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Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Tiling (mathematics).'
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Journal articles on the topic "Tiling (mathematics)":
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Fosnaugh, Linda S., and Marvin E. Harrell. "Covering the Plane with Rep-Tiles." Mathematics Teaching in the Middle School 1, no. 8 (January 1996): 666–70. http://dx.doi.org/10.5951/mtms.1.8.0666.
Because of its beauty and applicability in ancient as well as modern times, the art of tiling has interested humankind for centuries. Roman mosaics and Moslem religious buildings are among some of the oldest examples of tiling. More modern examples of tiling as an art form can be found in the works of the Dutch artist M. C. Escher. Senechal (1990) notes that the study of tilings is important in mathematics education because the study of shape “draws on and contributes to not only mathematics but also the sciences and the arts.” Some common uses of tilings include the covering of walls, floors, ceilings, streets, sidewalks, and patios.
A fractal tiling or [Formula: see text]-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. By substitution rule of tilings, this short paper presents a very simple strategy to create a great number of [Formula: see text]-tilings. The substitution tiling Equithirds is demonstrated to show how to achieve it in detail. The method can be generalized to every tiling that can be constructed by substitution rule.
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KWAPISZ, JAROSLAW. "Rigidity and mapping class group for abstract tiling spaces." Ergodic Theory and Dynamical Systems 31, no. 6 (March 14, 2011): 1745–83. http://dx.doi.org/10.1017/s0143385710000696.
AbstractWe study abstract self-affine tiling actions, which are an intrinsically defined class of minimal expansive actions of ℝdon a compact space. They include the translation actions on the compact spaces associated to aperiodic repetitive tilings or Delone sets in ℝd. In the self-similar case, we show that the existence of a homeomorphism between tiling spaces implies conjugacy of the actions up to a linear rescaling. We also introduce the general linear group of an (abstract) tiling, prove its discreteness, and show that it is naturally isomorphic with the (pointed) mapping class group of the tiling space. To illustrate our theory, we compute the mapping class group for a five-fold symmetric Penrose tiling.
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Amano, Kazuyuki, and Yoshinobu Haruyama. "On the Number of p4-Tilings by an n-Omino." International Journal of Computational Geometry & Applications 29, no. 01 (March 2019): 3–19. http://dx.doi.org/10.1142/s0218195919400016.
A plane tiling by the copies of a polyomino is called isohedral if every pair of copies in the tiling has a symmetry of the tiling that maps one copy to the other. We show that, for every [Formula: see text]-omino (i.e., polyomino consisting of [Formula: see text] cells), the number of non-equivalent isohedral tilings generated by 90 degree rotations, so called p4-tilings or quarter-turn tilings, is bounded by a constant (independent of [Formula: see text]). The proof relies on the analysis of the factorization of the boundary word of a polyomino. We also show an example of a polyomino that has three non-equivalent p4-tilings.
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AVELINO, CATARINA P., and ALTINO F. SANTOS. "DEFORMATION OF F-TILINGSVERSUSDEFORMATION OF ISOMETRIC FOLDINGS." International Journal of Mathematics 23, no. 09 (July 31, 2012): 1250092. http://dx.doi.org/10.1142/s0129167x12500929.
We present some relations between deformation of spherical isometric foldings and deformation of spherical f-tilings. The natural way to deform f-tilings is based on the Hausdorff metric on compact sets. It is conjectured that any f-tiling is (continuously) deformable in the standard f-tiling τs= {(x, y, z) ∈ S2: z = 0} and it is shown that the deformation of f-tilings does not induce a continuous deformation on its associated isometric foldings.
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DOMBI, E. R., and N. D. GILBERT. "THE TILING SEMIGROUPS OF ONE-DIMENSIONAL PERIODIC TILINGS." Journal of the Australian Mathematical Society 87, no. 2 (July 23, 2009): 153–60. http://dx.doi.org/10.1017/s144678870800075x.
AbstractA one-dimensional tiling is a bi-infinite string on a finite alphabet, and its tiling semigroup is an inverse semigroup whose elements are marked finite substrings of the tiling. We characterize the structure of these semigroups in the periodic case, in which the tiling is obtained by repetition of a fixed primitive word.
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Kurz, Terri L. "The Mathematics of Tiling." Teaching Children Mathematics 20, no. 7 (March 2014): 416–17. http://dx.doi.org/10.5951/teacchilmath.20.7.0416.
People who lay tile for a living use mathematics every day to decide how much tile, grout, and other supplies are required to complete each job. Measurement and geometry are an integral part of designing tile patterns. Collections of short activities focus on a monthly theme that includes four activities each for grade bands K–2, 3–4, and 5–6 and aims for an inquiry or problem-solving orientation.
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Lidjan, Edin, and Ðordje Baralic. "Homology of polyomino tilings on flat surfaces." Applicable Analysis and Discrete Mathematics, no. 00 (2021): 31. http://dx.doi.org/10.2298/aadm210307031l.
