Academic literature on the topic 'Euler's theorem'
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Journal articles on the topic "Euler's theorem"
Heinrich, Katherine, and Peter Horak. "Euler's Theorem." American Mathematical Monthly 101, no. 3 (March 1994): 260. http://dx.doi.org/10.2307/2975604.
Full textHeinrich, Katherine, and Peter Horak. "Euler's Theorem." American Mathematical Monthly 101, no. 3 (March 1994): 260–61. http://dx.doi.org/10.1080/00029890.1994.11996939.
Full textWardlaw, William P. "Euler's Theorem for Polynomials." Mathematics Magazine 65, no. 5 (December 1, 1992): 334. http://dx.doi.org/10.2307/2691245.
Full textWardlaw, William P. "Euler's Theorem for Polynomials." Mathematics Magazine 65, no. 5 (December 1992): 334–35. http://dx.doi.org/10.1080/0025570x.1992.11996048.
Full textÇÖKEN, A. CEYLAN. "ON EULER'S THEOREM IN SEMI-EUCLIDEAN SPACES $\mathbb{E}_{v}^{n+1}$." International Journal of Geometric Methods in Modern Physics 08, no. 05 (August 2011): 1117–29. http://dx.doi.org/10.1142/s0219887811005579.
Full textKandall, Geoffrey A. "Euler's Theorem for Generalized Quadrilaterals." College Mathematics Journal 33, no. 5 (November 2002): 403. http://dx.doi.org/10.2307/1559015.
Full textDubeau, F., and S. Labbe. "Euler's characteristics and Pick's theorem." International Journal of Contemporary Mathematical Sciences 2 (2007): 909–28. http://dx.doi.org/10.12988/ijcms.2007.07094.
Full textChen, William Y. C., and Kathy Q. Ji. "Weighted forms of Euler's theorem." Journal of Combinatorial Theory, Series A 114, no. 2 (February 2007): 360–72. http://dx.doi.org/10.1016/j.jcta.2006.06.005.
Full textGrünbaum, Branko, and Murray S. Klamkin. "Euler's Ratio-Sum Theorem and Generalizations." Mathematics Magazine 79, no. 2 (April 1, 2006): 122. http://dx.doi.org/10.2307/27642919.
Full textKoshy, Thomas. "82.6 A Generalisation of Euler's Theorem." Mathematical Gazette 82, no. 493 (March 1998): 80. http://dx.doi.org/10.2307/3620158.
Full textDissertations / Theses on the topic "Euler's theorem"
Melo, Henrique Alves de. "Euler's formula in the plan and for polyhedra." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11431.
Full textPolyhedra are geometric solids formed by a finite number of polygons they can be convex or non-convex, regular or not regular. This work we make three demonstrations of Eulerâs theorem for polyhedra in one plane being used graphs. We will adopt preliminary definitions of polygons, polyhedra and graphs and make a brief study of the theorem before the demonstrations analysis when the theorem is valid and what conditions exist polyhedra, since the theorem is accepted. The work brings some applications in the form of questions in the theory presented.
Os poliedros sÃo sÃlidos geomÃtricos formados por uma quantidade finita de polÃgonos. Eles podem ser convexos ou nÃo convexos, regulares ou nÃo regulares . Neste trabalho fazemos trÃs demonstraÃÃes do teorema de Euler para poliedros no plano, sendo uma utilizado grafos. Adotaremos definiÃÃes preliminares de polÃgonos, poliedros e grafos e faremos um breve estudo do teorema antes das demonstraÃÃes analisado quando o teorema à valido em quais condiÃÃes existem os poliedros, uma vez que o teorema à aceito. O trabalho traz algumas aplicaÃÃes em forma de questÃes da teoria apresentada.
Carvalho, Wesley da Silva. "Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/6970.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this dissertation, we first state Euler's polyhedral formula for a set of points with Euler characteristic 2. We address the two known ways to prove Euler's Theorem: beginning with the classical proof by using Euclidian Geometry and afterwards we take the advantage of Spherical Geometry to give another proof. Furthermore, we address a version of Euler's formula for planar polyhedron, as well as, Pick's formula and the equivalence between Euler and Pick's formula. In the end, we provide application of Euler and Pick's formula, via two pedagogy tools Geoplano and GeoGebra, by giving examples to teach in classroom.
