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Journal articles on the topic 'Mathematical pattern'

Author: Grafiati
Published: 28 May 2022
Last updated: 29 May 2022

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1

SATO, Atsushi. "Mathematical Methods for Pattern Recognition." IEICE ESS FUNDAMENTALS REVIEW 5, no. 4 (2012): 302–11. http://dx.doi.org/10.1587/essfr.5.302.

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2

Washburn, Dorothy. "Mathematical Symmetries for Pattern Analysis." Anthropology News 40, no. 3 (March 1999): 26–27. http://dx.doi.org/10.1111/an.1999.40.3.26.3.

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3

Sanchez, A., A. del Rio, J. L. Valenzuela, and L. Romero. "Mathematical pattern of diagnosis: Muskmelon." Communications in Soil Science and Plant Analysis 23, no. 17-20 (November 1992): 2763–70. http://dx.doi.org/10.1080/00103629209368771.

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4

Kodituwakku, Saluka R. "Mathematical structures in pattern organizations." Journal of Science of the University of Kelaniya Sri Lanka 4 (January 17, 2011): 46. http://dx.doi.org/10.4038/josuk.v4i0.2697.

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5

Milton, Graeme W., and Ornella Mattei. "Field patterns: a new mathematical object." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2198 (February 2017): 20160819. http://dx.doi.org/10.1098/rspa.2016.0819.

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Field patterns occur in space–time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. In one spatial direction plus time, the field patterns occur when the slope of the characteristics is, in a sense, commensurate with the space–time microstructure. Field patterns with different spatial shifts do not generally interact, but rather evolve as if they live in separate dimensions, as many dimensions as the number of field patterns. Alternatively one can view a collection as a multi-component potential, with as many components as the number of field patterns. Presumably, if one added a tiny nonlinear term to the wave equation one would then see interactions between these field patterns in the multi-dimensional space that one can consider them to live, or between the different field components of the multi-component potential if one views them that way. As a result of P T -symmetry many of the complex eigenvalues of an appropriately defined transfer matrix have unit norm and hence the corresponding eigenvectors correspond to propagating modes. There are also modes that blow up exponentially with time.
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6

Trautmann, Laura, and Attila Piros. "A New Mathematical Method for Pattern Development." Periodica Polytechnica Mechanical Engineering 63, no. 1 (November 21, 2018): 44–51. http://dx.doi.org/10.3311/ppme.12648.

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The specialty of the patterns is that they are present in many disciplines, even our world is organized by them. The application of a regular structure in the field of product design may also open new possibilities. An automatized pattern can be used in many industries, such as interior design, paper industry, and so on. In this article we can see an example for utilization in electronic industry. The innovation is the pattern applied to the product, which was created with a new mathematical method. The goal was to develop a fully automatized general method. The description of the Generalized Design Pattern Vector (GDPV) which contains the functions of geometric transformations is also included.
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7

Chichilnisky, Eduardo J. "A mathematical model of pattern formation." Journal of Theoretical Biology 123, no. 1 (November 1986): 81–101. http://dx.doi.org/10.1016/s0022-5193(86)80237-5.

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8

Rodrigues, Fátima, and Pedro J. Freitas. "TILES AND IDENTITY BY PATTERN CLASSIFICATION." ARTis ON, no. 8 (December 30, 2018): 69–80. http://dx.doi.org/10.37935/aion.v0i8.218.

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Walled tiles can be figurative or patterned. Whereas the figurative tiles can better be described by theme or author, tile patterns are traditionally classified using more abstract rules that describe either the motif or the pattern itself. In this paper, we present a traditional mathematical classification of plane patterns, the Washburn and Crowe Algorithm, and use it to identify or distinguish tile patterns. We present a complete mathematical classification of the tile patterns present in all places of public access in the Almada region and show how this classification can help recover damaged tiled walls and floors, in order to preserve our heritage. We extend this mathematical analysis to 20th century patterns and quasipatterns, hoping to show that this classification can add to our knowledge of the identity of these patterns.
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Puspasari, Ratih, Setyo Hartanto, Mohamad Gufron, Pradnyo Wijayanti, and Mega Teguh Budiarto. "Frieze Pattern on Shibori Fabric." Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang 6, no. 1 (January 21, 2022): 67. http://dx.doi.org/10.31331/medivesveteran.v6i1.1904.

