Artículos de revistas: "Geometria Euclidea"

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Binotto, Rosane Rossato y Julieta Ferronato. "A gamificação como estratégia para aprendizagem significativa de Geometria do 9° ano do Ensino Fundamental". Em Teia | Revista de Educação Matemática e Tecnológica Iberoamericana 14, n.º 3 (21 de noviembre de 2023): 20–43. http://dx.doi.org/10.51359/2177-9309.2023.257612.

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Neste artigo apresentamos resultados de uma pesquisa que objetivou analisar possíveis contribuições da gamificação, por meio do aplicativo Euclidea, para a aprendizagem significativa de geometria em uma turma do 9° Ano do Ensino Fundamental, realizada em uma escola pública de Santa Catarina (SC). Em uma experiência de ensino, os alunos participantes responderam a dois questionários e resolveram problemas/desafios de construções geométricas no aplicativo Euclidea, que possui estrutura de jogo. Essa pesquisa foi norteada pela abordagem qualitativa e utilizou a Análise de Conteúdo para categorizar os dados obtidos. Por meio da análise realizada, verificamos que o Euclidea tem características de material potencialmente significativo, houve engajamento dos alunos na realização das atividades propostas, indicando predisposição desses alunos para a aprendizagem. Logo, concluímos que a gamificação contribuiu para a aprendizagem significativa de geometria da maioria dos alunos participantes dessa pesquisa.

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Mammana, Maria Flavia y Mario Pennisi. "Ricordo di Biagio Micale". Bullettin of the Gioenia Academy of Natural Sciences of Catania 52, n.º 382 (22 de diciembre de 2019): O7—O16. http://dx.doi.org/10.35352/gioenia.v52i382.85.

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Il 20 febbraio 2018, a Catania, è mancato improvvisamente Biagio Micale, Professore ordinario di Matematiche complementari all’Università di Catania. Avrebbe compiuto 72 anni il 16 novembre 2018. È stato membro della Commissione Italiana per l’Insegnamento della Matematica e presidente della sezione Mathesis di Catania. Ha coordinato il Nucleo di Ricerca Didattica che opera presso il Dipartimento di Matematica e Informatica dell’Università di Catania. L’attività scientifica ha riguardato vari aspetti della matematica. In particolare nel periodo che va dagli studi post-laurea al 1986 ha indirizzato la ricerca principalmente verso questioni di fondamenti della matematica riguardanti soprattutto le algebre universali, in particolare gli $ \Omega $-gruppi di Higgins, e i sistemi algebrici. A partire dal 1987 ha arontato temi di ricerca riguardati la Combinatorica, in modo particolare i $ t $-design (sistemi di quadruple di Steiner, sistemi di terne e di quaterne orientate). Dal 1978 ha sviluppato un’ampia attività di ricerca riguardante tematiche di fondamenti della matematica e di didattica della matematica, con particolare riguardo per la geometria. Relativamente alla didattica della matematica, sviluppa una organica ricerca prevalentemente indirizzata su problemi riguardanti la didattica della geometria nelle scuole secondarie in relazione alle innovazioni contenute nei programmi di insegnamento in vigore o in via di sperimentazione. In modo particolare dà vita ad una serie di ricerche su problematiche didattiche legate allo sviluppo del tema sulle trasformazioni geometriche, avendo come obiettivo unitario quello di innestare e amalgamare tale tema con la tradizione “euclidea” dell’insegnamento della geometria nella nostra scuola.

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Gasparini, Adalinda. "Metamorficamente. Miti e psicoanalisi". EDUCAZIONE SENTIMENTALE, n.º 35 (septiembre de 2021): 92–109. http://dx.doi.org/10.3280/eds2021-035008.

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Seguendo l'ipotesi che la psicoanalisi sia una potente e preziosa mitologia contemporanea l'A. ripercorre le lotte fra generazioni dell'antica cosmogonia greca, che possono illuminare aspetti sottesi della vicenda edipica. I miti hanno una molteplicità di versioni, che sono tutte vere e tutte false, e la loro polisemia fa sì che, come nei sogni e nell'inconscio, allestiscano uno spazio nel quale può tran-sitare la follia. Nell'infanzia dell'A. il padre era sempre pronto ad ascoltarla e aveva una risposta per tutte le sue domande, tranne che sulla malattia del nonno, che periodicamente doveva essere ricoverato per crisi di psicosi maniaco depressiva. La psicoanalisi come il mito non esclude la follia, e riconosce per prima l'umanità profonda e perturbante di sofferenze che sono state sistematicamente rimosse dal senso comune e dalle istituzioni psichiatriche. Se mantiene come Freud lo sguardo sui sintomi nevrotici e sui deliri psicotici la psicoanalisi non può diventare un sistema compiuto e univoco, ma questo che sembra uno svan-taggio è invece la potenza della psicoanalisi, che è e resta una scienza delle do-mande, non delle risposte: sono le domande che aprono lo spazio metamorfico. Le analogie con la geometria non euclidea e la fisica quantistica sono importanti, ma è solo con le risorse originali della sua storia, della sua teoria e della sua clinica che la psicoanalisi potrà riconoscersi ed essere riconosciuta come scienza.

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Yıldırım, Abdurrahman y Pına Anapa Saban. "EFFECTS OF EUCLIDEAN REALITY GEOMETRY ACTIVITIES ON STUDENTS’ LEVELS OF VAN HIELE GEOMETRY, GEOMETRIC ATTITUDES AND THEIR SUCCESSES ACCORDING TO HEARING ABILITIES". e-Journal of New World Sciences Academy 9, n.º 4 (15 de octubre de 2014): 364–79. http://dx.doi.org/10.12739/nwsa.2014.9.4.1c0624.

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Nugroho, Khathibul Umam Zaid, Y. L. Sukestiyarno y Adi Nurcahyo. "Weaknesses of Euclidean Geometry: A Step of Needs Analysis of Non-Euclidean Geometry Learning through an Ethnomathematics Approach". Edumatika : Jurnal Riset Pendidikan Matematika 4, n.º 2 (10 de noviembre de 2021): 126–49. http://dx.doi.org/10.32939/ejrpm.v4i2.1015.

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Non-Euclidean Geometry is a complex subject for students. It is necessary to analyze the weaknesses of Euclidean geometry to provide a basis for thinking about the need for learning non-Euclidean geometry. The starting point of learning must be close to students' local minds and culture. The purpose of this study is to describe the weaknesses of Euclidean geometry as a step in analyzing the needs of non-Euclidean geometry learning through an ethnomathematics approach. This research uses qualitative descriptive methods. The subjects of this study were students of Mathematics Education at State Islamic University (UIN) Fatmawati Soekarno Bengkulu, Indonesia. The researcher acts as a lecturer and the main instrument in this research. Researchers used a spatial ability test instrument to explore qualitative data. The data were analyzed qualitatively descriptively. The result of this research is that there are two weaknesses of Euclidean geometry, namely Euclid’s attempt to define all elements in geometry, including points, lines, and planes. Euclid defined a point as one that has no part. He defined a line as length without width. The words "section", "length", and "width" are not found in Euclidean Geometry. In addition, almost every part of Euclid’s proof of the theorem uses geometric drawings, but in practice, these drawings are misleading. Local culture and ethnomathematics approach design teaching materials and student learning trajectories in studying Non-Euclid Geometry.

