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Journal articles on the topic 'Circumscribed circle'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Fujimuraa, Masayo. "The complex geometry of Blaschke products of degree 3 and associated ellipses." Filomat 31, no. 1 (2017): 61–68. http://dx.doi.org/10.2298/fil1701061f.

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A bicentric polygon is a polygon which has both an inscribed circle and a circumscribed one. For given two circles, the necessary and sufficient condition for existence of bicentric triangle for these two circles is known as Chapple?s formula or Euler?s theorem. As one of natural extensions of this formula, we characterize the inscribed ellipses of a triangle which is inscribed in the unit circle. We also discuss the condition for the ?circumscribed? ellipse of a triangle which is circumscribed about the unit circle. For the proof of these results, we use some geometrical properties of Blaschk

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2

Silvester, John R. "Variations on a Japanese Temple theorem." Mathematical Gazette 102, no. 553 (2018): 38–49. http://dx.doi.org/10.1017/mag.2018.6.

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The following Japanese Temple geometry theorem appears in Fukagawa and Rigby [1]:Thoerem 1: The products of the radii of the excircles on each pair of opposite sides of a circumscribed quadrilateral are equal.See Figure 1. A circumscribed quadrilateral (also called a tangential quadrilateral) is one that possesses an inscribed circle. Now the diagram contains four lines (the sides of the quadrilateral) and one circle S (the inscribed circle) that touches all four of them; this we call the base circle of the theorem. The other four circles each touch just three of the lines. For the moment, ass

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3

Osler, Thomas J., and Sky Waterpeace. "Vieta’s product for pi from the Archimedean algorithm." Mathematical Gazette 98, no. 543 (2014): 429–31. http://dx.doi.org/10.1017/s0025557200008123.

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In this paper we show how to derive Vieta’s famous product of nested radicals for π [1] from the Archimedean iterative algorithm for π, [2, 3]. Only simple algebraic manipulations are needed.The Archimedean iterative algorithm for calculating π uses a method involving the two equations:and In using this algorithm, we start with a circle of diameter 1. Imagine two regular polygons each with the same number of sides, circumscribed and inscribed to this circle. The larger one has perimeter a0, the smaller has perimeter b0. Since the perimeter of the circle is π we have b0 < π < a0. Now cons

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4

Osler, Thomas J., Walter Jacob, and Ryo Nishimura. "An infinite product of nested radicals for log x from the Archimedean algorithm." Mathematical Gazette 100, no. 548 (2016): 274–78. http://dx.doi.org/10.1017/mag.2016.64.

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The so-called Archimedean iterative algorithm for calculating π uses a method involving the two equations(1)and(2)(Note that (1) is the harmonic mean.) Imagine two regular polygons each with the same number of sides, circumscribed and inscribed to a circle of diameter one. The larger one has perimeter a0, the smaller has perimeter b0. (Archimedes used hexagons with and b0 = 3, but regular polygons of any number of sides can begin the iterations.) Since the perimeter of the circle is π we have b0 < π < a0. Now consider regular polygons with twice the number of sides that circumscribe and

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5

Görög, Augustín. "Number of Points for Roundness Measurement - Measured Results Comparison." Research Papers Faculty of Materials Science and Technology Slovak University of Technology 19, no. 30 (2011): 19–24. http://dx.doi.org/10.2478/v10186-010-0035-x.

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Number of Points for Roundness Measurement - Measured Results Comparison Paper deals with filtering roundness. It presents experimental results measured for roundness turning and cylindrical grinding. Roundness was measured using Prismo Navigator 5 coordinate measuring machine. Evaluation was done by four methods: Minimum zone reference circles (MZCI), Least squares reference circle (LSCI), Minimum circumscribed reference circle (MCCI) and Maximum inscribed reference circle (MICI). The filters used were: Gauss, Spline and no filter.

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6

Jaeger, Ted, and Stephen Long. "Effects of Contour Proximity and Lightness on Delboeuf Illusions Created by Circumscribed Letters." Perceptual and Motor Skills 105, no. 1 (2007): 253–60. http://dx.doi.org/10.2466/pms.105.1.253-260.

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32 observers judged the size of a letter, either an “A” or an “S,” which was surrounded by a circle. Both letters were overestimated, but larger surrounding circles reduced the illusion. Decreasing the lightness contrast of the surrounding circle relative to the central letter diminished the illusion. The results suggest that, like the Delboeuf illusion, these circumscribed letters illusions are produced by interactions among size-coding neurons.