Esta dissertação trata inicialmente da Fórmula de Euler e de sua validade para os conjuntos de pontos com característica de Euler igual a 2. São feitas duas demonstrações da Fórmula de Euler, uma utilizando conceitos de Geometria Euclidiana e uma outra via Geometria Esférica, além da apresentação de uma versão para poliedros planos da Fórmula de Euler. Posteriormente, é apresentada a Fórmula de Pick para o cálculo de áreas de polígonos simples reticulados e sua relação de equivalência com a Fórmula de Pick para poliedros planos. Finalmente mostramos duas possibilidades de trabalho com a Fórmula de Pick, no Geoplano e no software GeoGebra.
Gontijo, Helen Kássia Coelho. "Teorema de Euler em sala de aula." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/3876.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work is based on the study of the polyhedrons and the Euler's Theorem, by applying strategies of teaching using the concrete material, provoking improvements in the reasoning and in the geometrical perception the Euler's Theorem. Not mentioning a bit of history of tracks already made by several mathematicians who have contributed to the study of geometry, where the ideas previously applied by them teach us and help every day. Going to the presentation of a few concepts and de nitions about polyhedrons, as well as the demonstration that exist only ve polyhedrons of Plato. We've tried to expose the demonstration of the Euler's Theorem, through two researchers, Adrien Marie Legendre and of the professor Zoroastro Azambuja Filho, considering them very interesting and easy to understand. However, in the perspective that going from the concrete one is an alternative to improve the quality of teaching, it has been selected the activity Geometry of cutting soaps , which is in an article of Ana Maria Kale , see at [10], and Geometry of straws , at [9], which are based on work experiences of the same author. Before the new technologies we have opted for the mathematical software Poly, available on http://www.peda.com/poly which allows a better visualization of polyhedrons of di cult construction. All these activities have been presented to the students of the second grade in the Secondary Education to verify the Euler's Theorem through concrete experiences, obtaining this way a useful and creative geometrical knowledge, conquering the students' participation and interest.
Este trabalho baseia-se no estudo dos Poliedros e o Teorema de Euler, aplicando estratégias de ensinar usando o material concreto, desencadeando melhoras no raciocínio e na percepção geométrica do Teorema de Euler. Não deixando de mencionar um pouco da história de caminhos já trilhados por vários matemáticos que contribuíram para o estudo da geometria, onde as ideias anteriormente aplicadas por eles nos ensinam e ajudam no dia-a-dia. Partindo então para apresentação de alguns conceitos e de nições sobre Poliedros, bem como a demonstração de que só existem cinco poliedros de Platão. Buscamos expor a demonstração do Teorema de Euler, por dois pesquisadores, Adrien Marie Legendre e do professor Zoroastro Azambuja Filho, considerando-as bem interessantes e de fácil compreensão. Contudo, na perspectiva de que partir do concreto é uma alternativa para melhorar a qualidade de ensino, foi selecionada a atividade Geometria dos cortes de sabão , que se encontra em um artigo de Ana Maria Kale , veja em [10] e Geometria de Canudos , em [9], que são fundamentados em experiências de trabalho da mesma autora. Frente às novas tecnologias optamos pelo uso do software matemático Poly, disponível em http://www.peda.com/poly, que permite uma melhor visualização de poliedros de difícil construção. Todas estas atividades foram apresentadas para os alunos do 2o ano do Ensino Médio para a veri cação do Teorema de Euler através de experiências concretas, obtendo assim um conhecimento geométrico criativo e útil, conquistando a participação e interesse dos estudantes.
Silva, Hércules do Nascimento. "Poliedros Regulares no Ensino Médio." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/8042.
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In this work we present a study of the regular polyhedra, comparing and discussing the concepts and de nitions given in the study of regular polyhedra in textbooks most widely used in Brazilian high schools. We prove the theorem of Euler, we calculate surface areas and volumes of regular polyhedra. Finally, we present some mathematical software that can be used by students and mathematics teachers in the spatial geometry classes as auxiliary material in the teaching and learning of this subject in the classroom.