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BEESON, MICHAEL. "CONSTRUCTIVE GEOMETRY AND THE PARALLEL POSTULATE". Bulletin of Symbolic Logic 22, n.º 1 (marzo de 2016): 1–104. http://dx.doi.org/10.1017/bsl.2015.41.

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AbstractEuclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. This involves finding “uniform” constructions where normally a case distinction is used. For example, in finding a perpendicular to line L through point p, one usually uses two different constructions, “erecting” a perpendicular when p is on L, and “dropping” a perpendicular when p is not on L, but in constructive geometry, it must be done without a case distinction. Classically, the models of Euclidean (straightedge-and-compass) geometry are planes over Euclidean fields. We prove a similar theorem for constructive Euclidean geometry, by showing how to define addition and multiplication without a case distinction about the sign of the arguments. With intuitionistic logic, there are two possible definitions of Euclidean fields, which turn out to correspond to different versions of the parallel postulate.We consider three versions of Euclid’s parallel postulate. The two most important are Euclid’s own formulation in his Postulate 5, which says that under certain conditions two lines meet, and Playfair’s axiom (dating from 1795), which says there cannot be two distinct parallels to line L through the same point p. These differ in that Euclid 5 makes an existence assertion, while Playfair’s axiom does not. The third variant, which we call the strong parallel postulate, isolates the existence assertion from the geometry: it amounts to Playfair’s axiom plus the principle that two distinct lines that are not parallel do intersect. The first main result of this paper is that Euclid 5 suffices to define coordinates, addition, multiplication, and square roots geometrically.We completely settle the questions about implications between the three versions of the parallel postulate. The strong parallel postulate easily implies Euclid 5, and Euclid 5 also implies the strong parallel postulate, as a corollary of coordinatization and definability of arithmetic. We show that Playfair does not imply Euclid 5, and we also give some other independence results. Our independence proofs are given without discussing the exact choice of the other axioms of geometry; all we need is that one can interpret the geometric axioms in Euclidean field theory. The independence proofs use Kripke models of Euclidean field theories based on carefully constructed rings of real-valued functions. “Field elements” in these models are real-valued functions.

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Pettoello, Renato. "La geometria eterna. Nelson e le geometrie non-euclidee". RIVISTA DI STORIA DELLA FILOSOFIA, n.º 3 (septiembre de 2010): 483–506. http://dx.doi.org/10.3280/sf2010-003004.

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SAMSUMARLIN, SAMSUMARLIN. "SEGITIGA DAN SEGIEMPAT PADA GEOMETRI DATAR EUCLID CEVIAN SEGITIGA DAN SEGIEMPAT SIKLIK". Edumaspul - Jurnal Pendidikan 1, n.º 1 (28 de abril de 2018): 15–22. http://dx.doi.org/10.33487/edumaspul.v1i1.36.

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Geometri Euclidean adalah sistem matematika yang dikaitkan dengan Euclid, matematikawan dari Alexandria Yunani, yang dijelaskan dalam buku teksnya pada geometri: The Elemen. Perkembangan geometri yang membuat kajiannya lebih mendalam, mengakibatkan materi geometri sulit diajarkan seluruhnya pada tingkat sekolah menegah. Tulisan ini khusus membahas mengenai beberapa teorema terkait “cevian pada segitiga serta segiempat siklik” dan disajikan secara deduktif.

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Rizos, Ioannis y Evaggelos Foykas. "Utilization of “Byrne’s Euclid” in the Teaching of Geometry to Students with Special Learning Difficulties: A Qualitative Research". European Journal of Education and Pedagogy 4, n.º 2 (29 de marzo de 2023): 139–48. http://dx.doi.org/10.24018/ejedu.2023.4.2.623.

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The choice of the appropriate instructional method for teaching Euclidean Geometry to children with Special Learning Difficulties is an important topic. In this paper we study some theoretical issues related to the teaching of geometric concepts to students with Special Learning Difficulties, focusing on the teaching material. We present the design, implementation and results of a qualitative research conducted with six 9th grade students in a Special Vocational High School in Greece, on the use of the website “Byrne’s Euclid” in the teaching of propositions of Euclidean Geometry. The research showed that the children understood the key points of the proof of the proposition we presented and they assimilated basic geometric concepts and processes using colors and figures. The paper concludes with a discussion upon suggestions, perspectives and limitations for teaching that utilizes Byrne’s Euclid.

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Siebert, Harald. "Transformation of Euclid’s Optics in Late Antiquity". Nuncius 29, n.º 1 (2014): 88–126. http://dx.doi.org/10.1163/18253911-02901004.

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The tradition of Euclid’s Optics includes a number of versions and translations, whether in Greek, Arabic or Latin. They differ from each other to various extents with respect to their form, structure and content. Textual divergence concerns the very core of geometric optics, i.e. the opening definitions and first propositions. In these parts the variance of the different versions is most striking. Thus the tradition of the Euclidean text involved a transformation of the visual model that cannot be explained merely philologically or by incidental elements in the process of transmission. This paper aims to explain these textual transformations as an intentional process of updating and adapting geometric optics to the best of its understanding at a given time. For this purpose, the different versions of Euclid’s Optics are placed in the context of and compared with late antique and early medieval sources. From Ptolemy through al-Haytham, experience had been used as an argument either to refute or to defend the geometric model of vision. Indeed, the visual ray hypothesis turns out to be more or less or not at all compatible with experience in the various versions of Euclid’s Optics. Their divergence thus provides evidence of a lively tradition of Euclidean Optics whose core has been transformed by discussing and testing the visual model on empirical grounds.

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Kock, Anders. "Differential Calculus and Nilpotent Real Numbers". Bulletin of Symbolic Logic 9, n.º 2 (junio de 2003): 225–30. http://dx.doi.org/10.2178/bsl/1052669291.

