Relevant bibliographies by topics / Geometry

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Geometry'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Geometry"

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Rahmah, Salma Mu'allimatur. "Profil Berpikir Geometri Siswa SMP dalam Menyelesaikan Soal Geometri Ditinjau dari Level Berpikir Van Hiele." MATHEdunesa 9, no. 3 (January 28, 2021): 562–69. http://dx.doi.org/10.26740/mathedunesa.v9n3.p562-569.

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Abstrak Berpikir geometris merupakan serangkaian aktivitas yang dilakukan oleh siswa dalam menyelesaikan soal geometri meliputi visualisasi, konstruksi, dan penalaran. Terdapat perbedaan dalam proses berpikir geometris yang dilakukan para siswa dalam menyelesaikan soal. Salah satu yang mempengaruhi proses berpikir geometris siswa adalah level berpikir Van Hiele. Penelitian ini merupakan penelitian deskriptif kualitatif yang bertujuan untuk mendeskripsikan profil berpikir geometris siswa dalam menyelesaikan soal geometri ditinjau dari level berpikir Van Hiele. Subjek penelitian ini terdiri dari tiga siswa kelas IX SMP dengan tingkat berpikir Van Hiele yang berbeda yang dipilih berdasarkan hasil tes level berpikir Van Hiele yang dilakukan. Hasil menunjukkan subjek level 0 melakukan kesalahan dalam ketiga aktivitas kognitif berpikir geometris. Subjek level 0 mengkonstruksi objek geometri tidak berdasarkan aturan geometris, melakukan kesalahan dalam memvisualisasikan objek geometri, dan melakukan kesalahan dalam menarik kesimpulan. Subjek level 1 melakukan proses visualisasi dan konstruksi dengan benar, tetapi melakukan kesalahan dalam proses penalaran karena ketidaktelitian dalam perhitungan matematis. Subjek level 2 melakukan proses visualisasi, konstruksi, dan penalaran dengan benar. Kata Kunci: berpikir geometri, level berpikir Van Hiele, soal geometri. Abstract Geometric thinking is a series of activities carried out by students in solving geometric problems including visualization, construction, and reasoning. There are differences in the geometric thinking processes that students do in solving problems. One thing that influences students' geometric thinking process is Van Hiele's level of thinking. This research is a qualitative descriptive study which aims to describe the geometric thinking profile of students in solving geometry problems in terms of Van Hiele's thinking level. The subjects of this study consisted of three students of class IX JHS with different Van Hiele thinking levels who were selected based on the results of the Van Hiele thinking level test conducted. The results showed that level 0 subjects made mistakes in all three cognitive activities of geometric thinking. Level 0 subjects construct geometric objects not based on geometric rules, make mistakes in visualizing geometric objects, and make mistakes in drawing conclusions. Level 1 subjects performed the visualization and construction processes correctly, but made mistakes in the reasoning process due to inaccuracies in mathematical calculations. Level 2 subjects carry out the visualization, construction, and reasoning processes correctly. Keywords: geometric thinking, Van Hiele level’s, geometry problem
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Yasbiati, Yasbiati, and Titi Nurhayati. "PENINGKATAN KEMAMPUAN MENGENAL BENTUK GEOMTETRI MELALUI MEDIA COLOUR GEOMETRY BOOK (Penelitian Tindakan Kelas pada Kelompok A TK Al-Abror Kecamatan Mangkubumi Kota Tasikmalaya Tahun 2016/2017)." JURNAL PAUD AGAPEDIA 2, no. 1 (May 2, 2020): 23–35. http://dx.doi.org/10.17509/jpa.v2i1.24385.

