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Relevant bibliographies by topics / Triangle (Geometry)

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Academic literature on the topic 'Triangle (Geometry)'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Triangle (Geometry)"

1

Leversha, Gerry, and G. C. Smith. "Euler and triangle geometry." Mathematical Gazette 91, no. 522 (2007): 436–52. http://dx.doi.org/10.1017/s0025557200182087.

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There is a very easy way to produce the Euler line, using transformational arguments. Given a triangle ABC, let AʹBʹ'C be the medial triangle, whose vertices are the midpoints of the sides. These two triangles are homothetic: they are similar and corresponding sides are parallel, and the centroid, G, is their centre of similitude. Alternatively, we say that AʹBʹC can be mapped to ABC by means of an enlargement, centre G, with scale factor –2.

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Kalish, Arthur L. "Delving Deeper: Extending a Classical Geometry Problem." Mathematics Teacher 102, no. 8 (2009): 634–38. http://dx.doi.org/10.5951/mt.102.8.0634.

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In “The Surfer Problem: A ‘Whys’ Approach” (Mathematics Teacher 100, no. 1 [August 2006]: 14–19), Larry Copes and Jeremy Kahan introduced a variety of proofs to one of the classic geometry theorems: The sum of distances from all points in the interior of an equilateral triangle to the three edges is the same. The authors went on to prove that this constant distance is the height of the triangle. Although they presented a range of methods for proving this theorem, I offer one additional method that makes use of a lemma concerning isosceles triangles, introduced below. I will then extend the the

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Kalish, Arthur L. "Delving Deeper: Extending a Classical Geometry Problem." Mathematics Teacher 102, no. 8 (2009): 634–38. http://dx.doi.org/10.5951/mt.102.8.0634.

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In “The Surfer Problem: A ‘Whys’ Approach” (Mathematics Teacher 100, no. 1 [August 2006]: 14–19), Larry Copes and Jeremy Kahan introduced a variety of proofs to one of the classic geometry theorems: The sum of distances from all points in the interior of an equilateral triangle to the three edges is the same. The authors went on to prove that this constant distance is the height of the triangle. Although they presented a range of methods for proving this theorem, I offer one additional method that makes use of a lemma concerning isosceles triangles, introduced below. I will then extend the the

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Čerin, Zvonko. "On Napoleon triangles and propeller theorems." Mathematical Gazette 87, no. 508 (2003): 42–50. http://dx.doi.org/10.1017/s0025557200172092.

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In this paper we shall consider two situations in triangle geometry when equilateral triangles appear and then show that they are closely related.In the first (known as the Napoleon theorem) equilateral triangles BCAT, CABT, and ABCT, are built on the sides of an arbitrary triangle ABC and their centroids are (almost always) vertices of an equilateral triangle ANBNCN (known as a Napoleon triangle of ABC; see Figure 1).

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Adams, Thomasenia Lott, and Fatma Aslan-Tutak. "Math Roots: Serving Up Sierpinski!" Mathematics Teaching in the Middle School 11, no. 5 (2006): 248–53. http://dx.doi.org/10.5951/mtms.11.5.0248.

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The sierpinski triangle, created in 1916, has some very interesting characteristics. It is an impressive and valuable topic for mathematical exploration, since it combines Euclidean geometry (triangles and measurement) with fractal geometry. The Sierpinski triangle, also known as the Sierpinski gasket, is a fractal formed from an equilateral triangle. It is one of the most popular fractals to construct and analyze in middle school mathematics lessons. Since the 1960s, it has been possible to design fractals using a computer program, especially the complex examples that are often difficult to c

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Maran, A. K. "Maran's theorem (New theorem) on Right-angled triangle." Mapana - Journal of Sciences 3, no. 1 (2004): 7–10. http://dx.doi.org/10.12723/mjs.5.2.

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In Geometric, right-angled triangle is One Of the two—dimensional plane having three sides With one Of its angle is 9C and whk-h is important to solve problems related to Geometry and sometimes in Other subiect os well. Some fundamental concept 'theorems Of triangles are required to solve such problems and such theorems cre Pythagoras theorern' Pythagoras theorern (ii0 Appollonius theorem Euclids theorem' and (v) Eucli&s 20 theorem (Altitude theorem).3 I n addition to these, the author attempted to develop a new theorem related to right-angled triangle (Maran's theorem of right-angled tria

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Liu, Xinjin, and Xuzhong Su. "Theoretical Study of Effect of Ring Spinning Triangle Division on Fiber Tension Distribution." Journal of Engineered Fibers and Fabrics 10, no. 3 (2015): 155892501501000. http://dx.doi.org/10.1177/155892501501000314.