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Do there exist real numbers d with d2 = 0 (besides d = 0, of course)? The question is formulated provocatively, to stress a formalist view about existence: existence is consistency, or better, coherence.Also, the provocation is meant to challenge the monopoly which the number system, invented by Dedekind et al., is claiming for itself as THE model of the geometric line. The Dedekind approach may be termed “arithmetization of geometry”.We know that one may construct a number system out of synthetic geometry, as Euclid and followers did (completed in Hilbert's Grundlagen der Geometrie, [2, Chapter 3]): “geometrization of arithmetic”. (Picking two distinct points on the geometric line, geometric constructions in an ambient Euclidean plane provide structure of a commutative ring on the line, with the two chosen points as 0 and 1).Starting from the geometric side, nilpotent elements are somewhat reasonable, although Euclid excluded them. The sophist Protagoras presented a picture of a circle and a tangent line; the apparent little line segment D which tangent and circle have in common, are, by Pythagoras' Theorem, precisely the points, whose abscissae d (measured along the tangent) have d2 = 0. Protagoras wanted to use this argument for destructive reasons: to refute the science of geometry.A couple of millenia later, the Danish geometer Hjelmslev revived the Protagoras picture. His aim was more positive: he wanted to describe Nature as it was. According to him (or extrapolating his position), the Real Line, the Line of Sensual Reality, had many nilpotent infinitesimals, which we can see with our naked eyes.

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Pratama, Febriyana Putra y Julan Hernadi. "KONSISTENSI AKSIOMA-AKSIOMA TERHADAP ISTILAH-ISTILAH TAKTERDEFINISI GEOMETRI HIPERBOLIK PADA MODEL PIRINGAN POINCARE". EDUPEDIA 2, n.º 2 (27 de septiembre de 2018): 161. http://dx.doi.org/10.24269/ed.v2i2.148.

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This research aims to know the interpretation the undefined terms on Hyperbolic geometry and it’s consistence with respect to own axioms of Poincare disk model. This research is a literature study that discusses about Hyperbolic geometry. This study refers to books of Foundation of Geometry second edition by Gerard A. Venema (2012), Euclidean and Non Euclidean Geometry (Development and History) by Greenberg (1994), Geometry : Euclid and Beyond by Hartshorne (2000) and Euclidean Geometry: A First Course by M. Solomonovich (2010). The steps taken in the study are: (1) reviewing the various references on the topic of Hyperbolic geometry. (2) representing the definitions and theorems on which the Hyperbolic geometry is based. (3) prepare all materials that have been collected in coherence to facilitate the reader in understanding it. This research succeeded in interpret the undefined terms of Hyperbolic geometry on Poincare disk model. The point is coincide point in the Euclid on circle . Then the point onl γ is not an Euclid point. That point interprets the point on infinity. Lines are categoried in two types. The first type is any open diameters of . The second type is any open arcs of circle. Half-plane in Poincare disk model is formed by Poincare line which divides Poincare field into two parts. The angle in this model is interpreted the same as the angle in Euclid geometry. The distance is interpreted in Poincare disk model defined by the cross-ratio as follows. The definition of distance from to is , where is cross-ratio defined by . Finally the study also is able to show that axioms of Hyperbolic geometry on the Poincare disk model consistent with respect to associated undefined terms.

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Putri, Livia Agna. "EUCLIDEAN VOICE: APLIKASI PEMBELAJARAN GEOMETRI EUCLID BERBASIS ANDROID UNTUK PENYANDANG TUNANETRA". Jurnal Ilmiah Matematika Realistik 1, n.º 2 (29 de diciembre de 2020): 23–27. http://dx.doi.org/10.33365/ji-mr.v1i2.597.

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AbstrakBerdasarkan UU nomor 20 tahun 2003 sejatinya pendidikan merupakan hak dari seluruh warga negara Indonesia tidak terkecuali penyandang disabilitas, khususnya pada artikel ini adalah penyandang tunanetra. Seharusnya tidak ada perbedaan kemampuan antara siswa normal dan siswa tunanetra untuk dapat mempelajari suatu ilmu pengetahuan, termasuk matematika. Salah satu perbedaan mendasar hanyalah dari sisi penggunaan media yang dapat membantu penyandang tunanetra selayaknya siswa normal dalam menikmati indahnya ilmu pengetahuan dalam matematika. Artikel ini membahas tentang pengembangan media pembelajaran untuk siswa tunanetra berbasis suara yang dikemas pada apliaksi android agar penggunaannya dapat lebih fleksibel dan mudah untuk disebarluaskan kedepannya. Media tersebut dinamakan Euclidean Voice. Metode yang digunakan pada penelitian ini yaitu literature review dengan cara menganalisa referensi yang relevan dengan menggunakan bantuan matriks sintesis. Adapun hasil reviu menunjukkan bahwa aplikasi Euclidean Voice ini efektif dalam penggunaannya serta dapat optimal untuk dapat meningkatkan pemahaman siswa pada materi Geometri Euclid dan akan mendapatkan respon positif dari pengguna sehingga pengguna dapat tertarik belajar matematika tingkat lanjut.Kata Kunci: Aplikasi Android, Geometri Euclid, Tunanetra

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Madeira, Emily da Costa, Érica Letícia da Silva Madeira, Franco Deyvis Lima de Sena, Emerson Batista Gomes y Rubervan da Silva Leite. "Pensamento Geométrico no 6º ano do Ensino Fundamental: Análise Praxeológica de um Livro Didático". Jornal Internacional de Estudos em Educação Matemática 17, n.º 1 (26 de junio de 2024): 97–108. http://dx.doi.org/10.17921/2176-5634.2024v17n1p97-108.

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A partir de experiências vivenciadas no curso de Licenciatura em Matemática da Universidade do Estado do Pará (UEPA) - Campus X, discussões propiciadas no Grupo Colaborativo de Educação Matemática e Educação Afro-Brasileira (GCEM-EAB), no Programa Institucional de Bolsa de Iniciação à Docência (PIBID) e no estágio realizado via Residência Pedagógica, notou-se a relevância da Geometria Euclidiana, de seu ensino na escola básica em nível fundamental e do papel central do livro didático como uma ferramenta acessível à professores e alunos. Dessa forma, propôs-se a investigar: de que forma a Geometria Euclidiana está organizada no livro didático do 6º ano do Ensino Fundamental e como essa abordagem é verificada quanto ao desenvolvimento do Pensamento Geométrico? Para isso, foi efetuada uma análise de caráter qualitativo e bibliográfico, fundamentada na perspectiva da Teoria Antropológica do Didático, especificamente sobre as análises das parexologias observáveis, da unidade destinada a abordagem do conceito de Figuras Geométricas da versão do Manual do Professor do livro didático do 6º Ano, utilizado no município de Igarapé-Açu, estado do Pará. Diante da análise efetuada, considera-se que a pesquisa proposta pode contribuir para reflexão futura sobre a disposição do objeto no livro didático e de seu uso por professores de Matemática. Palavras-chave: Geometria Euclidiana. Pensamento Geométrico. Livro Didático. AbstractFrom experiences lived in the Degree in Mathematics course at the Universidade do Estado do Pará (UEPA) - Campus X, discussions propitiated in the Grupo Colaborativo de Educação Matemática e Educação Afro-Brasileira (GCEM-EAB), in the Programa Institucional de Bolsa de Iniciação à Docência (PIBID) and in the internship carried out via Residência Pedagógica, the relevance of Euclidean Geometry, its teaching in elementary school at the fundamental level and the central role of the textbook as an accessible tool for teachers and students was noted. Therefore, it was proposed to investigate: how is Euclidean Geometry organized in the textbook of the 6th year of Elementary School and how is this approach verified regarding the development of Geometric Thinking? For this, a qualitative and bibliographical analysis was carried out, based on the perspective of the Anthropological Theory of Didactics, specifically on the analyzes of observable parexologies, of the unit destined to approach the concept of Geometric Figures of the version of the Teacher's Manual of the didactic book of the 6th year, used in the municipality of Igarapé-Açu, state of Pará. In view of the analysis carried out, it is considered that the proposed research can contribute to future reflection on the arrangement of the object in the textbook and its use by mathematics teachers. Keywords: Euclidian Geometry. Geometric Thought. Textbook.