The homology group of a tiling introduced by M. Reid is studied for certain topological tilings. As in the planar case, for finite square grids on topological surfaces, the method of homology groups, namely the non-triviality of some specific element in the group allows a ?coloring proof? of impossibility of a tiling. Several results about the non-existence of polyomino tilings on certain square-tiled surfaces are proved in the paper.
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Xu, You. "Fractal n-hedral tilings of ℝd." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 66, no. 3 (June 1999): 403–17. http://dx.doi.org/10.1017/s1446788700036697.
AbstractAn n-hedral tiling of ℝd is a tiling with each tile congruent to one of the n distinct sets. In this paper, we use the iterated function systems (IFS) to generate n-hedral tilings of ℝd. Each tile in the tiling is similar to the attractor of the IFS. These tiles are fractals and their boundaries have the Hausdorff dimension less than d. Our results generalize a result of Bandt.
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CANNON, S., D. A. LEVIN, and A. STAUFFER. "Polynomial Mixing of the Edge-Flip Markov Chain for Unbiased Dyadic Tilings." Combinatorics, Probability and Computing 28, no. 3 (October 31, 2018): 365–87. http://dx.doi.org/10.1017/s0963548318000470.
We give the first polynomial upper bound on the mixing time of the edge-flip Markov chain for unbiased dyadic tilings, resolving an open problem originally posed by Janson, Randall and Spencer in 2002 [14]. A dyadic tiling of size n is a tiling of the unit square by n non-overlapping dyadic rectangles, each of area 1/n, where a dyadic rectangle is any rectangle that can be written in the form [a2−s, (a + 1)2−s] × [b2−t, (b + 1)2−t] for a, b, s, t ∈ ℤ⩾ 0. The edge-flip Markov chain selects a random edge of the tiling and replaces it with its perpendicular bisector if doing so yields a valid dyadic tiling. Specifically, we show that the relaxation time of the edge-flip Markov chain for dyadic tilings is at most O(n4.09), which implies that the mixing time is at most O(n5.09). We complement this by showing that the relaxation time is at least Ω(n1.38), improving upon the previously best lower bound of Ω(n log n) coming from the diameter of the chain.
Persons, Michael Joseph. "Methods for creating corner colored Wang tiles." Pullman, Wash. : Washington State University, 2010. http://www.dissertations.wsu.edu/Thesis/Spring2010/m_persons_041210.pdf.
Thesis (M.S. in computer science)--Washington State University, May 2010. Title from PDF title page (viewed on May 18, 2010). "School of Engineering and Computer Science." Includes bibliographical references (p. 104-106).
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Hillman, Chris. "Sturmian dynamical systems /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5806.
Son, Younghwan. "Some results on joint ergodicity, sets of recurrence and substitution and tiling systems." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1369046202.
Savinien, Jean P. X. "Cohomology and K-theory of aperiodic tilings." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24732.
Thesis (Ph.D.)--Mathematics, Georgia Institute of Technology, 2008. Committee Chair: Prof. Jean Bellissard; Committee Member: Prof. Claude Schochet; Committee Member: Prof. Michael Loss; Committee Member: Prof. Stavros Garoufalidis; Committee Member: Prof. Thang Le.
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Praggastis, Brenda L. "Markov partitions for hyperbolic toral automorphisms /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/5773.
Laperriere, Christiane. "Positive cocycles for minimal Zd-actions on a cantor set resulting from cut and project schemes: The octogonal tiling." Thesis, University of Ottawa (Canada), 2009. http://hdl.handle.net/10393/28269.
We study the cut and projection method, which is a way to construct tilings. This construction leads to a minimal Zd -action on the Cantor set. In this thesis, we will focus our attention on two examples that we will describe in full details. the Fibonacci tiling on R and the octogonal tiling on R2 . For the octogonal tiling, we find small strictly positive cocycles for the minimal action on specific cones of Z2 .
Kaplan, Craig. Introductory tiling theory for computer graphics. San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA): Morgan & Claypool Publishers, 2009.
Book chapters on the topic "Tiling (mathematics)":
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Soifer, Alexander. "Tiling a Checker Rectangle." In Geometric Etudes in Combinatorial Mathematics, 3–60. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-75470-3_1.
Ostwald, Michael J. "Aperiodic Tiling, Penrose Tiling and the Generation of Architectural Forms." In Architecture and Mathematics from Antiquity to the Future, 459–71. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-00143-2_31.
Singer, David A. "Tiling the Plane with Regular Polygons." In Undergraduate Texts in Mathematics, 21–47. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0607-1_2.
Soifer, Alexander. "Mitya Karabash and a Tiling Conjecture." In Geometric Etudes in Combinatorial Mathematics, 215–19. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-75470-3_5.
Soifer, Alexander. "Norton Starr’s 3-Dimensional Tromino Tiling." In Geometric Etudes in Combinatorial Mathematics, 221–25. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-75470-3_6.
Hitchman, Michael P. "Tile Invariants for Tackling Tiling Questions." In Foundations for Undergraduate Research in Mathematics, 61–84. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66065-3_3.