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Mathematics and culture are two things that are closely related to the activities of daily human life. Because Mathematics is a form of culture that is integrated in all people's lives. This means that, in culture we can find various kinds of mathematical concepts called ethnomathematics. Shibori is a technique of manipulating cloth originating from Japan, to create patterns through a dyeing method that has been around since the 8th century. The patterns created in Shibori generally depict an asymmetrical shape. In the Shibori motif there are several mathematical elements, one of which is the Frieze Group pattern. The Frieze Group is a subgroup of a symmetry group that is constructed by translation in one direction. The Frieze pattern has 7 (seven) types of patterns consisting of isometric combinations and can be classified as cyclic or dihedral groups. This study is an ethnographic study, with exploration and documentation of Shibori. The data analysis technique chosen is interview, observation and documentation. The research subjects were Shibori fabric craftsmen in Tulungagung district, East Java. The purpose of this research is to further examine the cultural patterns of Shibori Traditional cloth into Frieze patterns, as a way to understand mathematics through culture. The results of the research conducted have shown that there are mathematical concepts (geometry) in the Shibori motif, namely the Frieze pattern F1, F2, F3, F5, F6, F7. Keywords: Group Frizes; Ethnomathematics; Shibori
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10

Smith, Margaret S., Amy F. Hillen, and Christy L. Catania. "Using Pattern Tasks to Develop Mathematical Understandings and Set Classroom Norms." Mathematics Teaching in the Middle School 13, no. 1 (August 2007): 38–44. http://dx.doi.org/10.5951/mtms.13.1.0038.

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The capacity to reason algebraically is critical in shaping students' future opportunities and, as such, is a central theme of K–12 education (NCTM 2000). One component of algebraic reasoning is “the capacity to recognize patterns and organize data to represent situations in which input is related to output by well-defined functional rules” (Driscoll 1999, p. 2). Geometric pattern tasks can be a useful tool for helping students develop algebraic reasoning, because the tasks provide students with opportunities to build patterns with materials such as toothpicks or pattern blocks. These materials help students “focus on the physical changes and how the pattern is being developed” (Friel, Rachlin, and Doyle 2001, p. 10). Such work might help bridge students' earlier mathematical experiences and lay the foundation for more formal work in algebra (English and Warren 1998; Ferrini-Mundy, Lappan, and Phillips 1997; NCTM 2000). Finally, the relationships between the quantities in pattern tasks can be expressed using symbols, tables, and graphs, as well as words. Thus, pattern tasks can also give students opportunities to make connections among representations—a key component in developing an understanding of function (Knuth 2000).
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11

Lawton, Stephen L., and Lawrence S. Bartell. "Application of the overlap integral in X-ray diffraction powder pattern recognition." Powder Diffraction 9, no. 2 (June 1994): 124–35. http://dx.doi.org/10.1017/s088571560001410x.

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Use of the overlap integral in X-ray diffraction (XRD) powder pattern recognition of crystalline materials is presented. The mathematical expression, derived specifically for diffraction data, provides a measure of similarity between two patterns. Each pattern is represented by a normalized mathematical function. The index of similarity, or overlap integral, indicates how faithfully the two functions overlap and ranges from zero to unity, reaching the latter limit when the two patterns become identical.
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12

Calleja, James. "A spiral pattern investigation: making mathematical connections." Mathematical Gazette 104, no. 560 (June 18, 2020): 262–70. http://dx.doi.org/10.1017/mag.2020.49.

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Nowadays there is considerable agreement among educators that learning mathematics fundamentally involves making mathematics [1]. Students learn mathematics while working on tasks that they consider meaningful and worthwhile, and their interest is aroused when they can see the point of what they are being asked to do. Given that learning mathematics involves a process of meaning-making - the use of mathematical language, symbols and representations as learners negotiate ideas – activities should provide students with a variety of challenging experiences through which they can actively construct mathematical meanings for themselves.
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13

P. Singh, Brijesh. "Analysis of Fertility Pattern Through Mathematical Curves." American Journal of Theoretical and Applied Statistics 4, no. 2 (2015): 64. http://dx.doi.org/10.11648/j.ajtas.20150402.14.

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14

Asli Özgün-Koca, S., and Matt Enlow. "GPS: Pattern Recognition to Explore Mathematical Structure." Mathematics Teacher: Learning and Teaching PK-12 113, no. 8 (August 2020): 681–83. http://dx.doi.org/10.5951/mtlt.2020.0126.