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Silva, Raira Rössner da, Josias Neubert Savóis y Ricardo Silva Ribeiro. "Uma breve introdução às geometrias não euclidianas". Cuadernos de Educación y Desarrollo 16, n.º 5 (8 de mayo de 2024): e4144. http://dx.doi.org/10.55905/cuadv16n5-022.

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Este trabalho visa apresentar parte da realização de uma pesquisa bibliográfica referente ao contexto histórico do surgimento das geometrias não euclidianas. O estudo parte de um breve histórico da geometria euclidiana, com ênfase nas questões relacionadas ao quinto postulado do livro Os elementos de Euclides (postulado das paralelas) e nas tentativas frustradas de provar que o mesmo se tratava de um teorema. O fracasso dessas tentativas possibilitou a visualização de novos conceitos geométricos que não são contemplados pelas definições da geometria euclidiana plana, levando ao desenvolvimento de conjuntos de novas propriedades geométricas, não aceitas até então, conjuntos estes que formam as geometrias não euclidianas. Esta análise histórica possibilita compreender a construção e evolução da matemática conhecida atualmente, mostrando que, através da aceitação de conceitos que, às vezes parecem fugir do senso comum, é possível compreender os elementos do mundo real.

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Budiarto, Mega Teguh y Rini Setyaningsih. "KONFLIK KOGNITIF MAHASISWA DALAM MEMAHAMI KONSEP GEOMETRI HIPERBOLIK DAN ELLIPTIK". JUPITEK: Jurnal Pendidikan Matematika 2, n.º 2 (26 de febrero de 2020): 69–76. http://dx.doi.org/10.30598/jupitekvol2iss2pp69-76.

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Using schemes of Euclid's geometrical concepts in long-term memory to understand hyperbolic geometry and elliptic geometry concepts with assimilation and accommodation allows for cognitive conflict. This study aims to reduce the occurrence of cognitive conflict by understanding the mathematical content of the three of Euclidean geometries, hyperbolic and elliptic. The research was conduct used descriptive exploratory. The results indicate that Euclid's geometry representation is still used in representing hyperbolic and elliptic geometry so that cognitive conflict occurs. Cognitive conflicts that occur are related to the position of two lines, parallels, two triangles with the same that correspond angles, intersects one of two parallel lines, the number of angles in a triangle, and Sacherri's valid hypothesis. The efforts that can be made to reduce the occurrence of cognitive conflict are to change existing schemes or create new schemes so that the information obtained can be combined into existing schemes in a deductive axiomatic approach to material content through the accommodation process

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Kosiorek, Jarosław. "An axiom system for full $3$-dimensional Euclidean geometry". Mathematica Bohemica 116, n.º 2 (1991): 113–18. http://dx.doi.org/10.21136/mb.1991.126139.

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Ekayanti, Arta. "DIAGNOSIS KESALAHAN MAHASISWA DALAM PROSES PEMBUKTIAN BERDASARKAN NEWMANN ERROR ANALYSIS". Mosharafa: Jurnal Pendidikan Matematika 6, n.º 1 (24 de agosto de 2018): 105–16. http://dx.doi.org/10.31980/mosharafa.v6i1.298.

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Penelitian ini bertujuan untuk menganalisis kesalahan mahasiswa dalam menyelesaikan soal geometri euclide khususnya pada kasus pembuktian. Analisis yang digunakan berdasarkan pada Newmann Error Analysis yang meliputi reading error, comprehension error, transformation error, process skill error dan encoding error. Subyek penelitian ini adalah mahasiswa program studi pendidikan matematika Universitas Muhammadiyah Ponorogo yang sedang menempuh mata kuliah geometri euclide pada semester ganjil tahun akademik 2016/2017. Jenis dan pendekatan dalam penelitian ini yaitu jenis penelitian deskriptif dengan pendekatan kualitatif. Teknik pengumpulan data yang digunakan dalam penelitian ini dengan metode dokumentasi, tes dan wawancara. Analisis dilakukan dengan menganalisis hasil tes kemudian wawancara dengan beberapa mahasiswa dengan tipe kesalahan yang berbeda-beda. Berdasarkan hasil penelitian, diperoleh kesimpulan bahwa kesalahan mahasiswa terletak pada kesalahan teori/konsep dasar serta ketidaklengkapan justifikasi pada setiap langkah yang digunakan dalam pembuktian.This research aim to analyse the student error, when they solve the problems of euclidean geometry especially proofs. That is based on Newmann Error Analysis, such as error reading, error comprehension, error transformation, error skill process and error encoding. This research was conducted toward the student of Mathematic Department, Teacher Training and Education Faculty, Muhammadiyah University of Ponorogo who studied euclidean geometry in 2016/2017. This research was descriptive research with qualitative approach. Documentation method, interview and test was used to gathering data. The analysis process had been doing by analysed the student result test, and then interviewed with some student with different error type. The result of this research was misconception of previous concept and incompletely the justification of every proofs step.

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Hendroanto, Aan y Harina Fitriyani. "Pengembangan alat pembelajaran GeoKlik untuk pembelajaran geometri". Pythagoras: Jurnal Pendidikan Matematika 14, n.º 1 (28 de junio de 2019): 102–11. http://dx.doi.org/10.21831/pg.v14i1.22063.