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7

Kolar-Šuper, Ružica. "Gob’s Circles of a Triangle in the Isotropic Plane." Journal of Mathematics 2021 (April 26, 2021): 1–5. http://dx.doi.org/10.1155/2021/5513345.

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In this paper, we consider Gob’s circles of an allowable triangle in the isotropic plane and derive their equations in the case of a standard triangle. We prove that the potential axes of the circumscribed circle and Gob’s circles are the angle bisectors of the given triangle. We investigate some other interesting properties of Gob’s circles and some other circles related to the given triangle.

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8

Li, Xiuming, and Jingcai Zhang. "A joint method for the maximum inscribed circle and minimum circumscribed circle." Measurement 87 (June 2016): 189–93. http://dx.doi.org/10.1016/j.measurement.2016.03.016.

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9

Xiuming, Li, Zhang Jingcai, and Liu Hongqi. "Determination of the minimum zone circle based on the minimum circumscribed circle." Measurement Science and Technology 25, no. 1 (2013): 017002. http://dx.doi.org/10.1088/0957-0233/25/1/017002.

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10

Hansen, David W. "On Inscribed and Escribed Circles of Right Triangles, Circumscribed Triangles, and the Four-Square, Three-Square Problem." Mathematics Teacher 96, no. 5 (2003): 358–64. http://dx.doi.org/10.5951/mt.96.5.0358.

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For more than twenty years, I have been studying the fascinating relationships between right triangles and their inscribed and escribed circles. An inscribed circle is one that is tangent to all three sides of a triangle and whose center lies inside the triangle. An escribed circle is one that is tangent to one of the sides of the triangle and to the extensions of the other two sides and whose center lies outside the triangle. Every triangle has one inscribed and three escribed circles, as shown in figure 1.

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11

Zhao, Shi Zhen, and Xiu Ming Li. "Evaluation of Roundness Error Based on the Position of the Centers." Applied Mechanics and Materials 470 (December 2013): 420–24. http://dx.doi.org/10.4028/www.scientific.net/amm.470.420.

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This paper presents a simple algorithm for determining the minimum circumscribed circle which can select the control points accurately and efficiently from the entire data set. The first candidate point is selected based on the least square center, and then the second and third candidate points are determined based on the position of the centers. The control points for the minimum circumscribed circle were determined with the three candidate points easily, Extensive examples have been carried out to validate the effectiveness of the proposed algorithm.

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12

Li, Xiuming, and Zhaoyao Shi. "The relationship between the minimum zone circle and the maximum inscribed circle and the minimum circumscribed circle." Precision Engineering 33, no. 3 (2009): 284–90. http://dx.doi.org/10.1016/j.precisioneng.2008.04.005.

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13

Bonsangue, Martin V. "In Search of Archimedes: Measurement of a Circle." Mathematics Teacher 110, no. 1 (2016): 71–76. http://dx.doi.org/10.5951/mathteacher.110.1.0071.

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14

Lei, Xian Qing, and Feng Qin Ding. "Evaluating Method of Roundness Error Based on the Maximum Inscribed Circle and Minimum Circumscribed Circle." Advanced Materials Research 655-657 (January 2013): 847–50. http://dx.doi.org/10.4028/www.scientific.net/amr.655-657.847.

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Based on the geometric characteristics of maximum inscribed circle (MIC) and Minimum circumscribed circle (MCC), a novel method for roundness error evaluation using Geometric Approximation Searching Algorithm (GASA) has been presented in this paper. First, a square is allocated by taking the predetermined reference point as initial reference point, and the radius value of all the measured points are calculated by regarding each vertex of the square and the initial reference point as the ideal centres respectively. Second, the minimum and maximum radius are obtained when each vertex of the squa

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15

Liu, Fei, Guanghua Xu, Lin Liang, Qing Zhang, and Dan Liu. "Minimum Circumscribed Circle and Maximum Inscribed Circle of Roundness Deviation Evaluation With Intersecting Chord Method." IEEE Transactions on Instrumentation and Measurement 65, no. 12 (2016): 2787–96. http://dx.doi.org/10.1109/tim.2016.2601003.

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16

Liu, Ping, and Hui Yi Miao. "Mathematical Model for Evaluating Roundness Errors by Minimum Circumscribed Circle Method." Advanced Materials Research 328-330 (September 2011): 380–83. http://dx.doi.org/10.4028/www.scientific.net/amr.328-330.380.

