETRI RUANG BERBASIS ICT UNTUK MENINGKATKAN KEMAMPUAN BERPIKIR TINGKAT TINGGI MAHASISWA." Mosharafa: Jurnal Pendidikan Matematika 6, no. 1 (August 24, 2018): 57–68. http://dx.doi.org/10.31980/mosharafa.v6i1.294.

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Pembelajaran geometri ruang merupakan salah satu pembelajran yang memerlukan kemampuan analitis dan komunikatif mahasiswa. Tujuan penelitian ini adalah 1) untuk mengkaji penggunaan perangkat pembelajaran geometri ruang berbasis ICT dalam meningkatkan kemampuan berpikir tingkat tinggi, 2) untuk mengetahui respon mahasiswa terhadap penggunaan perangkat pembelajaran geometri berbasis ICT. Pembelajaran geometri memerlukan kemampuan mengkomunikasikan bangun yang sifatnya abstrak menjadi konkrit sehingga dapat meningkatkan kemampuan berpikir tingkat tinggi dengan menggunakan ICT. Hasil kajian ini menunjukkan perangkat pembelajaran berbasis ICT dengan program wingeom dapat meningkatkan kemampuan berpikir tingkat tinggi. Learning geometry of space is one pembelajran that require analytical and communicative abilities of students. The purpose of this study were 1) to assess the use of the learning device geometry of space-based ICT in enhancing the ability to think critically, 2) to study the response of students to use ICT-based learning device geometry. Learning geometry requires the ability to communicate wake which is abstract into the concrete so as to increase high-level thinking skills by using ICT. Results from this study indicate the ICT-based learning with wingeom programs can increase high-level thinking skills.
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32

Steckroth, Jeffrey. "A Transformational Approach to Slip-Slide Factoring." Mathematics Teacher 109, no. 3 (October 2015): 228–34. http://dx.doi.org/10.5951/mathteacher.109.3.0228.

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Dynamic geometry software coupled with a careful analytical investigation provides interesting algebraic and geometric connections between pairs of functions to detail a transformational approach to factoring.
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33

Mokhor, Volodymyr, Vitalii Bezshtanko, Serhii Honchar, Hryhorii Kravtsov, Ihor Kotsiuba, Olha Kruk, Oleksander Makarevych, Yevhen Maksymenko, and Vasyl Tsurkan. "Analytical geometry approach for information security risks analyses." Collection "Information technology and security" 3, no. 1 (June 30, 2015): 60–67. http://dx.doi.org/10.20535/2411-1031.2015.3.1.57731.

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34

Brimkov, V. E. "Analytical Honeycomb Geometry for Raster and Volume Graphics." Computer Journal 48, no. 2 (February 1, 2005): 180–99. http://dx.doi.org/10.1093/comjnl/bxh075.

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35

Baker, Jon. "An algorithm for geometry optimization without analytical gradients." Journal of Computational Chemistry 8, no. 5 (July 1987): 563–74. http://dx.doi.org/10.1002/jcc.540080502.

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36

Lalas, C., K. Tsirbas, K. Salonitis, and G. Chryssolouris. "An analytical model of the laser clad geometry." International Journal of Advanced Manufacturing Technology 32, no. 1-2 (March 16, 2006): 34–41. http://dx.doi.org/10.1007/s00170-005-0318-0.

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37

Joseph Leon, Stephen Leon, Alfred Franklin Varghese, Joseph Michel, and Gopinath Gunasekaran. "ANALYTICAL AND NUMERICAL THERMAL ANALYSIS ON FRICTION STIR WELDING USING POLYGONAL TOOL PIN." IIUM Engineering Journal 22, no. 2 (July 4, 2021): 352–63. http://dx.doi.org/10.31436/iiumej.v22i2.1707.