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Objek matematika sebagian besar bersifat abstrak dan sulit untuk dibayangkan sehingga banyak siswa yang kesulitan untuk memahaminya. Salah satu solusi untuk membantu siswa dalam hal ini yaitu dengan menggunakan alat-alat Euclid seperti penggaris, jangka, dan busur untuk menggambar objek geometri di papan tulis atau whiteboard. Namun, penggunaan alat-alat Euclid untuk menggambar terkadang tidak maksimal dikarenakan kurang efisien dan merepotkan. Akibatnya, banyak guru yang kemudian justru menggambar objek geometri tanpa menggunakan alat-alat ini sehingga gambar yang seharusnya membantu siswa memahami materi, justru malah membuat mereka semakin tidak paham. Penelitian ini bertujuan untuk menghasilkan alat yang dinamakan GeoKlik untuk mendukung kegiatan pembelajaran geometri. GeoKlik merupakan penggabungan alat-alat menggambar geometri Euclid yang didesain agar penggunaannya lebih fleksibel dan mudah sehingga guru maupun siswa dapat menggunakannya dalam proses belajar mengajar tanpa kesulitan. Pengembangan pada penelitian ini menggunakan model pengembangan 4D yang terdiri dari 4 tahap pengembangan yaitu define, design, development, dan dissemination. Penelitian pengembangan ini dilakukan di Program Studi Pendidikan Matematika FKIP UAD. Analisis data dalam penelitian ini menggunakan metode deskriptif kualitatif. Namun demikian, analisis data tetap melibatkan data kuantitatif dan perhitungan statistika sederhana. Berdasarkan hasil validasi ahli media, alat GeoKlik mendapat penilaian sangat baik dari ahli media dengan nilai rata-rata 4,79. Dari segi aspek desain, GeoKlik mendapat nilai rata-rata sebesar 4,78 dengan kategori sangat baik. Aspek keefektifan GeoKlik juga memperoleh skor sangat baik dengan nilai rata-rata 4,81. Sedangkan untuk aspek kepraktisan, GeoKlik mendapat nilai rata-rata 4,75 dengan kategori sangat baik. Respon yang diberikan guru dan siswa terhadap alat GeoKlik ini juga sangat positif dengan nilai rata-rata keseluruhan yaitu 4,79 untuk respon guru, sedangkan nilai respon rata-rata siswa yaitu sebesar 4,51.The development of the learning tool "GeoKlik" for geometry learningAbstractMathematical objects are mostly abstract and difficult to imagine so that many students have difficulty understanding them. One solution to help students, in this case, is by using Euclid tools such as rulers, rows, and arcs to draw geometric objects on the board or whiteboard. However, the use of Euclid tools for drawing is sometimes not optimal because it is less efficient and troublesome. As a result, many teachers then draw geometric objects without using these tools so that images that should help students understand the material actually make them even less understanding. This study aims to produce a tool called GeoKlik to support geometry learning activities. GeoKlik is a combination of Euclid's geometric drawing tools designed so that its use is more flexible and easy so that teachers and students can use it in the learning process without difficulty. The development of this study used a 4D development model consisting of 4 stages of development, namely: 1) Define 2) Design 3) Development, and 4) Dissemination. This development research was conducted at the Mathematics Education Study Program FKIP UAD. Data analysis in this research used the descriptive qualitative method. However, data analysis still involved quantitative data and simple statistical calculations. Based on the results of the media expert validation, the GeoKlik tool was very well rated by media experts with an average value of 4.79. In terms of design aspects, GeoKlik scored an average of 4.78 with very good categories. The aspect of GeoKlik effectiveness also scored very well with an average value of 4.81. Whereas for the practicality aspect, GeoKlik got an average value of 4.75 with a very good category. The response given by the teacher and students to the GeoKlik tool was also very positive with an overall mean value of 4.79 for the teacher's response, while the average response value of the student was 4.51.

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20

Gunn, Charles. "Geometric Algebras for Euclidean Geometry". Advances in Applied Clifford Algebras 27, n.º 1 (26 de febrero de 2016): 185–208. http://dx.doi.org/10.1007/s00006-016-0647-0.

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21

Loiola, Carlos Augusto Gomes y Chrsitine Sertã Costa. "AS CÔNICAS NA GEOMETRIA DO TÁXI". Ciência e Natura 37 (7 de agosto de 2015): 179. http://dx.doi.org/10.5902/2179460x14596.

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http://dx.doi.org/10.5902/2179460X14596This paper aims to present conics when defined in a non-Euclidean geometry: the Taxicab geometry. The choice of this geometry was due to the simplicity of its definitions enabling diverse applications in Basic Education. It differs from Euclidean geometry by its metric and presents interesting and surprising results that enable the development of a more critical and meaningful learning.

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22

Kimuya, Alex M. y Stephen Mbugua Karanja. "Incompatibility between Euclidean Geometry and the Algebraic Solutions of Geometric Problems". European Journal of Mathematics and Statistics 4, n.º 4 (10 de julio de 2023): 14–23. http://dx.doi.org/10.24018/ejmath.2023.4.4.90.

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The transition from the “early-modern” mathematical and scientific norms of establishing conventional Euclidean geometric proofs has experienced quite mixed modes of reasoning. For instance, a careful investigation based on the continued attempts by different practitioners to resolve the geometric trisectability of a plane angle suggests serious hitches with the established algebraic angles non-trisectability proofs. These faults found the root for the difficult geometric question about having straightedge and compass proofs for either the trisectability or the non-trisectability of angles. One of the evident gaps regarding the norms for establishing the Euclidean geometric proofs concerns the incompatibility between the smugly asserted algebraic-geometric proofs and the desired inherent Euclidean geometric proofs. We consider an algebraically translated proof of the geometric angle trisection scheme proposed by [1]. We assert and prove that there is a complete incompatibility between the geometric and the algebraic methods of proofs, and hence the algebraic methods should not be used as authoritative means of proving Euclidean geometric problems. The paper culminates by employing the incompatibility proofs in justifying the independence of the Euclidean geometric system.

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23

Rodrigues Neto, Guilherme. "Euclides e a geometria do raio visual". Scientiae Studia 11, n.º 4 (diciembre de 2013): 873–92. http://dx.doi.org/10.1590/s1678-31662013000400007.

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24

Burnett, Charles. "Questiones super geometriam Euclidis". Annals of Science 71, n.º 1 (20 de enero de 2012): 111–13. http://dx.doi.org/10.1080/00033790.2011.627465.

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25

Ma, Wancang y David Minda. "Euclidean linear invariance and uniform local convexity". Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 52, n.º 3 (junio de 1992): 401–18. http://dx.doi.org/10.1017/s1446788700035114.

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AbstractLet S(p) be the family of holomorphic functions f defined on the unit disk D, normalized by f(0) = f1(0) – 1 = 0 and univalent in every hyperbolic disk of radius p. Let C(p) be the subfamily consisting of those functions which are convex univalent in every hyperbolic disk of radius p. For p = ∞ these become the classical families S and C of normalized univalent and convex functions, respectively. These families are linearly invariant in the sense of Pommerenke; a natural problem is to calculate the order of these linearly invariant families. More precisely, we give a geometrie proof that C(p) is the universal linearly invariant family of all normalized locally schlicht functions of order at most coth(2p). This gives a purely geometric interpretation for the order of a linearly invariant family. In a related matter, we characterize those locally schlicht functions which map each hyperbolically k-convex subset of D onto a euclidean convex set. Finally, we give upper and lower bounds on the order of the linearly invariant family S(p) and prove that this class is not equal to the universal linearly invariant family of any order.