Neste trabalho apresentamos um estudo sobre os poliedros regulares, comparando e discutindo os conceitos e as de nições que são dadas no estudo dos poliedros regulares nos livros didáticos mais utilizados nas escolas brasileiras de Ensino Médio. Provamos o teorema de Euler, calculamos áreas de superfícies e os volumes dos poliedros regulares. Por m, apresentamos alguns softwares matemáticos que podem ser utilizados pelos alunos e professores de Matemática nas aulas de geometria espacial como material auxiliar no processo de ensino e aprendizagem deste tema em sala de aula.
Silva, Eduardo Alves da. "Formas ponderadas do Teorema de Euler e partições com raiz : estabelecendo um tratamento combinatório para certas identidades de Ramanujan." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2018. http://hdl.handle.net/10183/183163.
Full textThe article Weighted forms of Euler's theorem by William Y.C. Chen and Kathy Q. Ji in response to the questioning of George E. Andrews, American mathematician, about nding combinatorial proofs for two identities in Ramanujan's Lost Notebook shows us some weighted forms of Euler's Theorem on partitions with odd parts and distinct parts through the introduction of the concept of rooted partition. The purpose of this work involves the presentation of results on rooted partitions in order to make combinatorial formulations of Ramanujan's identities, seeking to establish connections with weighted forms of Euler's Theorem. In particular, the Sylvester's bijection and the Pak's iteration of the Dyson's map are primordial elements to obtain them.
Justino, Gildeci José. "A característica de Euler." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7471.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This dissertation is focused on the Euler's theorem for polyhedra homeomorphic to the sphere. Present statements made by Cauchy, Poincaré and Legendre. As a consequence we show that there are only ve regular convex polyhedra, called polyhedra Plato.
Esta dissertação tem como tema central o Teorema de Euler para poliedros homeomorfos à esfera. Apresentamos demonstrações feitas por Cauchy, Poincaré e Legendre. Como consequência mostramos a existência de apenas cinco poliedros convexos regulares, os chamados poliedros de Platão.
Parreira, José Roberto Penachia. "Poliedros e o Teorema de Euler." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tde/2970.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work aims is to demonstrate the Euler's Theorem for polyhedra, given by the equation V A + F = 2, where V; A and F are the numbers of vertices, edges and faces, respectively, the polyhedron. A historical survey of the main characters who contributed to the theme was elaborated. De nitions and properties of polygons and polyhedra were given. The statements were constructed in three distinct ways. The rst by Cauchy, commented by Professor Elon Lages Lima. This statement is valid for any polyhedron homeomorphic to a sphere and has the path planning of the polyhedron withdrawing one of its faces. The second statement was prepared by the professor Zoroastro Azambuja Filho, valid for any convex polyhedron, and its path projection of the polyhedron on a plane and comparison of the internal angles of polygons with projection angles of the polygon faces. The third statements was presented by Legendre, also valid for any convex polyhedron, and its path in the projection of a spherical polyhedron surface. We use the Girard's Formula, the sum of the interior angles of a spherical triangle, to complete the demonstration. This work also suggests methods of applying the proof of Euler's Theorem in the classroom for high school students, and resolution of vestibular exercises involving the subject.
Este trabalho tem por objetivo a demonstra c~ao do Teorema de Euler para poliedros, dado pela equa ção V A + F = 2, onde V; A e F são os n úmeros de v értices, arestas e faces, respectivamente, do poliedro. Foi elaborada uma pesquisa hist orica dos principais personagens que contribuiram para o tema. Foram dadas de ni ções e propriedades de pol ígonos e poliedros. As demonstra ções foram constru ídas em três caminhos distintos. A primeira por Cauchy, comentada pelo professor Elon Lages Lima. Esta demonstra ção é v álida para qualquer poliedro homeomorfo a uma esfera e tem como caminho a plani fica ção do poliedro retirando-se uma de suas faces. A segunda demonstra c~ao foi elaborada pelo professor Zoroastro Azambuja Filho, v álida para qualquer poliedro convexo e tem como caminho a proje ção do poliedro num plano e a compara c~ao dos ângulos internos dos pol ígonos da proje ção com os ângulos dos pol gonos das faces. A terceira demonstra c~ao foi apresentada por Legendre, tamb ém v álida para qualquer poliedro convexo e tem como caminho a projeção do poliedro em uma superf ície esf érica. Utiliza-se a F ormula de Girard, da soma dos ângulos internos de um tri^angulo esf érico, para concluir a demonstra ção. Este trabalho tamb ém sugere metodologias de aplica ção da demonstração do Teorema de Euler em sala de aula, para alunos do Ensino M édio, e resolu ção de exercí cios de vestibulares envolvendo o tema.