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An unconstrained optimization model is established for assessing roundness errors by the minimum circumscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing

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17

Xiuming, Li, and Zhang Jingcai. "Evaluation for the minimum circumscribed circle based on the rotation method." Measurement Science and Technology 25, no. 9 (2014): 097001. http://dx.doi.org/10.1088/0957-0233/25/9/097001.

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18

Cao, Ming. "A new Delaunay triangulation algorithm based on constrained maximum circumscribed circle." Wuhan University Journal of Natural Sciences 20, no. 4 (2015): 313–17. http://dx.doi.org/10.1007/s11859-015-1098-5.

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19

Jurkin, Ema. "Curves of Brocard Points in Triangle Pencils in Isotropic Plane." KoG, no. 22 (2018): 20–23. http://dx.doi.org/10.31896/k.22.3.

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In this paper we consider a triangle pencil in an isotropic plane consisting of the triangles that have the same circumscribed circle. We study the locus of their Brocard points, two curves of order 4.

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20

Wu, Zhong Yong, Jin Gou, and Chang Cai Cui. "An Improved Particle Swarm Optimization Algorithm Applied to the Unified Evaluation of Circularity Error." Applied Mechanics and Materials 44-47 (December 2010): 3937–41. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.3937.

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Minimum zone circle (MZC), minimum circumscribed circle (MCC), maximum inscribed circle (MIC) and least square circle (LSC) are four common methods used to evaluate circularity errors. A novel particle swarm optimization algorithm based on self-adapted comprehensive learning (ACL-PSO) is proposed to evaluate circularity errors with real coded strategy. In the algorithm, population learning mechanism and velocity mutation strategy are adopted. In the meantime, ACL-PSO is applied to the unified evaluation of circularity error. The experiment results evaluated by different methods indicate that t

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21

Huang, Jingzhi, Runze Yang, Haiqiao Ge, and Jiubin Tan. "An effective determination of the minimum circumscribed circle and maximum inscribed circle using the subzone division approach." Measurement Science and Technology 32, no. 7 (2021): 075014. http://dx.doi.org/10.1088/1361-6501/abf803.

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22

Papuga, Jan, Eva Cízová, and Aleksander Karolczuk. "Validating the Methods to Process the Stress Path in Multiaxial High-Cycle Fatigue Criteria." Materials 14, no. 1 (2021): 206. http://dx.doi.org/10.3390/ma14010206.

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The paper discusses one of the key features in the multiaxial fatigue strength evaluation—the procedure in which the stress path is analyzed to provide relevant measures of parameters required by multiaxial criteria. The selection of this procedure affects the complete equivalent stress derived for any multiaxial load combinations. Three major concepts—the minimum circumscribed circle, minimum circumscribed ellipse, and moment of inertia methods—are described. Analytical solutions of their evaluation for multiaxial stress state with components described by harmonic functions are provided. The

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23

Egereva, Elvira, Dmitry Surovtsev, and Zakhar Nepovinnyy. "Flat area characteristics of polygons circumscribing parabolic figures." E3S Web of Conferences 164 (2020): 02004. http://dx.doi.org/10.1051/e3sconf/202016402004.

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The works elucidates the extremum areas of the polygons circumscribing parabolic figures. It is shown that the ratio of the areas of the polygons circumscribed near parabolic figures to the areas of the corresponding figures always remains a constant value, independent of the coefficients characterizing the quadratic function. The only point at which the function under study reaches its minimum value is found. The question of the necessary conditions for the existence of a circle circumscribed about a parabolic quadrilateral found in the Ptolemy theorem is being considered.

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24

Coghetto, Roland. "Some Facts about Trigonometry and Euclidean Geometry." Formalized Mathematics 22, no. 4 (2014): 313–19. http://dx.doi.org/10.2478/forma-2014-0031.

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Summary We calculate the values of the trigonometric functions for angles: [XXX] , by [16]. After defining some trigonometric identities, we demonstrate conventional trigonometric formulas in the triangle, and the geometric property, by [14], of the triangle inscribed in a semicircle, by the proposition 3.31 in [15]. Then we define the diameter of the circumscribed circle of a triangle using the definition of the area of a triangle and prove some identities of a triangle [9]. We conclude by indicating that the diameter of a circle is twice the length of the radius

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25

Kang, Jae Youn, Byung Ik Choi, Hak Joo Lee, Sang Rok Lee, Joo Sung Kim, and Kee Joo Kim. "Genetic Algorithm Application in Multiaxial Fatigue Criteria Computation." International Journal of Modern Physics B 17, no. 08n09 (2003): 1678–83. http://dx.doi.org/10.1142/s0217979203019502.