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26

Kuz’mich, V. I., L. V. Kuzmich, A. G. Savchenko y K. V. Valko. "Geometric interpretation and visualization of particular geometric concepts at metric spaces study". Journal of Physics: Conference Series 2288, n.º 1 (1 de junio de 2022): 012024. http://dx.doi.org/10.1088/1742-6596/2288/1/012024.

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Abstract The paper considers the issues of studying method of geometric properties of metric spaces. These questions arise when students learn the basic concepts of the metric spaces theory. Difficulty in the concepts understanding arises due to the lack of the geometric interpretation or appropriate visualization. To build a geometric interpretation of rectilinear and flat placement of points of metric space, it is proposed to build the appropriate analogues in two-dimensional and three-dimensional arithmetic Euclidean spaces. To visualize these concepts, it is proposed to use a dynamic geometric environment GeoGebra 3D. This approach allows to demonstrate both the similarity of individual geometric concepts of metric space with the corresponding concepts of Euclidean geometry, and cases of the “non-Euclidean”. The study is useful for teachers and students of higher education institutions majoring in physics and mathematics. Some examples can be used in the study of basic geometric concepts by students of secondary education, in-depth study of mathematics and in various types of informal education.

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27

Caristi, G., A. Puglisi y E. Saitta. "Geometric Probabilities in Euclidean Space E3". PROOF 1 (12 de julio de 2021): 51–55. http://dx.doi.org/10.37394/232020.2021.1.8.

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In the last year G. Caristi and M. Stoka [2] have considered Laplace type problem for different lattice with or without obstacles and compute the associated probabilities by considering bodies test not-uniformly distributed. We consider a lattice with fundamental cell a parallelepiped in the Ecuclidean Space E3. We compute the probability that a random segment of constant length, with exponential distribution, intersects a side of the lattice

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28

Javtokas, A. "Geometric Zeta-Function and Euclidean Action". Nonlinear Analysis: Modelling and Control 8, n.º 2 (25 de julio de 2003): 41–53. http://dx.doi.org/10.15388/na.2003.8.2.15182.

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29

Chew, L. Paul, Michael T. Goodrich, Daniel P. Huttenlocher, Klara Kedem, Jon M. Kleinberg y Dina Kravets. "Geometric pattern matching under Euclidean motion". Computational Geometry 7, n.º 1-2 (enero de 1997): 113–24. http://dx.doi.org/10.1016/0925-7721(95)00047-x.

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30

Diogo, Gilson Francisco Contreiras. "A aplicação da geometria na confecção de roupas através do axiomas de Euclides de Alexandria". INTERMATHS 4, n.º 1 (30 de junio de 2023): 103–17. http://dx.doi.org/10.22481/intermaths.v4i1.11909.

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A presente pesquisa tem como tema aplicação da geometria na confecção de roupas através dos axiomas de Euclides de Alexandria. Aluz de encontrar resposta na investigação que se apresenta, foi possível definir o seguinte objetivo principal: compreender as formas de aplicação da geometria na confecção de roupas através dos axiomas de Euclides de Alexandria. Com isso, afim de entendermos o objetivo geral desta pesquisa, foi necessário aprofundar de forma rigorosa nos demais teóricos bibliográficos de vários autores que escreveram sobre a temática em questão nomeadamente: Aplicação, geometria, confecção, roupas, axioma, breve historial sobre confecção, antropométrica e ergonomia, etapas de confecção de roupas, método e modelagem de roupas, desenvolvimento axiomático de Euclides de Alexandria e posteriormente a aplicação da geometria na confecção de roupas. Em linhas gerais, o foco da investigação que aqui se propõe é compreendermos qual a importância da Geometria para o processo de ensino - aprendizagem nos diversos campo de estudo.

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31

Paterson, Alan L. T. "G. W. F. Hegel: Geometrical Studies Introduction". Hegel Bulletin 29, n.º 1-2 (2008): 118–31. http://dx.doi.org/10.1017/s026352320000080x.

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Throughout his life, Hegel showed great interest in physics and mathematics. His most sustained, surviving treatment of Euclidean geometry is his early work ‘Geometrische Studien’, which he completed while he was a private tutor [Hoffmeister] in Frankfurt, shortly before leaving for Jena to join Schelling. GS is not easy reading, but despite that, it seems to me that Hegel presents in it a remarkably erudite as well as interesting and insightful critique of geometry. He investigates some of the themes from the foundations of geometry, in particular from the first book of the Elements of Euclid. Like the mathematical philosophies of Kant and Frege, Hegel's understanding of geometry is conceptually based, but unlike them, it is also grounded in the classical Greek philosophy of mathematics, which achieved its definitive expression in Proclus's great commentary on Euclid 1. Much of this classical philosophy of geometry is forgotten nowadays, under the influence of the great modern mathematical philosophers (in particular, Cantor, Frege and Gödel). In my view, it well deserves reconsideration, especially since, as illustrated by Gödel's incompleteness theorems, modern mathematical philosophy has failed in its attempt to ground mathematics within the framework of formal systems.Much of GS has not survived, and what remains is condensed and fragmentary. It seems that originally, Hegel covered all of the propositions of Euclid 1 rather than just the 14 propositions (1-12, 26, 29) that are covered in what remains of the original GS. I have given detailed treatment of GS together with related material in Hegel's Jena dissertation elsewhere (Paterson 2004/2005). The objective of the present paper is to introduce the translation of GS.

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32

Sukestiyarno, Yohanes Leonardus, Khathibul Umam Zaid Nugroho, Sugiman Sugiman y Budi Waluya. "Learning trajectory of non-Euclidean geometry through ethnomathematics learning approaches to improve spatial ability". Eurasia Journal of Mathematics, Science and Technology Education 19, n.º 6 (1 de junio de 2023): em2285. http://dx.doi.org/10.29333/ejmste/13269.

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Non-Euclidean geometry is an abstract subject and difficult to learn, but mandatory for students. The ethnomathematics approach as a learning approach to improve students’ spatial abilities. The aim of this research is to discover new elements of the spatial abilities of non-Euclidean geometry; determine the relationship between spatial abilities for Euclid, Lobachevsky, and Riemann geometry. This study used the micro genetic method with a 2×2 factorial experimental research design. The sample of this research is 100 students of mathematics education. There are three valid and reliable research instruments through expert trials and field trials. Data collection was carried out in two ways, namely tests and observations. Quantitative data were analyzed through ANCOVA, and observational data were analyzed through the percentage of implementation of the learning trajectory stages. The result is that the spatial ability of students who are given the ethnomathematics learning approach is higher than students who are given the conventional learning approach for Lobachevsky geometry material after controlling for the effect of Euclidean geometry spatial ability. Also, the same thing happened for the spatial abilities of Riemann geometry students. The learning trajectory is conveying learning objectives (learning objective); providing ethnomathematics-based visual problems; students do exploration; students make conclusions and summaries of exploration results; and ends with students sharing conclusions/summaries about concepts and principles in geometric systems. It was concluded that learning non-Euclid geometry through learning paths with an ethnomathematics approach had a positive impact on increasing students’ spatial abilities.