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ABSTRACTThe purpose of this research is to increase the ability to recognize geometry shape through Color Geometry Book media in the children of Group A in Al-Abror Kindergarten of Mangkubumi Sub-district of Tasikmalaya City. The forms of geometry that are introduced are circle, triangle, square, and rectangle. The type of research used is classroom action research, conducted in collaboration with classroom teachers. Sunjek research as many as 13 children, consisting of 5 men and 8 women. The object of this research is the ability to recognize geometry form through Color Geometry Book media. Techniques of data collection using obserbasi and documentation. The research instrument uses check list observation sheet and documentation. Data analysis technique used descriptive analysis and quantitative analysis. The indicator of success in this study is if at least 75% of all children are able to achieve the criteria of Growing Up Expectations (BSH) on each indicator. The results showed that the ability to recognize geometric shapes seen from indicators of the ability to mention geometric shapes, to show geometric shapes, to group geometric shapes, and to draw geometric shapes. Increasing the ability of children to recognize geometry shape through Color Geometry Book media in the implementation of Pre action on indicator ability mentioned 84.61% (BB) 15.39% (MB), then in Cycle III increased to 30.77% (BSH) 69.23 % (BSB), ability to show on Pre action implementation 92.31% (BB) 7.69% (MB) Cycle III increased to 7.69% (MB) 23.08% (BSH) 69.23% (BSB) Ability to classify Pre action implementation 23.08% (MB) 7.69% (BSH) 69.23% (BSB) Cycle III increased to 100% (BSB), while the ability to draw Pre action 92.31% (BB) shape 7, 69% (MB), Cycle III increased to 15.38% (MB) 30.77% (BSH) and 53.85% (BSB). Tujuan pelaksanaan penelitian ini adalah untuk meningkatkan kemampuan mengenal bentuk geometri melalui media Colour Geometry Book pada anak Kelompok A di TK Al- Abror Kecamatan Mangkubumi Kota Tasikmalaya. Bentuk geometri yang dikenalkan adalah lingkaran, segitiga, persegi, dan persegi panjang. Jenis penelitian yang digunakan adalah penelitian tindakan kelas, dilakukan bekerjasama dengan guru kelas. Sunjek penelitian sebanyak 13 anak, yang terdiri dari 5 laki-laki dan 8 perempuan. Objek penelitian ini adalah kemampuan mengenal bentuk geometri melalui media Colour Geometry Book. Teknik pengumpulan data menggunakan obserbasi dan dokumentasi. Instrumen penelitian menggunakan lembar observasi check list dan dokumentasi. Teknik analisis data menggunakan analisis deskriptif dan analisis kuantitatif. Indikator keberhasilan dalam penelitian ini adalah jika minimal 75% dari seluruh anak mampu mencapai kriteria Berkembang Sesuai Harapan (BSH) pada setiap indikatornya. Hasil penelitian menunjukan adanya peingkatan kemampuan mengenal bentuk geometri yang terlihat dari indikator kemampuan menyebutkan bentuk-bentuk geometri, menunjukan bentuk- bentuk geometri, mengelompokkan bentuk-bentuk geometri, dan menggambar bentuk-bentuk geometri. Peningkatan kemampuan anak dalam mengenal bentuk geometri melalui mediai Colour Geometry Book dalam pelaksanaan Pratindakan pada indikator kemampuan menyebutkan 84,61% (BB)15,39% (MB), kemudian pada Siklus III meningkat menjadi 30,77% (BSH) 69,23% (BSB), kemampuan menunjukan pada pelaksanaan Pratindakan 92,31% (BB) 7,69% (MB) Siklus III meningkat menjadi 7,69% (MB) 23,08% (BSH) 69,23% (BSB), kemampuan mengelompokkan pelaksanaan Pratindakan 23,08% (MB) 7,69% (BSH) 69,23% (BSB) Siklus III meningkat menjadi 100% (BSB), sedangkan kemampuan menggambar bentuk geometri Pratindakan 92,31% (BB) 7,69% (MB) ,Siklus III meningkat menjadi 15,38 % (MB) 30,77 % (BSH) dan 53,85 % (BSB).
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Lestari, Dinar Dwi Putri, Mega Teguh Budiarto, and Agung Lukito. "Analisis Kemampuan Spatial Visualization Siswa Sekolah Dasar dalam Pemecahan Masalah Geometri: Ditinjau dari Kemampuan Matematika Tingkat Tinggi." ELSE (Elementary School Education Journal) : Jurnal Pendidikan dan Pembelajaran Sekolah Dasar 5, no. 1 (February 16, 2021): 55. http://dx.doi.org/10.30651/else.v5i1.7371.