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Both critical plane and stress invariant approaches are used to evaluate fatigue limit criteria of machine component subjected to non-proportional cyclic loading. Critical plane methods require finding the smallest circle enclosing all the tips of shear stress vectors acting on the critical plane. In stress invariant methods, the maximum amplitude of the second invariant of the stress deviator should be determined. In this paper, the previous algorithms for constructing the minimum circumscribed circle or hyper-sphere are briefly reviewed and the method using genetic algorithm is proposed.

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26

Lee, Geunho, Seokhoon Yoon, Nak Young Chong, and Henrik Christensen. "A Mobile Sensor Network Forming Concentric Circles Through Local Interaction and Consensus Building." Journal of Robotics and Mechatronics 21, no. 4 (2009): 469–77. http://dx.doi.org/10.20965/jrm.2009.p0469.

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We address the problem of a swarm of autonomous mobile robotic sensors generating geometric shapes to build wireless ad hoc surveillance sensor networks. Robot swarms with limited observation are required to form different shapes under different task conditions. To do this, we propose decentralized coordination enabling a robot swarm dispersed across an area to form a desired shape. Our approach has emphn robots generate a circumscribed circle of a regular emphn-polygon based on local interaction with neighboring robots. The approach also enables a large robot swarm to form concentric circles

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27

Wasserman, Nicholas H., and Itar N. Arkan. "Technology Tips: An Archimedean Walk." Mathematics Teacher 104, no. 9 (2011): 710–14. http://dx.doi.org/10.5951/mt.104.9.0710.

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The circle, so simple and yet complex, has fascinated mathematicians since the earliest civilizations. Archimedes, a well–known Greek mathematician born in 287 BCE, began to unravel part of the mystery involving π by applying iteration to the circle. Building on Euclid's postulates and theorems, Archimedes used iterations of inscribed and circumscribed regular polygons to find upper and lower bounds for the value of π. These bounds are close approximations of the value of π, and one is still used today: 22/7 differs from π only in the third place to the right of the decimal (see fig. 1).

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Wasserman, Nicholas H., and Itar N. Arkan. "Technology Tips: An Archimedean Walk." Mathematics Teacher 104, no. 9 (2011): 710–14. http://dx.doi.org/10.5951/mt.104.9.0710.

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The circle, so simple and yet complex, has fascinated mathematicians since the earliest civilizations. Archimedes, a well–known Greek mathematician born in 287 BCE, began to unravel part of the mystery involving π by applying iteration to the circle. Building on Euclid's postulates and theorems, Archimedes used iterations of inscribed and circumscribed regular polygons to find upper and lower bounds for the value of π. These bounds are close approximations of the value of π, and one is still used today: 22/7 differs from π only in the third place to the right of the decimal (see fig. 1).

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29

Li, Xiuming, Zhikan Wen, Hanbing Zhu, Zhen Guo, and Yuwei Liu. "An improved algorithm for evaluation of the minimum circumscribed circle and maximum inscribed circle based on the local minimax radius." Review of Scientific Instruments 91, no. 3 (2020): 035103. http://dx.doi.org/10.1063/5.0002233.

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30

Kopas, Peter, Milan Vaško, and Marián Handrik. "Computational Modeling of the Microplasticization State in the Nodular Cast Iron." Applied Mechanics and Materials 474 (January 2014): 285–90. http://dx.doi.org/10.4028/www.scientific.net/amm.474.285.

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The article deals with the creation of models for the analysis of plastic zones generation in ductile cast iron. The aim is the study of the microplasticization process near the graphite particles border. In creating the graphite particle model there is randomly chosen shape and orientation of the particle. The basic characteristic of the shape is ovality (the ratio of the inscribed circle to the circumscribed circle). The size of plastic deformation and the size of the plastic area are monitored by the microplasticization process analysis. The results are statistically elaborated to determine

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31

Korobko, Viktor, Natalia Kalashnikova, and Stanislav Shlyakhov. "The approximate method of determining the integral physical characteristics in some problems of technical theory of plates." MATEC Web of Conferences 251 (2018): 04018. http://dx.doi.org/10.1051/matecconf/201825104018.