Reeder, Patrick F. "Internal Set Theory and Euler's Introductio in Analysin Infinitorum." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366149288.
Full textPaião, Ana Pedro Lemos. "Introduction to optimal control theory and its application to diabetes." Master's thesis, Universidade de Aveiro, 2015. http://hdl.handle.net/10773/16806.
Full textO Cálculo das Variações e o Controlo Ótimo são dois ramos da Matemática que estão muito interligados entre si e também com outras áreas. Como exemplo, podemos citar a Geometria, a Física, a Mecânica, a Economia, a Biologia, bem como a Medicina. Nesta tese estudamos vários tipos de problemas variacionais e de Controlo Ótimo, estabelecendo a ligação entre alguns destes. Fazemos uma breve introdução sobre a Diabetes Mellitus, uma vez que estudamos um modelo matemático que traduz a interação entre a glicose e a insulina no sangue por forma a otimizar o estado de uma pessoa com diabetes tipo 1.
The Calculus of Variations and the Optimal Control are two branches of Mathematics that are very interconnected with each other and with other areas. As example, we can mention Geometry, Physics, Mechanics, Economics, Biology and Medicine. In this thesis we study various types of variational problems and of Optimal Control, establishing the connection between some of these. We make a brief introduction to the Diabetes Mellitus, because we study a mathematical model that reflects the interaction between glucose and insulin in the blood in order to optimize the state of a person with diabetes type 1.
Badar, Muhammad, and Ansir Iqbal. "Polya's Enumeration Theorem : Number of colorings of n-gons and non isomorphic graphs." Thesis, Linnaeus University, School of Computer Science, Physics and Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-6199.
Full textPolya’s theorem can be used to enumerate objects under permutation groups. Using grouptheory, combinatorics and some examples, Polya’s theorem and Burnside’s lemma arederived. The examples used are a square, pentagon, hexagon and heptagon under theirrespective dihedral groups. Generalization using more permutations and applications tograph theory.Using Polya’s Enumeration theorem, Harary and Palmer [5] give a function whichgives the number of unlabeled graphs n vertices and m edges. We present their work andthe necessary background knowledge.
Books on the topic "Euler's theorem"
Chen, Jingkai. Nonlocal Euler–Bernoulli Beam Theories. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69788-4.
Full text1707-1783, Euler Leonhard, ed. Leonhard Euler et la découverte progressive des sommations des séries infinies. Paris: Compagnie littéraire, 2010.
Find full textTurner, J. C. Number trees for Pythagoras, Plato, Euler, and the modular group. Hamilton, N.Z: University of Waikato, 1990.
Find full textHakfoort, Casper. Optics in the age of Euler: Conceptions of the nature of light, 1700-1795. Cambridge: Cambridge University Press, 1995.
Find full textEuler through time: A new look at old themes. Providence, R.I: American Mathematical Society, 2006.
Find full textDiskin, Boris. New factorizable discretizations for the Euler equations. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.
Find full textShimura, Gorō. Euler products and Eisenstein series. Providence, R.I: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1997.
Find full textDeshpande, Suresh M. A second-order accurate kinetic-theory-based method for inviscid compressible flows. Hampton, Va: Langley Research Center, 1986.
Find full textOptica in de eeuw van Euler: Opvattingen over de natuur van het licht, 1700-1795 = Optics in the age of Euler : conceptions of the nature of light, 1700-1795. Amsterdam: Rodopi, 1986.
Find full textTadmor, Eitan. A minimum entropy principle in the gas dynamics equation. Hampton, Va: ICASE, 1986.
Find full textBook chapters on the topic "Euler's theorem"
Effinger, Gove, and Gary L. Mullen. "Euler's Formula and Euler's Theorem." In An Elementary Transition to Abstract Mathematics, 129–34. Boca Raton : CRC Press, Taylor … Francis Group, 2020.: CRC Press, 2019. http://dx.doi.org/10.1201/9780429324819-19.