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15

Jonathan R. Potts and Mark A. Lewis. "A Mathematical Approach to Territorial Pattern Formation." American Mathematical Monthly 121, no. 9 (2014): 754. http://dx.doi.org/10.4169/amer.math.monthly.121.09.754.

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16

Kumar, Navdeep, and Pankaj Garg. "A New Mathematical Approach for Pattern Generation." International Journal of Computer Applications 24, no. 2 (June 30, 2011): 39–42. http://dx.doi.org/10.5120/2920-3853.

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17

Pedrycz, Witold. "Granular Mathematical Models in Pattern Classification Problems." Journal of Advanced Mathematics and Applications 1, no. 1 (September 1, 2012): 54–62. http://dx.doi.org/10.1166/jama.2012.1005.

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18

Houssart, Jenny. "Perceptions of Mathematical Pattern amongst Primary Teachers." Educational Studies 26, no. 4 (December 2000): 489–502. http://dx.doi.org/10.1080/03055690020003665.

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19

McKee, T. A. "Generalized equivalence: A pattern of mathematical expression." Studia Logica 44, no. 3 (1985): 285–89. http://dx.doi.org/10.1007/bf00394447.

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20

Girit Yildiz, Dilek, and Burcu Durmaz. "A Gifted High School Student’s Generalization Strategies of Linear and Nonlinear Patterns via Gauss’s Approach." Journal for the Education of the Gifted 44, no. 1 (February 7, 2021): 56–80. http://dx.doi.org/10.1177/0162353220978295.

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Mathematically gifted students have a high potential for understanding and thinking through mathematical relations and connections between mathematical concepts. Currently, it is thought that generalizing patterns algebraically can serve to provide challenges and opportunities that match their potential. This article focuses on a mathematically gifted student’s use of generalization strategies to identify linear and nonlinear patterns in the context of a matchstick problem. Data were collected from a 10th-grade gifted student’s problem-solving process in a qualitative research design. It was observed that the gifted student’s ways of generalizing the linear and nonlinear patterns were different. In a generalization process, the student used figural reasoning in the linear pattern and numerical reasoning in the nonlinear patterns. It was noted that the student explored using Gauss’s approach in structuring the general rules of nonlinear patterns. Accordingly, aside from assisting their more gifted students, mathematics teachers may want to consider ways to introduce Gaussian thinking to the benefit of all their students.
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21

Sugimura, Kaoru, Tadashi Uemura, and Atsushi Mochizuki. "1P491 Mathematical modeling for pattern formation of dendrite(24. Mathematical biology,Poster Session,Abstract,Meeting Program of EABS & BSJ 2006)." Seibutsu Butsuri 46, supplement2 (2006): S269. http://dx.doi.org/10.2142/biophys.46.s269_3.

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22

Raup, David M. "Mathematical models of cladogenesis." Paleobiology 11, no. 1 (1985): 42–52. http://dx.doi.org/10.1017/s0094837300011386.

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The evolutionary pattern of speciation and extinction in any biologic group may be described by a variety of mathematical models. These models provide a framework for describing the history of taxonomic diversity (clade shape) and other aspects of larger evolutionary patterns. The simplest model assumes time homogeneity: that is, speciation and extinction probabilities are constant through time and within taxonomic groups. In some cases the homogeneous model provides a good fit to real world paleontological data, but in other cases the model serves only as a null hypothesis that must be rejected before more complex models can be applied. In cases where the homogeneous model does not fit the data, time-inhomogeneous models can be formulated that specify change, regular or episodic, in speciation and extinction probabilities. An appendix provides a list of the most useful equations based on the homogeneous model.
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23

Dawes, Michael J., and Michael J. Ostwald. "The mathematical structure of Alexander’s A Pattern Language: An analysis of the role of invariant patterns." Environment and Planning B: Urban Analytics and City Science 47, no. 1 (February 28, 2018): 7–24. http://dx.doi.org/10.1177/2399808318761396.