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The paper considers the dimensionless geometric characteristic R/r (R is the maximum radius of a circle inscribed in a given region, r is the minimum radius of a circle circumscribed around it), which is used as a geometric analogue of integral characteristics in problems of the technical theory of plates and theory of elasticity. By numerical experiment the authors showed that using this characteristic as the only argument made it possible to approximate with one elementary function all the solutions for short plates, which satisfied the condition (0.5 < R/r < 1) in problems of trans-ve

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32

Worley, Shelby C. "The geometry of reflection." GEOPHYSICS 58, no. 2 (1993): 293–97. http://dx.doi.org/10.1190/1.1443413.

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The two‐dimensional (2-D) reflection path from a dipping plane between an offset source‐receiver combination in a constant velocity medium can be described with several parameters (coordinates, offsets, angles, and lengths). Although there are many parameters, only four independent ones are needed to locally determine the reflection geometry. Given four determining parameters, the evaluations of other ones present problems that range from trivial to formidable. The circumscribed circle about the source, receiver, and specular point turns out to have a number of remarkable properties that are u

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33

QI, Zi-cheng, Pei-jun NI, Wei JIANG, Zhi-min GUO, and Hong-li GAO. "Spatial resolution measurement of industrial CT system based on equal diameter circumscribed circle phantom." Optics and Precision Engineering 29, no. 1 (2021): 61–71. http://dx.doi.org/10.37188/ope.20212901.0061.

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34

Du, Can Xun, Wei Hua Gui, Zhi Kun Hu, and Chun Bo Liu. "The Minimum Circumscribed Circle Based Method for Hydro-Turbine Generator Unit Bearing Clearance Adjustment Analysis." Advanced Materials Research 630 (December 2012): 193–202. http://dx.doi.org/10.4028/www.scientific.net/amr.630.193.

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Hydro-turbine generator unit turning test is a key step to check the installation quality of the shafting system. The unit turning data is very important for bearing clearance adjustment. The traditional unit turning test and bearing clearance adjustment are based on a condition of that the spindle turning orbit is an approximate circle. It is simple to be used in the field operation and applicable to the most units. The trajectory of the turning orbit shows irregular shape when the spindle has a certain part of the flaw. If the traditional method is used for the unit turning and adjusting the

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35

Thai, Ha Thi Thu, and Phuoc Hong Nguyen. "MAXIMUM- INSCRIBED AND MINIMUM-CIRCUMSCRIBED FITTING FOR CO-ORDINATE MEASURING MACHINE." Science and Technology Development Journal 13, no. 3 (2010): 5–13. http://dx.doi.org/10.32508/stdj.v13i3.2130.

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This paper describes algorithms that fit geometric shapes to data sets according to maximum- inscribed (MI) and minimum- circumscribed (MC) fit. We use these fits to build the CMM’s (Coordinate Measuring Machine) software in cases of circle, sphere and cylinder. For each case, we obtain the fit by two methods: first, by (relative easy) least squares fit method and then refine by MI and MC fit method. Although, the later method is substantially more complicated than the former one, Its results are used to make comparision with the the results of least squares method in order to give more option

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36

Grigorenko, Elena L., Sergey A. Kornilov, and Oksana Yu Naumova. "Epigenetic regulation of cognition: A circumscribed review of the field." Development and Psychopathology 28, no. 4pt2 (2016): 1285–304. http://dx.doi.org/10.1017/s0954579416000857.

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AbstractThe last decade has been marked by an increased interest in relating epigenetic mechanisms to complex human behaviors, although this interest has not been balanced, accentuating various types of affective and primarily ignoring cognitive functioning. Recent animal model data support the view that epigenetic processes play a role in learning and memory consolidation and help transmit acquired memories even across generations. In this review, we provide an overview of various types of epigenetic mechanisms in the brain (DNA methylation, histone modification, and noncoding RNA action) and

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37

FarzanehKaloorazi, MohammadHadi, Mehdi Tale Masouleh, and Stéphane Caro. "Collision-free workspace of parallel mechanisms based on an interval analysis approach." Robotica 35, no. 8 (2016): 1747–60. http://dx.doi.org/10.1017/s0263574716000497.