Divincenzo, D. P. "Topics in Aperiodicity: Penrose Tiling Growth and Quantum Circuits." In The Mathematics of Long-Range Aperiodic Order, 127–40. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8784-6_6.
Kortenkamp, Ulrich. "Paving the Alexanderplatz Efficiently with a Quasi-Periodic Tiling." In Architecture and Mathematics from Antiquity to the Future, 473–81. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-00143-2_32.
Penrose, Roger. "Remarks on Tiling: Details of a (1 + ε + ε2)-Aperiodic Set." In The Mathematics of Long-Range Aperiodic Order, 467–97. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8784-6_18.
Conference papers on the topic "Tiling (mathematics)":
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Escudero, Juan García, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Topological Invariants and CW Complexes of Cartesian Product and Hexagonal Tiling Paces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636937.
Tan, Yean-Nee, and Chee Kit Ho. "I-tromino tilings of holey squares." In PROCEEDINGS OF THE 13TH IMT-GT INTERNATIONAL CONFERENCE ON MATHEMATICS, STATISTICS AND THEIR APPLICATIONS (ICMSA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5012184.
Say-awen, April Lynne D., Ma Louise Antonette N. de Las Peñas, and Teofina A. Rapanut. "On color fixing groups associated with colored symmetrical tilings." In INTERNATIONAL CONFERENCE ON MATHEMATICS, ENGINEERING AND INDUSTRIAL APPLICATIONS 2014 (ICoMEIA 2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4915645.
Avelino, Catarina P., Altino F. Santos, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Dihedral f-Tilings of the Sphere by Isosceles Triangles and Isosceles Trapezoids." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241518.
Ji, Ruihang, and Jie Ma. "Mathematical Modeling and Analysis of a Quadrotor with Tilting Propellers." In 2018 37th Chinese Control Conference (CCC). IEEE, 2018. http://dx.doi.org/10.23919/chicc.2018.8482899.
Chatterjee, Mayurika, Mangesh Kale, and B. N. Chaudhari. "Mathematical modelling of chassis dynamics of electric narrow tilting three wheeled vehicle." In 2015 Annual IEEE India Conference (INDICON). IEEE, 2015. http://dx.doi.org/10.1109/indicon.2015.7443585.
Kurabayashi, Shuichi. "Kinetics: A Mathematical Model for an On-Screen Gamepad Controllable by Finger-Tilting." In CHI PLAY '19: The Annual Symposium on Computer-Human Interaction in Play. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3341215.3356289.
Grillanda, Nicola, Andrea Chiozzi, Gabriele Milani, and Antonio Tralli. "Shear capacity assessment of dry joint masonry panels through tilting tests: Experimental test and numerical representation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0081520.
Nicoletti, Rodrigo, and Ilmar Ferreira Santos. "Frequency Response Analysis of an Actively Lubricated Rotor/Tilting-Pad Bearing System." In ASME Turbo Expo 2004: Power for Land, Sea, and Air. ASMEDC, 2004. http://dx.doi.org/10.1115/gt2004-54034.
In the present paper, the dynamic response of a rotor supported by an active lubricated tilting-pad bearing is investigated in the frequency domain. The theoretical part of the investigation is based on a mathematical model obtained by means of rigid body dynamics. The oil film forces are inserted into the model by using two different approaches: (a) linearized active oil film forces and the assumption that the hydrodynamic forces and the active hydraulic forces can be decoupled; (b) equivalent dynamic coefficients of the active oil film and the solution of the modified Reynolds equation for the active lubrication. The second approach based on the equivalent dynamic coefficients leads to more accurate results since it includes the frequency dependence of the active hydraulic forces. Theoretical and experimental results reveal the feasibility of reducing resonance peaks by using the active lubricated tilting-pad bearing. By applying a simple proportional controller, it is possible to reach 30% reduction of the resonance peak associated with the first rigid body mode shape of the system. One of the most important consequences of such a vibration reduction in rotating machines is the feasibility of increasing their operational range by attenuating resonance peaks and reducing vibration problems.
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Dourado, Arinan De P., Jefferson S. Barbosa, Tobias S. Morais, Aldemir Ap Cavalini, and Valder Steffen. "Uncertainty Analysis of a Francis Hydropower Unit." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85428.
This contribution is dedicated to the analysis of uncertainties affecting the vibration responses of a Francis hydropower unit. The system is composed by a vertical rotor and three hydrodynamic bearings: i) a combined tilting-pad guide/thrust bearing, located close to the generator; ii) an intermediate radial tilting-pad bearing; iii) and a cylindrical bearing located close to the Francis turbine. The bearings are represented by using linearized stiffness and damping coefficients. A fuzzy uncertainty analysis was applied aiming at determining the extreme vibration responses of the system. In this case, the bearings stiffness coefficients, generator mass, and Young’s modulus of the shaft were considered as uncertain information. The fuzzy analysis was carried out through the so-called α-level optimization approach due to its mathematical simplicity. Finally, a sensitivity analysis was performed based on the obtained results to determine the uncertain parameters that most affect the rotor responses. The obtained results demonstrate the representativeness of the conveyed methodology.