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In 1977 Christopher Alexander and his colleagues from the Centre for Environmental Structure published A Pattern Language, an innovative design guide aimed at restoring life and beauty to the built environment. Since then, A Pattern Language has become one of the most widely read architectural treatises ever published. However, despite its popularity, the structure of A Pattern Language remains poorly understood. In response to this situation, this paper uses graph theory to examine Alexander’s language including the entire set of 253 patterns and over 1800 relationships between them. Through this mathematical analysis the paper tests two hypotheses about the ‘invariant patterns’ Alexander was most confident in. The first hypothesis tests whether invariant patterns occupy more prominent positions within the language, and the second tests whether invariant patterns form a core structure within the language that supports less developed patterns. Through this process the paper illuminates several previously unconsidered aspects of the structure of A Pattern Language while providing the first graphic representation of the entire underlying structure that unites the individual patterns into a coherent language.
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24

Klefenz, Frank, and Adam Williamson. "Modeling the Formation Process of Grouping Stimuli Sets through Cortical Columns and Microcircuits to Feature Neurons." Computational Intelligence and Neuroscience 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/290358.

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A computational model of a self-structuring neuronal net is presented in which repetitively applied pattern sets induce the formation of cortical columns and microcircuits which decode distinct patterns after a learning phase. In a case study, it is demonstrated how specific neurons in a feature classifier layer become orientation selective if they receive bar patterns of different slopes from an input layer. The input layer is mapped and intertwined by self-evolving neuronal microcircuits to the feature classifier layer. In this topical overview, several models are discussed which indicate that the net formation converges in its functionality to a mathematical transform which maps the input pattern space to a feature representing output space. The self-learning of the mathematical transform is discussed and its implications are interpreted. Model assumptions are deduced which serve as a guide to apply model derived repetitive stimuli pattern sets toin vitrocultures of neuron ensembles to condition them to learn and execute a mathematical transform.
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25

Cuerno, R., C. Escudero, J. M. García-Ruiz, and M. A. Herrero. "Pattern formation in stromatolites: insights from mathematical modelling." Journal of The Royal Society Interface 9, no. 70 (October 12, 2011): 1051–62. http://dx.doi.org/10.1098/rsif.2011.0516.

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To this day, computer models for stromatolite formation have made substantial use of the Kardar–Parisi–Zhang (KPZ) equation. Oddly enough, these studies yielded mutually exclusive conclusions about the biotic or abiotic origin of such structures. We show in this paper that, at our current state of knowledge, a purely biotic origin for stromatolites can neither be proved nor disproved by means of a KPZ-based model. What can be shown, however, is that whatever their (biotic or abiotic) origin might be, some morphologies found in actual stromatolite structures (e.g. overhangs) cannot be formed as a consequence of a process modelled exclusively in terms of the KPZ equation and acting over sufficiently large times. This suggests the need to search for alternative mathematical approaches to model these structures, some of which are discussed in this paper.
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26

Stafford, F. S., and G. M. Barnwell. "Mathematical Models of Central Pattern Generators in Locomotion." Journal of Motor Behavior 17, no. 1 (March 1985): 3–26. http://dx.doi.org/10.1080/00222895.1985.10735335.

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27

Stafford, F. S., and G. M. Barnwell. "Mathematical Models of Central Pattern Generators in Locomotion." Journal of Motor Behavior 17, no. 1 (March 1985): 27–59. http://dx.doi.org/10.1080/00222895.1985.10735336.

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28

Stafford, F. S., and G. M. Barnwell. "Mathematical Models of Central Pattern Generators in Locomotion." Journal of Motor Behavior 17, no. 1 (March 1985): 60–76. http://dx.doi.org/10.1080/00222895.1985.10735337.

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29

Eremin, I. I., V. D. Mazurov, and N. N. Astaf 'ev. "Linear inequalities in mathematical programming and pattern recognition." Ukrainian Mathematical Journal 40, no. 3 (1989): 243–51. http://dx.doi.org/10.1007/bf01061299.

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30

Young, Elaine. "Mathematical Exploration: Trapezoids to Triangles." Mathematics Teaching in the Middle School 15, no. 7 (March 2010): 414–19. http://dx.doi.org/10.5951/mtms.15.7.0414.

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Pattern blocks are often used in math class during geometry lessons to support concepts of shape, angle, tessellations, and symmetry. They are also used with fraction study (e.g., Lanius 2007; NCTM 2009a). Using pattern blocks to construct other larger geometric shapes can help students understand the relationships among various shapes. Algebraic relationships and functions emerge when students count blocks and measure figures. The activities in this article support the development of such geometric vocabulary as perimeter, area, sequence, and nonstandard measurement.
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31

Alabdulkader, A. M., A. I. Al-Amoud, and F. S. Awad. "  Optimization of the cropping pattern in Saudi Arabia using a mathematical programming sector model." Agricultural Economics (Zemědělská ekonomika) 58, No. 2 (March 5, 2012): 56–60. http://dx.doi.org/10.17221/8/2011-agricecon.