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The spinning triangle is a critical region in the spinning process of staple yarn. Its geometry influences the distribution of fiber tension at spinning triangle directly and affects the qualities of spun yarns. Taking appropriate measures to change the ring spinning triangle geometry and improve the qualities of yarn has attracted more and more interest recently. Spinning triangle division is one of the most effective measures, such as solospun technology. Therefore, in this paper, the effect of ring spinning triangle division on fiber tension distribution was studied theoretically. The gener

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ZHANG, XIN-MIN, L. RICHARD HITT, BIN WANG, and JIU DING. "SIERPIŃSKI PEDAL TRIANGLES." Fractals 16, no. 02 (2008): 141–50. http://dx.doi.org/10.1142/s0218348x08003934.

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We generalize the construction of the ordinary Sierpiński triangle to obtain a two-parameter family of fractals we call Sierpiński pedal triangles. These fractals are obtained from a given triangle by recursively deleting the associated pedal triangles in a manner analogous to the construction of the ordinary Sierpiński triangle, but their fractal dimensions depend on the choice of the initial triangles. In this paper, we discuss the fractal dimensions of the Sierpiński pedal triangles and the related area ratio problem, and provide some computer-generated graphs of the fractals.

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Silvester, John R. "On cardioids and Morley's theorem." Mathematical Gazette 105, no. 562 (2021): 40–51. http://dx.doi.org/10.1017/mag.2021.6.

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Morley’s trisector theorem says that the three intersections of the trisectors of the angles of a triangle, lying near the three sides respectively, form an equilateral triangle. See Figure 1. Morley discovered his theorem in 1899, and news of it quickly spread. Over the years many proofs have been published, by trigonometry or by geometry, but a simple angle-chasing argument is elusive. See [1] for a list up to 1978. Perhaps the easiest proof is that of John Conway [2], who assembles a triangle similar to the given triangle by starting with an equilateral triangle and surrounding it by triang

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Haleem, Noman, Stuart Gordon, Xin Liu, Christopher Hurren, and Xungai Wang. "Dynamic analysis of spinning triangle geometry part 2: spinning triangle geometry and yarn quality." Journal of The Textile Institute 110, no. 5 (2018): 671–79. http://dx.doi.org/10.1080/00405000.2018.1511227.

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Dissertations / Theses on the topic "Triangle (Geometry)"

1

Winer, Michael Loyd. "Students' Reasoning with Geometric Proofs that use Triangle Congruence Postulates." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1500037701968622.

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Ramos, Romero Jose Francisco. "LODStrips:Continuous Level of Detail using Triangle Strips." Doctoral thesis, Universitat Jaume I, 2008. http://hdl.handle.net/10803/10480.

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In recent years, multiresolution models have progressed substantially. At the beginning, discrete models were employed in graphics applications, due mainly to the low degree of complexity involved in implementing them, which is the reason why nowadays they are still used in applications without high graphics requirements. Nevertheless, the increase in realism in graphics applications makes it necessary to use multiresolution models which are more exact in their approximations, which do not call for high storage costs and which are faster in visualization. This has given way to continuous model

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Huang, Haifei. "The common self-polar triangle of conics and its applications to computer vision." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/407.

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In projective geometry, the common self-polar triangle has often been used to discuss the location relationship of two planar conics. However, there are few researches on the properties of the common self-polar triangle, especially when the two planar conics are special conics. In this thesis, the properties of the common self-polar triangle of special conics are studied and their applications to computer vision are presented. Specifically, the applications focus on the two topics of the computer vision: camera calibration and homography estimation. This thesis first studies the common self-po

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LeDrew, Janice. "Three-dimensional geometry and evolution of the Lovett River Triangle Zone, central Alberta Foothills." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq24678.pdf.

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Löwgren, Martin, and Niklas Olin. "PN-triangle tessellation using Geometry shaders : The effect on rendering speed compared to the fixed function tessellator." Thesis, Blekinge Tekniska Högskola, Sektionen för datavetenskap och kommunikation, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-3818.

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With each computer game generation there is always a demand for more visually pleasing environments. This pushes game developers to create more powerful rendering techniques and game artists to create more detailed art. With a visually stunning backdrop also comes the need for high-resolution models. A common issue is that if all models in a scene are high-resolution it would not only require immensely powerful hardware, it would also be wasteful as only the models in the foreground are close enough that we would recognize the increased details. The common solution to this problem has been to

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Ferreira, Fernanda Lima Silva. "Ensinar e aprender geometria." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/5613.