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Frictional heat generation in the tool/matrix interface followed by the stirring of material along the weld line causes plasticized solid state joining in friction stir welding. In this paper, the existing torque based thermo-mechanical model for the tools with cylindrical pins is remodified for the polygonal tool pin profile by introducing novel multiplication factors with respect to the number of sides in the tool pin geometry. The variation in the effective heat supply with respect to the chosen pin geometry was analyzed. A comparative analysis of the proposed analytical model with the existing model was also carried out to understand the accuracy of the proposed model. Furthermore, a transient thermal numerical modelling was carried out in the view of understanding the change in process peak temperature in the stir zone and change in temperature gradient along the heat affected zone with respect to the change in pin geometry for the opted set of process input parameters. An analytically estimated heat-input-based numerical model was adopted in the present study. It was observed that the process peak temperature was directly proportional to the number of sides in the tool pin. ABSTRAK: Penjanaan haba geseran antara muka pada alat/matrik diikuti dengan pengacauan material sepanjang garis kimpalan menyebabkan keadaan plastik pepejal melekat bersama geseran kimpalan pengacau. Kajian ini berkaitan tork sedia ada berdasarkan model mekanikal-terma bagi alat pin silinder yang terubah suai bagi profil pin alat poligon dengan memperkenalkan faktor gandaan berdasarkan bilangan sisi geometri alat pin. Perubahan pada bekalan haba efektif berdasarkan geometri pin pilihan telah dikaji. Analisis bandingan pada model analitik yang dicadang bersama model sedia ada, telah dilakukan bagi memahami ketepatan model cadangan. Tambahan, model transien numerikal terma telah dibuat bagi memahami proses perubahan suhu puncak ketika zon pengacauan dan perubahan gradien suhu sepanjang zon terkena haba perubahan geometri pin pada set proses parameter input terpilih. Kajian ini mengaplikasi model numerik berdasarkan input anggaran haba secara analitik. Dapatan kajian menunjukkan suhu puncak proses adalah berkadar langsung dengan bilangan sisi pin alat.
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Budiarto, Mega Teguh, and Rudianto Artiono. "GEOMETRI DAN PERMASALAHAN DALAM PEMBELAJARANNYA (SUATU PENELITIAN META ANALISIS)." JUMADIKA : Jurnal Magister Pendidikan Matematika 1, no. 1 (May 28, 2019): 9–18. http://dx.doi.org/10.30598/jumadikavol1iss1year2019page9-18.

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Geometry teaches us not only about how to give appreciation for something, but also how to find connections that occur between geometry material and other lecture material. In addition, geometry also trains communication through exploration, discussion, conjecture and investigation. The problems that exist in basic geometry skills in a row are problems related to logic skills, drawing skills, visual skills, verbal skills, and applied skills. Based on geometric learning using analytical presentation, the problem of using axiomatic deductive is at the top, then the problem of perception. Misconceptions about visual processes and activities, and finally problems with the use of procedures, concepts, and principles
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39

Bello-Chávez, Jhon Helver. "Elementa Curvarum Linearum more Apollonius that Descartes." Visión electrónica 2, no. 2 (December 6, 2019): 435–38. http://dx.doi.org/10.14483/22484728.18442.

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This document shows an analysis of the second book Elementa Curvarum Linearum written by Jan De Witt, published for the first time in the second edition of Geometry [1]. This writing is considered the first analytical geometry textbook. The influence of the work carried out by Apollonius in his conics book is studied, the use and interpretation of diagrams is debated. The development of the analytical method and the generation of curves by means of movement are also studied. Some propositions were renewed versions in terms of eighteenth-century mathematics, they used symbology, algebraic techniques and curves were classified by means of their symbolic representations, in these propositions a work closer to Apollonius is seen, the conic is not generated, it is assumed its existence, its nature is geometric. The study concludes that, although the textbook was published in the second edition of Geometry, the genesis of the curves remains geometric. The conics appear as objects of study in action immersed in the symbolic and algebraic practice characteristic of the time.
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Belic, Cedomir, Rodoljub Simovic, and Koviljka Stankovic. "A method of approximate green's function for solving reflection of particles in plane geometry." Nuclear Technology and Radiation Protection 31, no. 3 (2016): 228–32. http://dx.doi.org/10.2298/ntrp1603228b.

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A method for approximate analytical solution of transport equation for particles in plane geometry is developed by solving Fredholm integral equations. Kernels of these equations are the Green's functions for infinite media treated approximately. Analytical approximation of Green's function is based on decomposition of the functions into terms that are exactly analytically solved and those which are approximately obtained by usual low order DPN approximation. Transport of particles in half-space is treated, and reflection coefficient is determined in the form of an analytical function. Comparison with the exact numerical solution and other approximate methods justified the proposed analytical technique.
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41

Girsh, A. "New Problems of Descriptive Geometry. Continuation." Geometry & Graphics 9, no. 4 (April 14, 2022): 3–10. http://dx.doi.org/10.12737/2308-4898-2022-9-4-3-10.