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A mathematical sector model has been formulated to optimize the cropping pattern in Saudi Arabia aiming at maximizing the net annual return of the agricultural sector in Saudi Arabia and ensuring the efficient allocation of the scarce water resources and arable land among the competing crops. The results showed the potential for Saudi Arabia to optimize its cropping pattern and to generate an estimated net return equivalent to about 2.42 billion US$ per year. The optimized cropping pattern in Saudi Arabia has been coupled with about 53% saving in the water use and about 48% reduction in the arable land use compared to the base-year cropping pattern. Comparable weights was given to different crop groups by allocating about 48.4%, 35.4%, 13.1%, and 3.2% to grow cereals, fruits, forages, and vegetables, respectively. These findings were in line with the national strategy to rationalize the cultivation of water-intensive crops in favour of highly water-efficient crops.  
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32

Abdurrahman, Muhammad Sani. "Pupil’s Behaviour Pattern and Non-Routine Mathematical Problem-Solving Strategy based on Multiple Intelligences." Journal of Advanced Research in Dynamical and Control Systems 12, no. 3 (March 20, 2020): 466–85. http://dx.doi.org/10.5373/jardcs/v12i3/20201214.

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33

Jean, Roger V. "Phyllotaxis: a reappraisal." Canadian Journal of Botany 67, no. 10 (October 1, 1989): 3103–7. http://dx.doi.org/10.1139/b89-389.

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The field of research known as pyllotaxis has been the object of intense studies in the last 15 years. The present article proposes a reflection on the subject and on the objectives of this discipline and places it in a broader perspective. It stresses the necessity of a systemic and synergetic approach. The "biological problem" of phyllotaxis is redefined in the light of the fact that patterns identical to phyllotactic patterns are found in other areas of research. It is underlined that this organizational problem is fundamentally a "mathematical problem," the mathematical approach being able indeed to reach the explanatory level and the fundamental causes as well. To replace the narrow term phyllotaxis, the logo PPM, for primordial pattern morphogenesis and pyramidal pattern modelling, is proposed to underline the synergy of biological and mathematical approaches.
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34

Moh, Zayyadi, and Kurniati Dian. "Mathematics reasoning and proving of students in generalizing the pattern." International Journal of Engineering & Technology 7, no. 2.10 (April 2, 2018): 15. http://dx.doi.org/10.14419/ijet.v7i2.10.10945.

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The purpose of this study was to identify students' reasoning in generalizing the patterns that proved by generalizing the structural generalizations with involve the mathematical structures and empirical generalizations that emphasize perceptions or evidence derived from the found regularities. The subjects in this research were the 7th semester students of Mathematics Education of University of Madura, Indonesia. The research steps in this research were (1) giving the reasoning tests to the research subjects, (2) analyzing the results of reasoning tests to identify reasoning and mathematical proofs, (3) conducting in-depth interviews as the triangulation method, and (4) summarizing the tendencies of reasoning and proof of student in generalize pattern. Based on the results and discussion can be obtained that in the process of reasoning and verification, students in identifying the same pattern with trial and error, so by using trial and error students find many ways to generalize the existing pattern. However, sometimes through the use of ways of trial and error students find the right pattern. Therefore, the student only identifies a reasonable pattern and does not identify mathematical patterns, then makes reasonable assumptions about finding a relationship but only hypothetical and needs to prove the allegations and only do a few stages of reasoning and not doing the stages of proof, giving no argument and not doing a validation of the evidence.
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35

Kadir, Abdul, Rochmad Rochmad, and Iwan Junaedi. "Mathematical Connection Ability of Grade 8th Students’ in terms of Self-Concept in Problem Based Learning." Journal of Primary Education 9, no. 3 (May 31, 2020): 258–66. http://dx.doi.org/10.15294/jpe.v9i3.37547.