Full textNewman, Peter. "Euler’s Theorem." In The New Palgrave Dictionary of Economics, 1–2. London: Palgrave Macmillan UK, 1987. http://dx.doi.org/10.1057/978-1-349-95121-5_230-1.
Full textNewman, Peter. "Euler’s Theorem." In The New Palgrave Dictionary of Economics, 1–2. London: Palgrave Macmillan UK, 2008. http://dx.doi.org/10.1057/978-1-349-95121-5_230-2.
Full textNewman, Peter. "Euler’s Theorem." In The New Palgrave Dictionary of Economics, 3935–37. London: Palgrave Macmillan UK, 2018. http://dx.doi.org/10.1057/978-1-349-95189-5_230.
Full textChilds, Lindsay N. "Orders and Euler’s Theorem." In Springer Undergraduate Texts in Mathematics and Technology, 117–33. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15453-0_8.
Full textChilds, Lindsay N. "Fermat’s and Euler’s Theorems." In A Concrete Introduction to Higher Algebra, 134–54. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4419-8702-0_9.
Full textNg, Xian Wen. "Euler’s Theorem and Grand Composite Curves." In Concise Guide to Heat Exchanger Network Design, 63–108. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53498-1_3.
Full textLonguski, James M., José J. Guzmán, and John E. Prussing. "The Euler-Lagrange Theorem." In Optimal Control with Aerospace Applications, 39–59. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8945-0_3.
Full textChilds, Lindsay N. "Applications of Fermat’s and Euler’s Theorems." In A Concrete Introduction to Higher Algebra, 155–79. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4419-8702-0_10.
Full textPąk, Karol. "Readable Formalization of Euler’s Partition Theorem in Mizar." In Lecture Notes in Computer Science, 211–26. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20615-8_14.
Full textConference papers on the topic "Euler's theorem"
Zhu, Wen Tao. "Analyzing Euler-Fermat Theorem Based Multicast Key Distribution Schemes with Chinese Remainder Theorem." In 2008 IFIP International Conference on Network and Parallel Computing (NPC). IEEE, 2008. http://dx.doi.org/10.1109/npc.2008.29.
Full textBert, Charles W., and Chun-Do Kim. "Whirling of Composite-Material Driveshafts Including Bending-Twisting Coupling and Transverse Shear Deformation." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0182.
Full textFigliolini, Giorgio, and Ettore Pennestrì. "Kinematic Synthesis of Quasi-Homokinetic Four-Bar Linkages Through the Burmester and Chebyshev Theories." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34951.
Full textKawarabayashi, Ken-ichi, and Anastasios Sidiropoulos. "Beyond the Euler Characteristic." In STOC '15: Symposium on Theory of Computing. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2746539.2746583.
Full textPrasanth, R., and R. Mehra. "Nonlinear aeroservoelastic control using Euler-Lagrange theory." In Guidance, Navigation, and Control Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1999. http://dx.doi.org/10.2514/6.1999-4089.
Full textKozlova, Irina Vasilevna. "The study of the structure of carbon nanoparticles using the Euler theorem." In International Research and Practical Conference for Pupils, chair Elena Vladimirovna Shirokova. TSNS Interaktiv Plus, 2018. http://dx.doi.org/10.21661/r-474636.
Full textYao, Bin, Shiying Kang, Xiao Zhao, Yuyan Chao, and Lifeng He. "A graph-theory-based Euler number computing algorithm." In 2015 IEEE International Conference on Information and Automation (ICIA). IEEE, 2015. http://dx.doi.org/10.1109/icinfa.2015.7279470.
Full textBauchau, Olivier A., and Shilei Han. "Advanced Beam Theory for Multibody Dynamics." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12416.
Full textZhu, Yang, Jean W. Zu, and Minghui Yao. "Modeling of Piezoelectric Energy Harvester: A Comparison Between Euler-Bernoulli Theory and Timoshenko Theory." In ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2011. http://dx.doi.org/10.1115/smasis2011-4995.
Full textRibeiro, Aureliano, José Juliano de Lima Junior, and Felipe Eloy. "DIFFERENTIAL TRANSFORM METHOD APPLIED TO EULER-BERNOULLI BEAM THEORY." In 25th International Congress of Mechanical Engineering. ABCM, 2019. http://dx.doi.org/10.26678/abcm.cobem2019.cob2019-2420.
Full text