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33

Cho, Kyungjin, Jihun Shin y Eunjin Oh. "Approximate Distance Oracle for Fault-Tolerant Geometric Spanners". Proceedings of the AAAI Conference on Artificial Intelligence 38, n.º 18 (24 de marzo de 2024): 20087–95. http://dx.doi.org/10.1609/aaai.v38i18.29987.

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In this paper, we present approximate distance and shortest-path oracles for fault-tolerant Euclidean spanners motivated by the routing problem in real-world road networks. A fault-tolerant Euclidean spanner for a set of points in Euclidean space is a graph in which, despite the deletion of small number of any points, the distance between any two points in the damaged graph is an approximation of their Euclidean distance. Given a fault-tolerant Euclidean spanner and a small approximation factor, our data structure allows us to compute an approximate distance between two points in the damaged spanner in constant time when a query involves any two points and a small set of failed points. Additionally, by incorporating additional data structures, we can return a path itself in time almost linear in the length of the returned path. Both data structures require near-linear space.

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34

Kazan, Ahmet, Mustafa Altın y Dae Yoon. "Geometric characterizations of canal hypersurfaces in Euclidean spaces". Filomat 37, n.º 18 (2023): 5909–20. http://dx.doi.org/10.2298/fil2318909k.

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In the present paper, firstly we obtain the general expression of canal hypersurfaces in Euclidean n-space and deal with canal hypersurfaces in Euclidean 4-space E4. We compute Gauss map, Gaussian curvature and mean curvature of canal hypersurfaces in E4 and obtain an important relation between the mean and Gaussian curvatures as 3H? = K?3 ? 2. We prove that, the flat canal hypersurfaces in Euclidean 4-space are only circular hypercylinders or circular hypercones and minimal canal hypersurfaces are only generalized catenoids. Also, we state the expression of tubular hypersurfaces in Euclidean spaces and give some results about Weingarten tubular hypersurfaces in E4.

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35

Gómez Urgellés, Joan Vicenç. "Euclides no vivió en Manhattan: Geometría urbana". Modelling in Science Education and Learning 12, n.º 1 (8 de febrero de 2019): 59. http://dx.doi.org/10.4995/msel.2019.10808.

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Se presenta una experiéncia de una situación real de geometria urbana. La situación plantea a partir de un conjunto de puntos del plano determinar las regiones de influenciaen de estos puntos. El problema consiste en encontrar los correspondientes diagramas de Voronoi pero con taxi geometria. La experiencia se realiza como proyecto de aula con alumnos de ingenieria informática de la EPSEVG-UPC

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36

Jesus, Josenilton Santos de y Elias Santiago de Assis. "Aprendizagem de Geometria Esférica Por Meio do Geogebra". Jornal Internacional de Estudos em Educação Matemática 16, n.º 3 (26 de febrero de 2024): 353–62. http://dx.doi.org/10.17921/2176-5634.2023v16n3p353-362.

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Este artigo tem como objetivo identificar as contribuições do software GeoGebra no processo de aprendizagem da Geometria Esférica, um tipo de geometria não euclidiana. Neste sentido, foi realizada uma pesquisa de campo, de natureza qualitativa, envolvendo um grupo de estudantes de um curso de licenciatura em matemática de uma universidade pública do estado da Bahia. As técnicas de coleta de dados consistiram na na realização de entrevistas semiestruturadas e na aplicação de uma sequência de atividades contendo construções geométricas que foram realizadas pelos participantes no GeoGebra. Os resultados obtidos apontaram que construções realizadas no software favorecem a introdução de conceitos da Geometria Esférica, seja na criação ou refutação de conjecturas, seja na validação de resultados. Palavras-chave: Geometria Esférica. GeoGebra, Aprendizagem de Geometria. Abstract This article aims to identify the contributions of GeoGebra software in the process of learning Spherical Geometry, a type of non-Euclidean geometry. In this sense, a qualitative field research was carried out, involving a group of students from an undergraduate course in mathematics at a public university in the state of Bahia. The techniques of data collection consisted of applying a sequence of activities involving geometric constructions in the GeoGebra and conducting semi-structured interviews. The results showed that, through these constructions, it was possible to introduce GE to the participants. It was possible to identify the Spherical Geometry contents properly understood by these actors and the contributions of the software in this process.Idem resumo. Keywords: Spherical Geometry. Geogebra. Geometry Learning.

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37

Oxman, Victor y Avi Sigler. "Surprise Meeting: Euclidean Algorithm and Geometric Constructions". Resonance 27, n.º 3 (marzo de 2022): 435–42. http://dx.doi.org/10.1007/s12045-022-1331-4.

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38

Caristi, Giuseppe, Alfio Puglisi y Antonino Andrea Arnao. "Some geometric probability problems in Euclidean plane". Applied Mathematical Sciences 14, n.º 8 (2020): 371–82. http://dx.doi.org/10.12988/ams.2020.914207.

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39

Bronstein, Michael M., Joan Bruna, Yann LeCun, Arthur Szlam y Pierre Vandergheynst. "Geometric Deep Learning: Going beyond Euclidean data". IEEE Signal Processing Magazine 34, n.º 4 (julio de 2017): 18–42. http://dx.doi.org/10.1109/msp.2017.2693418.

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40

Van Laarhoven, Jon W. y Kurt M. Anstreicher. "Geometric conditions for Euclidean Steiner trees inℜd". Computational Geometry 46, n.º 5 (julio de 2013): 520–31. http://dx.doi.org/10.1016/j.comgeo.2011.11.007.

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41

Joyce, W. P. y P. H. Butler. "The geometric associative algebras of Euclidean space". Advances in Applied Clifford Algebras 12, n.º 2 (diciembre de 2002): 195–233. http://dx.doi.org/10.1007/bf03161247.

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42

Shiguo, Yang y Wang Jia. "Some geometric inequalities in non-euclidean space". Journal of Geometry 56, n.º 1-2 (julio de 1996): 196–201. http://dx.doi.org/10.1007/bf01222696.

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43

Ferreira, Denise Helena Lombardo, Tadeu Fernandes De Carvalho y Sandro Joel Mariano De Oliveira. "Um Estudo Sobre o Matemático Português Pedro Nunes". Jornal Internacional de Estudos em Educação Matemática 13, n.º 1 (22 de junio de 2020): 94–102. http://dx.doi.org/10.17921/2176-5634.2020v13n1p94-102.