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SUMMARYThis paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped

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38

Nasyiitoh, Hikma Khilda. "KETAKSAMAAN JUMLAHAN SINUS PANGKAT 2^n YANG BERLAKU PADA SEGITIGA LANCIP." JURNAL SILOGISME : Kajian Ilmu Matematika dan Pembelajarannya 3, no. 1 (2018): 21. http://dx.doi.org/10.24269/js.v3i1.955.

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Let \alpha, \beta, \gamma are angles in acute triangle ABC and a,b,c are the length of the triangle. By using the sine of angles as the relationship between the length of triangle and the radius of the circle circumscribed about a plane triangle, will be proven the sum inequality of quadratic sine in acute triangle. Then, by using the quadratic sum inequality of the sides of triangle will be extended for the case of the sum inequality of sine of order 2^n in acute triangle.

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Burievich, Toshov Javohir. "The Questions of the Dynamics of Drilling Bit on the Surface of Well Bottom." Archives of Mining Sciences 61, no. 2 (2016): 275–83. http://dx.doi.org/10.1515/amsc-2016-0020.

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Abstract The purpose of this study was to investigate the dynamics of drilling bit on the well bottom as a function of their geometrical parameters. The frame of this method for this study includes former existed objective data on the unstable drilling devices as cantilever suspension. Research methods and calculation results are as follows: square coverage by tools blade working in different rotation regime; radius of the inscribed and circumscribed circle which leads to introduce and prospectively and solve problems on process optimization of mining rock at drilling the well bottom.

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40

Lintaman, Daniel. "Unusual canvasses: resolving copyright infringement through the lens of community customs." Interactive Entertainment Law Review 3, no. 1 (2020): 3–20. http://dx.doi.org/10.4337/ielr.2020.01.01.

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The evolution of video game technology is outpacing intellectual property law. As augmented realities and online gaming environments continue to collapse the distinction between real and virtual worlds, they have rendered traditional frameworks for copyright law unworkable. Gaming environments were traditionally circumscribed by the magic circle. Video games now interact with the outside world in a way that obscures the divide between the public domain and the private. Such disruption undermines copyright's core purpose of balancing interests, and transforms issues such as implied license, fai

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41

Пшуков, Тагир, Tagir Pshukov, Мурат Мамчуев, and Murat Mamchuev. "Approximate Solution for Squaring the Circle Problem." Geometry & Graphics 6, no. 4 (2019): 32–38. http://dx.doi.org/10.12737/article_5c21f593838774.44754853.

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It is known that squaring the circle (the problem consisting in construction of a square with the same area as a given circle), together with duplication of cube and angle trisection, is one of the most famous unsolv able problems of constructive geometry for construction with compass and straightedge. The solution of squaring the circle problem is reduced to the straightening of the circle, that is, to the construction of a segment equal in length to the circle, and its insolvability is connected with the pi character transcendence. In this paper, the limiting case of one of Christian Huygens

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Turanov, Khabibulla, and Mukhaya Shaumarova. "Incorrect application of the epicycloid equation to the planetary mechanism of the cotton harvester." E3S Web of Conferences 164 (2020): 06034. http://dx.doi.org/10.1051/e3sconf/202016406034.

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The content of the paper is based on the mathematical construction of the parametric equation of the epi- and hypocycloid curve described by a circle point. The purpose of the paper is to present the equations of epi- and hypocycloids in a parametric form in relation to the epi- and hypocyclic mechanism in a form convenient for calculation; to present the results of computational experiments on constructing phase trajectories of motion of a moving point of an epi- and hypocycloid. A detailed analysis of the analytical model of epi- and hypocycloids circumscribed by a point of a circle (on a mo

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Qu, Zi Hang, Bo Tang, Bin Chen, Yu Li, and You Xian Peng. "Power Transformer Core Column Section Optimization Model and Design." Advanced Materials Research 986-987 (July 2014): 948–51. http://dx.doi.org/10.4028/www.scientific.net/amr.986-987.948.

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The progression of power transformer core is usually determined by the core diameter and the width and thickness of the silicon-steel sheet is determined by the graphing method. Therefore, coil section can’t be fully utilized. To analyze the manufacturing characteristics of power transformer core columns from the performance and material savings and the nonlinear integer regression programming model is established. Taking the circumscribed circle diameter is 800mm, progression equal to 17 as an example. The optimized design of column section is solved by using the MATLAB. The results show that

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Fraivert, David. "Pascal-points quadrilaterals inscribed in a cyclic quadrilateral." Mathematical Gazette 103, no. 557 (2019): 233–39. http://dx.doi.org/10.1017/mag.2019.54.