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MMathematical connections ability is a demand in mathematics education to develop mathematical ideas and problem-solving in one another. This study aims to find mathematical connection ability patterns in terms of self-concept. The research method used is mixed methods with concurrent embedded design, quantitative research analysis using true experimental design, while qualitative research analysis uses the Miles and Huberman model. The population in this study was eighth-grade students of SMP Negeri 13 Semarang, Indonesia, and sampling was done by random sampling technique. The results showed that the mathematical connection ability pattern in terms of mathematical self-concepts is diverse. It is found that there were two patterns of mathematical connection ability in subjects with high self-concept. In subjects with moderate self-concept, three patterns of mathematical connection ability subjects with low self-concept, three patterns of mathematical connection ability are found
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Sagar, B. S. Daya. "Cartograms via mathematical morphology." Information Visualization 13, no. 1 (March 26, 2013): 42–58. http://dx.doi.org/10.1177/1473871613480061.

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Visualization of geographic variables as spatial objects of size proportional to variable strength is possible via generating cartograms. We developed a methodology based on mathematical morphology to generate contiguous cartograms. This methodology relies on weighted skeletonization by zone of influence. This weighted skeletonization by zone of influence determines the points of contact of multiple frontlines propagating from centroids of various planar sets (states) at the traveling rates depending upon the variable’s strength. The contiguous cartogram generated via this morphology-based algorithm preserves the global shape and local shapes and yields minimal area errors. We generated a cartogram for a population variable to demonstrate the proposed approach. Furthermore, the population cartograms for the United States generated via four other approaches are compared with the morphology-based cartogram in terms of errors with respect to area, local shape, and global shape. This approach for generating cartograms preserves the global shape at the expense of compromising with area errors. It is inferred from the comparative error analysis that the proposed morphology-based approach could be further extended by exploring the applicability of additional characteristics of B, which controls the dilation propagation speed and direction of dilation while performing weighted skeletonization by zone of influence, to minimize the local shape errors and area errors.
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37

Preston, Kendall. "Three-dimensional mathematical morphology." Image and Vision Computing 9, no. 5 (October 1991): 285–95. http://dx.doi.org/10.1016/0262-8856(91)90033-l.

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38

Silva, Francisco de Assis Tavares Ferreira da, Magno Prudêncio de Almeida Filho, Antonio Macilio Pereira de Lucena, and Alexandre Guirland Nowosad. "Pattern recognition on FPGA for aerospace applications." Research, Society and Development 10, no. 12 (September 14, 2021): e83101219181. http://dx.doi.org/10.33448/rsd-v10i12.19181.

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This paper presents a low power near real-time pattern recognition technique based on Mathematical Morphology-MM implemented on FPGA (Field Programmable Gate Array). The key to the success of this approach concerns the advantages of machine learning paradigm applied to the translation invariant template-matching operators from MM. The paper shows that compositions of simple elementary operators from Mathematical Morphology based on ELUTs (Elementary Look-Up Tables) are very suitable to embed in FPGA hardware. The paper also shows the development techniques regarding all mathematical modeling for computer simulation and system generating models applied for hardware implementation using FPGA chip. In general, image processing on FPGAs requires low-level description of desired operations through Hardware Description Language-HDL, which uses high complexity to describe image operations at pixel level. However, this work presents a reconfiguring pattern recognition device implemented directly in FPGA from mathematical modeling simulation under Matlab/Simulink/System Generator environment. This strategy has reduced the hardware development complexity. The device will be useful mainly when applied on remote sensing tasks for aerospace missions using passive or active sensors.
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39

Anderson, Katie L. "Pattern-block frenzy." Teaching Children Mathematics 19, no. 2 (September 2012): 116–21. http://dx.doi.org/10.5951/teacchilmath.19.2.0116.

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Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.
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40

Land, Jill E., and Paul G. Becher. "A Teacher's Journal: Liz's Pattern." Teaching Children Mathematics 3, no. 6 (February 1997): 301–4. http://dx.doi.org/10.5951/tcm.3.6.0301.

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41

Putnam, Lance. "The Harmonic Pattern Function: A Mathematical Model Integrating Synthesis of Sound and Graphical Patterns." Leonardo 50, no. 5 (October 2017): 535. http://dx.doi.org/10.1162/leon_a_01498.

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42

Ding, Jun, Anthony S. Wexler, and Stuart A. Binder-Macleod. "Development of a mathematical model that predicts optimal muscle activation patterns by using brief trains." Journal of Applied Physiology 88, no. 3 (March 1, 2000): 917–25. http://dx.doi.org/10.1152/jappl.2000.88.3.917.