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Trata-se de um artigo que tem por objetivo estudar as obras do matemático português Pedro Nunes, ou Petrus Nonius, destacando a obra intitulada Libro de Algebra em Arithmetica y Geometria. Para a elaboração deste trabalho foram usados informações e dados que se encontram disponíveis na internet e na literatura científica. Foram estudados os métodos de resolução de equações, para os quais Nunes usava tanto a álgebra quanto a geometria para suas demonstrações, além dos conhecimentos aprofundados dos livros de Euclides, os Elementos. Além disso, Nunes criou diversos instrumentos de medida, dentre os quais, anel náutico, instrumento de sombras e o nônio, mencionados neste trabalho. Palavras-chave: Pedro Nunes. Álgebra. Geometria. Instrumentos de Navegação. Abstract It is an article that aims to study the works of the Portuguese mathematician Pedro Nunes, or Petrus Nonius, highlighting the work entitled Book of Algebra in Arithmetic and Geometry. For the elaboration of this work, information and data were used that are available in the internet and in the scientific literature. Methods for solving equations were studied, for which Nunes used both algebra and geometry for his demonstrations, as well as the in-depth knowledge of Euclid's books, the Elements. In addition, Nunes created several measuring instruments, among them, nautical ring, shadow instrument and the vernier, mentioned in this work. Keywords: Pedro Nunes. Algebra. Geometry. Navigation instruments.

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44

Khatamov, Ibrohim M. "THE TRAJECTORY OF ORGANIZING AND TEACHING A FACULTATIVE COURSE ON NON-EUCLIDEAN GEOMETRIES AT SCHOOL". American Journal of Applied Science and Technology 03, n.º 01 (1 de enero de 2023): 6–14. http://dx.doi.org/10.37547/ajast/volume03issue01-02.

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The article reveals the trajectory of organizing and teaching a facultative course in order to familiarize students with non-Euclidean geometries in schools. It shows why students should be introduced to non-Euclidean geometries in schools, and what goals can be achieved by teaching non-Euclidean geometries. The most important aspect is the trajectory of the organization of the optional course. When organizing a facultative course, it is indicated what topics to choose, how many hours to allocate, and the program of the facultative course is developed.

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45

Dal Magro, Tamires y Manuel J. García-Perez. "On Euclidean diagrams and geometrical knowledge". THEORIA. An International Journal for Theory, History and Foundations of Science 34, n.º 2 (25 de septiembre de 2019): 255. http://dx.doi.org/10.1387/theoria.20026.

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We argue against the claim that the employment of diagrams in Euclidean geometry gives rise to gaps in the proofs. First, we argue that it is a mistake to evaluate its merits through the lenses of Hilbert’s formal reconstruction. Second, we elucidate the abilities employed in diagram-based inferences in the Elements and show that diagrams are mathematically reputable tools. Finally, we complement our analysis with a review of recent experimental results purporting to show that, not only is the Euclidean diagram-based practice strictly regimented, it is rooted in cognitive abilities that are universally shared.

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46

Cerchiai, B. L., G. Fiore y J. Madore. "Geometrical Tools for Quantum Euclidean Spaces". Communications in Mathematical Physics 217, n.º 3 (marzo de 2001): 521–54. http://dx.doi.org/10.1007/pl00005553.

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47

Livadiotis. "Geometric Interpretation of Errors in Multi-Parametrical Fitting Methods Based on Non-Euclidean Norms". Stats 2, n.º 4 (29 de octubre de 2019): 426–38. http://dx.doi.org/10.3390/stats2040029.

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The paper completes the multi-parametrical fitting methods, which are based on metrics induced by the non-Euclidean Lq-norms, by deriving the errors of the optimal parameter values. This was achieved using the geometric representation of the residuals sum expanded near its minimum, and the geometric interpretation of the errors. Typical fitting methods are mostly developed based on Euclidean norms, leading to the traditional least–square method. On the other hand, the theory of general fitting methods based on non-Euclidean norms is still under development; the normal equations provide implicitly the optimal values of the fitting parameters, while this paper completes the puzzle by improving understanding the derivations and geometric meaning of the optimal errors.

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48

Sherzod, Fayzullaev. "FULFILLMENT OF LOBACHEVSKY'S AXIOM IN EUCLIDEAN SPACE OF THE POINCARE INTERPRETATION OF LOBACHEVSKY'S GEOMETRY". American Journal of Applied Science and Technology 4, n.º 2 (1 de febrero de 2024): 12–17. http://dx.doi.org/10.37547/ajast/volume04issue02-03.

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It is known that the Poincaré interpretation of Lobachevsky’s geometry is used in solving many technical problems, in problems related to the theory of complex variable functions.In this article, we show the Poincaré interpretation of the Lobachevsky plane, which is interpreted in a circle in a plane, using one circle of a two-section hyperboloid, using the method of spatial representation, and the Lobachevsky axiom and the results derived from it are also valid.

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49

Hirsch, C., D. Neuhäuser, C. Gloaguen y V. Schmidt. "First Passage Percolation on Random Geometric Graphs and an Application to Shortest-Path Trees". Advances in Applied Probability 47, n.º 2 (junio de 2015): 328–54. http://dx.doi.org/10.1239/aap/1435236978.

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We consider Euclidean first passage percolation on a large family of connected random geometric graphs in the d-dimensional Euclidean space encompassing various well-known models from stochastic geometry. In particular, we establish a strong linear growth property for shortest-path lengths on random geometric graphs which are generated by point processes. We consider the event that the growth of shortest-path lengths between two (end) points of the path does not admit a linear upper bound. Our linear growth property implies that the probability of this event tends to zero sub-exponentially fast if the direct (Euclidean) distance between the endpoints tends to infinity. Besides, for a wide class of stationary and isotropic random geometric graphs, our linear growth property implies a shape theorem for the Euclidean first passage model defined by such random geometric graphs. Finally, this shape theorem can be used to investigate a problem which is considered in structural analysis of fixed-access telecommunication networks, where we determine the limiting distribution of the length of the longest branch in the shortest-path tree extracted from a typical segment system if the intensity of network stations converges to 0.

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Hirsch, C., D. Neuhäuser, C. Gloaguen y V. Schmidt. "First Passage Percolation on Random Geometric Graphs and an Application to Shortest-Path Trees". Advances in Applied Probability 47, n.º 02 (junio de 2015): 328–54. http://dx.doi.org/10.1017/s0001867800007886.

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We consider Euclidean first passage percolation on a large family of connected random geometric graphs in the d-dimensional Euclidean space encompassing various well-known models from stochastic geometry. In particular, we establish a strong linear growth property for shortest-path lengths on random geometric graphs which are generated by point processes. We consider the event that the growth of shortest-path lengths between two (end) points of the path does not admit a linear upper bound. Our linear growth property implies that the probability of this event tends to zero sub-exponentially fast if the direct (Euclidean) distance between the endpoints tends to infinity. Besides, for a wide class of stationary and isotropic random geometric graphs, our linear growth property implies a shape theorem for the Euclidean first passage model defined by such random geometric graphs. Finally, this shape theorem can be used to investigate a problem which is considered in structural analysis of fixed-access telecommunication networks, where we determine the limiting distribution of the length of the longest branch in the shortest-path tree extracted from a typical segment system if the intensity of network stations converges to 0.

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