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This paper presents some new theorems about the Pascal points of a quadrilateral. We shall begin by explaining what these are.Let ABCD be a convex quadrilateral, with AC and BD intersecting at E and DA and CB intersecting at F. Let ω be a circle through E and F which meets CB internally at M and DA internally at N. Let CA meet ω again at L and let DB meet ω again at K. By using Pascal’s theorem for the crossed hexagons EKNFML and EKMFNL and which are circumscribed by ω, the following results can be proved [1]:– (a)NK, ML and AB are concurrent (at a point P internal to AB)(b)NL, KM and CD are c

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TIAN, ZHONG WEI, and ZI NIU WU. "A study of two-dimensional flow past regular polygons via conformal mapping." Journal of Fluid Mechanics 628 (June 1, 2009): 121–54. http://dx.doi.org/10.1017/s0022112009006168.

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In this paper we study two-dimensional flow around regular polygons with an arbitrary but even number of edges N and one apex pointing to the free stream, with comparison to circular-cylinder flow. Both inviscid flow and low-Reynolds-number viscous flow are addressed. For inviscid flow, we obtained the exact solution for pure potential flow through Schwarz–Christoffel transformation, with the emphasis on the role of edge number, N, on the flow details. We also studied the behaviour, stationary lines and stability of vortex pair and found new stationary lines compared to circular cylinder. For

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Zhang, Y., G. Q. Zhou, S. H. Tang, P. W. Xing, and C. C. Huang. "RESEARCH ON EVALUATION METHOD OF AIRBORNE LIDAR POSITIONING ACCURACY." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-3/W10 (February 8, 2020): 825–30. http://dx.doi.org/10.5194/isprs-archives-xlii-3-w10-825-2020.

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Abstract. Due to the semi-random characteristics of ground points collected by airborne LIDAR system, it is difficult to control the laser pin points to fall on the control points with known coordinates in actual measurement, so the accuracy can not be evaluated by directly comparing coordinate data. In this paper, based on the target plate designed by air-to-ground, the fuzzy c-means clustering analysis algorithm is proposed to extract the point cloud data on the target according to the different echo intensity data of laser on different ground objects. The center point coordinates of the tar

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Xie, Botao, Liang Gao, Shuai Jiang, Shangda Zhang, Chen Wu, and Xu Ran. "Notched tensile response and damage mechanism of the GLARE laminate." Journal of Composite Materials 54, no. 22 (2020): 3037–46. http://dx.doi.org/10.1177/0021998320907963.

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Glass laminate aluminum reinforced epoxy, as an attractive material for advanced aerospace applications, is most likely to face the challenge of various blunt notched damages. In this paper, the tensile tests of the glass laminate aluminum reinforced epoxy with circular and square blunt notches are conducted. The effects of notch geometry, such as notch diameter, notch corner radius, and off-axis angle, on the laminated tensile behaviors of glass laminate aluminum reinforced epoxy laminate are explored. A characteristic distance function representing the damage-affected region of notch is empi

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Osserman, Robert. "Circumscribed Circles." American Mathematical Monthly 98, no. 5 (1991): 419. http://dx.doi.org/10.2307/2323859.

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Osserman, Robert. "Circumscribed Circles." American Mathematical Monthly 98, no. 5 (1991): 419–22. http://dx.doi.org/10.1080/00029890.1991.12000781.

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Şanlι, A. Metin, Saruhan Çekirge, and Zeki Şekerci. "Aneurysm of the distal anterior cerebral artery radiologically mimicking a ventricular mass." Journal of Neurosurgery 114, no. 4 (2011): 1061–64. http://dx.doi.org/10.3171/2010.6.jns10370.

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The ventricular system is a rare localization for intracranial aneurysms. Most ventricular aneurysms arise from a distal branch of the choroidal arteries and a major branch point of the circle of Willis. A 41-year-old-man suffering from dizziness of 2 weeks' duration was admitted to the clinic. On radiological examination, he had a well-circumscribed mass involving the frontal horn of the right lateral ventricle without radiological evidence of a prior or recent hemorrhage. Localization and radiological appearance were not typical of a ventricular mass and did not allow diagnosis. After cerebr

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