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Complex geometry is a synthesis of Euclidean E-geometry (circle geometry) and pseudo-Euclidean M-geometry (hyperbola geometry). Each of them individually defines a non-closed system in which a correctly posed problem may not give a solution. Analytical geometry represents a closed system. In it, a correctly posed problem always gives solutions in the form of complex numbers, for each of which, one of the parts may be equal to zero. Finding imaginary solutions and imaginary figures formed by a set of such solutions is a new problem in descriptive geometry. Degenerated conics and quadrics, or curves and surfaces of higher orders, constitute a new class of figures and a new class of problems in descriptive geometry. For example, null-circle, null-sphere, null-cylinder, null-torus. In this paper the problem for studying the shape of second (conics, quadrics), third (conoid), and fourth (torus) order figures is posed. The latest suggest a meeting with new geometric properties of figures. Geometric operations are still immersed in the complex space E + M or real - imaginary. The examples under consideration continue a series of degenerated figures in which the null-circle splits into isotropic lines. Isotropic lines are taken as generators of surfaces. They form a cone of revolution and a hyperbolic paraboloid (an oblique plane).
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42

Miragliotta, Elisa, and Anna E. Baccaglini-Frank. "Enhancing the Skill of Geometric Prediction Using Dynamic Geometry." Mathematics 9, no. 8 (April 9, 2021): 821. http://dx.doi.org/10.3390/math9080821.

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This study concerns geometric prediction, a process of anticipation that has been identified as key in mathematical reasoning, and its possible constructive relationship with explorations within a Dynamic Geometry Environment (DGE). We frame this case study within Fischbein’s Theory of Figural Concepts and, to gain insight into a solver’s conceptual control over a geometrical figure, we introduce a set of analytical tools that include: the identification of the solver’s geometric predictions, theoretical and phenomenological evidence that s/he may seek for, and the dragging modalities s/he makes use of in the DGE. We present fine-grained analysis of data collected during a clinical interview as a high school student reasons about a geometrical task, first on paper-and-pencil, and then in a DGE. The results suggest that, indeed, the DGE exploration has the potential of strengthening the solver’s conceptual control, promoting its evolution toward theoretical control.
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43

Klepikov, P. N. "Mathematical Modeling in Problems of Homogeneous (Pseudo)Riemaimian Geometry." Izvestiya of Altai State University, no. 1(111) (March 6, 2020): 95–98. http://dx.doi.org/10.14258/izvasu(2020)1-15.

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Currently, mathematical and computer modeling, as well as systems of symbolic calculations, are actively used in many areas of mathematics. Popular computer math systems as Maple, Mathematica, MathCad, MatLab allow not only to perform calculations using symbolic expressions but also solve algebraic and differential equations (numerically and analytically) and visualize the results. Differential geometry, like other areas of modern mathematics, uses new computer technologies to solve its own problems. The applying is not limited only to numerical calculations; more and more often, computer mathematics systems are used for analytical calculations. At the moment, there are many examples that prove the effectiveness of systems of analytical calculations in the proof of theorems of differential geometry.This paper demonstrates how symbolic computation packages can be used to classify neither conformally flat nor Ricci parallel four-dimensional Lie groups with leftinvariant (pseudo)Riemannian metric of the algebraic Ricci soliton with the zero Schouten-Weyl tensor.
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44

Ramadhan, Fauzan Akbar, Yuliadi, and Noor Fauzi Isniarno. "Pengaruh Geometri Peledakan Terhadap Getaran Tanah dan Fragmentasi Batuan pada PT. Gunung Kulalet, Kecamatan Baleendah Kabupaten Bandung, Provinsi Jawa Barat." Bandung Conference Series: Mining Engineering 2, no. 2 (July 26, 2022): 283–89. http://dx.doi.org/10.29313/bcsme.v2i2.2925.