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Because muscles must be repetitively activated during functional electrical stimulation, it is desirable to identify the stimulation pattern that produces the most force. Previous experimental work has shown that the optimal pattern contains an initial high-frequency burst of pulses (i.e., an initial doublet or triplet) followed by a low, constant-frequency portion. Pattern optimization is particularly challenging, because a muscle's contractile characteristics and, therefore, the optimal pattern change under different physiological conditions and are different for each person. This work describes the continued development and testing of a mathematical model that predicts isometric forces from fresh and fatigued muscles in response to brief trains of electrical pulses. By use of this model and an optimization algorithm, stimulation patterns that produced maximum forces from each subject were identified.
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Muldiana, Fitriani, Shofa Laelatul, Neng Ani Karleni, and Nani Ratnaningsih. "ESTETIKA MATEMATIS MOTIF SONGKET PADA ANYAMAN MENDONG TASIKMALAYA." Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi 9, no. 2 (December 1, 2021): 109–21. http://dx.doi.org/10.34312/euler.v9i2.11259.

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Mathematics is an enigmatic and captivating idea. Mathematics can also be defined in the context of patterns. This is because mathematics contains patterns, structures, and depictions of an object that grows and is rooted in real life. The structure or pattern that is arranged systematically will produce work, objects, and even an agreement. Life mathematics and mathematics in school learning can be combined with aesthetic studies to achieve contextual learning. This study uses qualitative research with an ethnographic approach. The purpose of this study was to reveal the aesthetic value and mathematical concepts of the mendong woven pattern with the songket motif. The location of this research is Babakan Cikawung Village, Margabakti Village, Cibeureum Awipari District, Tasikmalaya Regency. This study involved 3 subjects. Data collection techniques were carried out through unstructured interviews, observation, documentation, and literature review. Unstructured interviews were used to ask about the craft of mendong and the process of making mending weave with songket motifs. Observations or observations are made to find mathematical concepts and mathematical aesthetic values by studying the aesthetics of Thomas Aquinas' theory. The results of the research are mathematical aesthetics by examining the theory of Thomas Aquinas. Mathematical concepts such as repeating patterns 1-2-3-4 and 4-3-2-1, geometric concepts such as parallel lines, reflection, congruence, and rhombus flat shapes.
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Zhuo, Zhiyi. "New Mathematical model of Retailer-to-Individual Customer Optimal Product Supply Strategies Under False Demand Pattern: Customer Discount Mode." Journal of Mathematics Research 12, no. 1 (January 12, 2020): 36. http://dx.doi.org/10.5539/jmr.v12n1p36.

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This paper develops a new mathematical model by using the false demand function and the retailer profit function, to study the retailer-to-individual customer optimal product supply strategies under the false demand pattern, and solve the product profit optimal problem. The research contribution of this paper is to construct the mathematical model of customer discount mode for the retailer-to-individual customer product supply strategies under the false demand pattern. The study results provide a reference for retailers to develop different supply strategies for different types of customers in different demand patterns, enabling them to improve operational performance effectively.
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Hunt, R. D., and R. V. Jean. "Mathematical Approach to Pattern and Form in Plant Growth." Biometrics 41, no. 2 (June 1985): 594. http://dx.doi.org/10.2307/2530889.

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Ripley, B. D., and U. Grenander. "General Pattern Theory: A Mathematical Theory of Regular Structures." Journal of the Royal Statistical Society. Series A (Statistics in Society) 158, no. 3 (1995): 635. http://dx.doi.org/10.2307/2983457.

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Dougoud, Michaël, Christian Mazza, Beat Schwaller, and László Pecze. "Extending the Mathematical Palette for Developmental Pattern Formation: Piebaldism." Bulletin of Mathematical Biology 81, no. 5 (January 28, 2019): 1461–78. http://dx.doi.org/10.1007/s11538-019-00569-1.

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Ramírez Uclés, Rafael, Aurora del Río Cabeza, and Pablo Flores Martínez. "Mathematical Talent in Braille Code Pattern Finding and Invention." Roeper Review 40, no. 4 (October 2, 2018): 255–67. http://dx.doi.org/10.1080/02783193.2018.1501782.

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McVarish, Judith. "Pattern and order: a mathematical lens for reflective writing." Reflective Practice 10, no. 4 (September 2009): 465–76. http://dx.doi.org/10.1080/14623940903138324.

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Senger, Elizabeth S. "Student-Invented Numeration Systems: Pattern-Analysis and Mathematical Understanding." School Science and Mathematics 97, no. 3 (March 1997): 139–49. http://dx.doi.org/10.1111/j.1949-8594.1997.tb17357.x.

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