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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-06-02T12:00:44Z No. of bitstreams: 2 Dissertação - Fernanda Lima Silva Ferreira - 2015.pdf: 1505864 bytes, checksum: e9e6548a522455e10dbd70b19ba5e696 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-06-02T12:04:10Z (GMT) No. of bitstreams: 2 Dissertação - Fernanda Lima Silva Ferreira - 2015.pdf: 1505864 bytes, checksum: e9e6548a522455e10dbd70b19ba5e696 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b8

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Rabay, Yara Silvia Freire. "Estudo e aplicações da geometria fractal." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7651.

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Submitted by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-27T11:58:14Z No. of bitstreams: 1 arquivototal.pdf: 8972192 bytes, checksum: e0a82ad433e62b83d048d78778d60dd2 (MD5)<br>Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-11-30T10:51:37Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 8972192 bytes, checksum: e0a82ad433e62b83d048d78778d60dd2 (MD5)<br>Made available in DSpace on 2015-11-30T10:51:37Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 8972192 bytes, checksum: e0a82ad433e62b83d048d78778d60dd2 (MD5) Previous issue date: 2013-0

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Araujo, Osmar Rodrigues de. "Contribuições pedagógicas do ensino de pontos notáveis de um triângulo por meio do origami." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4653.

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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-16T14:32:10Z No. of bitstreams: 2 Dissertação - OsmarRodriguesAraujo - 2015.pdf: 7405460 bytes, checksum: ea95512c567631973f91d277bb7bf915 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-16T14:36:30Z (GMT) No. of bitstreams: 2 Dissertação - OsmarRodriguesAraujo - 2015.pdf: 7405460 bytes, checksum: ea95512c567631973f91d277bb7bf915 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Ma

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Kitaoka, Alessandra de Carvalho. "O uso de tecnologias como ferramenta de apoio às aulas de geometria." Universidade Federal de São Carlos, 2013. https://repositorio.ufscar.br/handle/ufscar/5942.

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Made available in DSpace on 2016-06-02T20:29:23Z (GMT). No. of bitstreams: 1 5405.pdf: 3455845 bytes, checksum: 749a1a7ca8b7d3b9399b8de99a655175 (MD5) Previous issue date: 2013-08-16<br>Financiadora de Estudos e Projetos<br>This project's main goal is propose the application of a Teaching Sequence about how finding the notable points of a triangle, in particular, the circumcenter. Introducing in the sequence geometric objects primaries of Euclidean geometry with the axioms and the theorems necessary to construct the circumcenter. The geometric objects will be built through educational softwa

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Magalhães, Elton Jones da Silva. "Pontos notáveis do triângulo: quantos você conhece?" Mestrado Profissional em Matemática, 2013. https://ri.ufs.br/handle/riufs/6525.

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This thesis aims to show that the notable points of the triangles are not limited to Incentro, circumcenter, Baricentro and Orthocenter which are the best known. In fact, the Encyclopedia of Triangle Centers (ETC), see [5], features over five thousand notable points. Are points with several interesting properties as we will see throughout this work. In addition to the points already mentioned will also present the points of Feuerbach, the Lemoine point, the point Gergonne, the Nagel point, the Spieker point and the points of Fermat. Will be also presented some important theorems, among them we

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Books on the topic "Triangle (Geometry)"

1

Tahta, Dick. Some triangle geometry. [s.n.], 1990.

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author, Law Felicia, and Phillips Mike 1961 illustrator, eds. Stone age geometry: Triangles. Crabtree Publishing Company, 2014.

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How does one cut a triangle? Center for Excellence in Mathematical Education, 1990.

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Triangles. Marshall Cavendish Benchmark, 2006.

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Bailey, Gerry. Stone age geometry: Spheres. Crabtree Publishing Company, 2014.

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author, Law Felicia, and Phillips Mike 1961 illustrator, eds. Stone age geometry: Cubes. Crabtree Publishing Company, 2014.

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author, Law Felicia, and Phillips Mike 1961 illustrator, eds. Stone age geometry: Lines. Crabtree Publishing Company, 2014.

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Lorbiecki, Marybeth. Triangles. Red Wagon, 2008.

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Triangles. QEB Pub., 2010.

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Radunsky, Vladimir. Square, triangle, round, skinny: 4 little books. Candlewick Press, 2002.

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Book chapters on the topic "Triangle (Geometry)"

1

Bottema, O., and Reinie Erne. "Morley’s Triangle." In Topics in Elementary Geometry. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-78131-0_10.

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Freeman, Christopher M. "Centers of a Triangle." In Hands-On Geometry. Routledge, 2021. http://dx.doi.org/10.4324/9781003235477-3.

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Bottema, O., and Reinie Erne. "Inequalities in a Triangle." In Topics in Elementary Geometry. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-78131-0_11.

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Gévay, Gábor. "Pascal’s Triangle of Configurations." In Discrete Geometry and Symmetry. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78434-2_10.