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Abstract. Blasting activity is the process of spreading a material so that later it can be moved and processed further. One of the factors that influence the success of blasting is the blasting geometry. The blasting geometry will affect the fragmentation and vibration of the blasted soil. Therefore, a study was conducted to determine the effect of blast geometry on ground vibrations resulting from blasting and rock fragmentation. The analytical study in this study uses trendline analysis techniques. Blasting was carried out at 8 points and data were collected on blast geometry, rock fragmentation and ground vibrations resulting from the explosion. Predictors Langefors and Kiehlstrom, IS 6922 and Ambraseys and Hendrion were used to predict ground vibration values. The results of the analysis of the effect of blasting geometry on ground vibration coefficient correlation coefficient of powder column is 0.704 (70.4%) and hole depth is 0.697 (69.7%) and the effect of blasting geometry to fragmentation load correlation coefficient is 0.952 (95.2%), spaced 0.991 (99.1%) and 0.797 (79.7%). Abstrak. Kegiatan peledakan merupakan proses pemberaian suatu material agar nantinya dapat dipindahkan dan diproses lebih lanjut. Salah satu faktor yang mempengaruhi keberhasilan peledakan adalah geometri peledakan. Geometri peledakan akan mempengaruhi fragmentasi dan getaran tanah hasil peledakan. Oleh karena itu dilakukan penelitian untuk mengetahui pengaruh dari geometri peledakan terhadap getaran tanah hasil peledakan dan fragmentasi batuan. Kajian analisis pada penelitian menggunakan teknik analisis trendline. Peledakan dilakukan pada 8 titik dan dilakukan pengambilan data geometri peledakan, fragmentasi batuan dan getaran tanah hasil peledakan. Prediktor Langefors and Kiehlstrom, IS 6922 dan Ambraseys and Hendrion digunakan untuk memprediksi nilai getaran tanah. Hasil analisis pengaruh dari geometri peledakan terhadap getaran tanah menghasilkan koefisien korelasi powder coloumn 0,704 (70,4%) dan hole depth 0,697 (69,7%) dan pengaruh dari geometri peledakan terhadap fragmentasi menghasilkan koefisien korelasi burden 0,952 (95,2%), spasi 0,991 (99,1%) dan 0,797 (79,7%).
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45

Brecher, C. Prof, M. Fey, and M. Hildebrand. "Planetenrollengewindetriebe mit neuer Geometrie*/Planetary roller screws with new geometry." wt Werkstattstechnik online 106, no. 05 (2016): 325–28. http://dx.doi.org/10.37544/1436-4980-2016-05-39.

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Innerhalb der Rollengewindetriebe sind Planetenrollengewindetriebe aufgrund der sehr hohen Tragfähigkeit, Steifigkeit und Positioniergenauigkeit die am meisten verbreitete Bauart. Diesen Vorteilen steht eine bauartbedingte Einschränkung der realisierbaren Gesamtsteigung gegenüber. Es konnte anhand analytischer und experimenteller Untersuchungen gezeigt werden, dass sich diese Einschränkung durch eine Variation der Gewindegangzahlen der Spindel und der Mutter positiv beeinflussen lässt.   Due to the very high load capacity, rigidity and positioning accuracy, planetary roller screws are the most common type of roller screw drives. These advantages are contrasted by a limitation of total pitch caused by geometry parameters of this type. It was shown on the basis of analytical and experimental studies that this limitation can be positively influenced by a variation of the thread numbers of the spindle and the nut.
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OHTA, Makoto, and Daniel A. RUFENACHT. "822 Three Dimensional Geometry Measurements of Cerebral Aneurysms and Vessel Sizes for Analytical Geometry(2)." Proceedings of the Fluids engineering conference 2006 (2006): _822–1_—_822–4_. http://dx.doi.org/10.1299/jsmefed.2006._822-1_.

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47

OHTA, Makoto, and Daniel A. RUFENACHT. "822 Three Dimensional Geometry Measurements of Cerebral Aneurysms and Vessel Sizes for Analytical Geometry(1)." Proceedings of the Fluids engineering conference 2006 (2006): _822—a_. http://dx.doi.org/10.1299/jsmefed.2006._822-a_.

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48

Atak, H., and A. Yilmazer. "An analytical benchmark of MYRRHA ADS in cylindrical geometry." Kerntechnik 76, no. 5 (November 2011): 347–55. http://dx.doi.org/10.3139/124.110168.

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49

SCHIPPA, LEONARDO. "Analytical treatment of source terms for complex channel geometry." Journal of Hydraulic Research 46, no. 6 (2008): 753. http://dx.doi.org/10.3826/jhr.2008.3211.

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50

Woodhouse, N. M. J. "SYMPLECTIC GEOMETRY AND ANALYTICAL MECHANICS (Mathematics and Its Applications)." Bulletin of the London Mathematical Society 20, no. 4 (July 1988): 377–79. http://dx.doi.org/10.1112/blms/20.4.377.

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