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Bærentzen, Jakob Andreas, Jens Gravesen, François Anton, and Henrik Aanæs. "Curvature in Triangle Meshes." In Guide to Computational Geometry Processing. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-4075-7_8.

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Bærentzen, Jakob Andreas, Jens Gravesen, François Anton, and Henrik Aanæs. "Simplifying and Optimizing Triangle Meshes." In Guide to Computational Geometry Processing. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-4075-7_11.

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Bærentzen, Jakob Andreas, Jens Gravesen, François Anton, and Henrik Aanæs. "Triangle Mesh Generation: Delaunay Triangulation." In Guide to Computational Geometry Processing. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-4075-7_14.

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Bottema, O., and Reinie Erne. "Two Unusual Conditions for a Triangle." In Topics in Elementary Geometry. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-78131-0_17.

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Bottema, O., and Reinie Erne. "Coordinate Systems with Respect to a Triangle." In Topics in Elementary Geometry. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-78131-0_6.

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Shewchuk, Jonathan Richard. "Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator." In Applied Computational Geometry Towards Geometric Engineering. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0014497.

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Conference papers on the topic "Triangle (Geometry)"

1

Huu-Tai, P. Chau. "Geometry of random interactions." In MAPPING THE TRIANGLE: International Conference on Nuclear Structure. AIP, 2002. http://dx.doi.org/10.1063/1.1517959.

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Cranston, Charles B., and Hanan Samet. "Indexing Point Triples Via Triangle Geometry." In 2007 IEEE 23rd International Conference on Data Engineering. IEEE, 2007. http://dx.doi.org/10.1109/icde.2007.367939.

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Frank, A. "The Geometry of the IBM with Configuration Mixing." In MAPPING THE TRIANGLE: International Conference on Nuclear Structure. AIP, 2002. http://dx.doi.org/10.1063/1.1517933.

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Azmi, Mohd Sanusi, Mohammad Faidzul Nasrudin, Khairuddin Omar, Che Wan Shamsul Bahri Che Wan Ahmad, and Khadijah Wan Mohd Ghazali. "Exploiting features from triangle geometry for digit recognition." In 2013 International Conference on Control, Decision and Information Technologies (CoDIT). IEEE, 2013. http://dx.doi.org/10.1109/codit.2013.6689658.

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Arbain, Nur Atikah, Mohd Sanusi Azmi, Azah Kamilah Draman Muda, Amirul Ramzani Radzid, and Azrina Tahir. "A Review of Triangle Geometry Features in Object Recognition." In 2019 IEEE 9th Symposium on Computer Applications & Industrial Electronics (ISCAIE). IEEE, 2019. http://dx.doi.org/10.1109/iscaie.2019.8743997.

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Chatterjee, S. M., A. Deb, C. V. Rao, P. K. Reddy, A. Sanyal, and K. Yadagiri. "Triangle zone geometry in Cachar thrust‐fold belt, India." In SEG Technical Program Expanded Abstracts 2006. Society of Exploration Geophysicists, 2006. http://dx.doi.org/10.1190/1.2369715.

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Wu, Hongchun, Guoming Liu, Liangzhi Cao, and Qichang Chen. "Determinant Methods for Solving Neutron Transport Equation in Unstructured Geometry." In 18th International Conference on Nuclear Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/icone18-29442.

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The spherical harmonics (Pn) finite element method, the Sn finite element method, the triangle transmission probability method and the discrete triangle nodal method were all introduced to solve the neutron transport equation for unstructured fuel assembly respectively. The computing codes of each method were encoded and numerical results were discussed and compared. It was demonstrated that these four methods can solve neutron transport equations with unstructured-meshes very effectively and correctly, they can be used to solve unstructured fuel assembly problem.

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Hongnian, Liu, Liu Bo, and Zhang Hongbin. "Progressive Geometry-Driven Compression for Triangle Mesh Based on Binary Tree." In 2009 Second International Conference in Visualisation (VIZ). IEEE, 2009. http://dx.doi.org/10.1109/viz.2009.17.

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Dricot, Antoine, and Joao Ascenso. "Adaptive Multi-level Triangle Soup for Geometry-based Point Cloud Coding." In 2019 IEEE 21st International Workshop on Multimedia Signal Processing (MMSP). IEEE, 2019. http://dx.doi.org/10.1109/mmsp.2019.8901791.

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Cayre, Francois, Patrice R. Alface, Francis J. M. Schmitt, and Henri Maitre. "Compression and watermarking of 3D triangle mesh geometry using spectral decomposition." In International Symposium on Optical Science and Technology, edited by Andrew G. Tescher. SPIE, 2002. http://dx.doi.org/10.1117/12.455356.

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