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Abstrak: Kemampuan spasial sangat berkaitan erat dengan geometri. Kemampuan spasial mendukung pemahaman tentang dunia geometris. Penelitian ini bertujuan untuk mendeskripsikan profil kemampuan spasial siswa SD khususnya spatial visualization dengan kemampuan matematika tinggi dalam memecahkan masalah geometri. Subjek dalam penelitian ini adalah siswa kelas 6 SD. Hasil penelitian yang berpendekatan kualitatif ini menggunakan indikator kemampuan spasial yang diadaptasi dari penelitian Lawrie, et al. (2016) dilaksanakan dengan mengggunakan metode triangulasi waktu yakni membandingkan hasil tes dari siswa beserta wawancaranya dengan hasil tes yang setara beserta wawancaranya pada waktu yang berbeda. Hasil penelitian ini menunjukkan bahwa siswa kemampuan tinggi mempunyai kemampuan spatial visualization yang berbeda dalam menyelesaikan tugas pemecahan masalah geometri.Kata Kunci: Kemampuan Spasial, Spatial Visualization, Geometri Sekolah Dasar, Matematika SD Abstract: Spatial ability is closely related to geometry. Spatial abilities support understanding of the geometric world. This study aims to describe the profile of elementary school students' spatial abilities, especially spatial visualization, with high mathematical skills in solving geometric problems. The subjects in this study were students of grade VI SD. The results of this research using a qualitative approach using spatial ability indicators adapted from Lawrie's research were carried out by using the time triangulation method, namely comparing test results from students and their interviews with test results that were equivalent to tests and interviews at different times. The results of this study indicate that high ability students have different spatial visualization abilities in solving geometry problem solving tasks.Keywords: Spatial Ability, Spatial Visualization, Elementary School Geometry, Elementary Mathematics
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Puspananda, Dian Ratna, Anis Umi Khoirutunnisa’, M. Zainudin, Anita Dewi Utami, and Nur Rohman. "GEOMETRY TOWER ADVENTURE PADA ANAK USIA DINI DI DESA SUKOREJO KECAMATAN BOJONEGORO." J-ABDIPAMAS : Jurnal Pengabdian Kepada Masyarakat 1, no. 1 (October 20, 2017): 56. http://dx.doi.org/10.30734/j-abdipamas.v1i1.81.

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ABSTRACTThe introduction of geometry is considered important since early age because part of form recognition learning. This is one of the earliest concepts that children must master in cognitive development. Children can distinguish objects by shape first before based on other features. By giving the introduction of geometric shapes from an early age means that the child will have a learning experience that will support the learning of mathematics in the next level of education. Community Service Activities under the title Geometry Tower Adventure at Early Childhood in Sukorejo Village Bojonegoro District Bojonegoro District aims to train children to know the type of shapes, colors, and soft and coarse motor skills by using their preferred game. This PKM activity started on September 11, 2017 until September 16, 2017, followed by all Singajaya Islam Kindergarten students, amounting to 100 students. As the activity progresses the students follow the game path with enthusiasm and joy. In addition we also provide five sets of props in the form of geometry towers and the steps of its use in learning to the school to be utilized in the future.Keywords: Geomerty tower adventure, Early childhoodABSTRAKPengenalan geometri dianggap penting dikenalkan sejak usia dini karena bagian dari pembelajaran pengenalan bentuk. Hal ini merupakan salah satu dari konsep paling awal yang harus dikuasai oleh anak dalam pengembangan kognitif. Anak dapat membedakan benda berdasarkan bentuk terlebih dahulu sebelum berdasarkan ciri-ciri lainnya. Dengan memberikan pengenalan bentuk geometri sejak usia dini berarti anak mendapatkan pengalaman belajar yang akan menunjang untuk pembelajaran matematika di tingkat pendidikan selanjutnya. Kegiatan Pengabdian kepada Masyarakat dengan judul Geometry Tower Adventure pada Anak Usia Dini di Desa Sukorejo Kecamatan Bojonegoro Kabupaten Bojonegoro bertujuan melatih anak untuk mengetahui jenis bentuk, warna, serta melatih motorik halus dan kasar dengan menggunakan permainan yang disukai mereka. Kegiatan PKM ini dimulai pada tanggal 11 September 2017 sampai dengan 16 September 2017, diikuti oleh seluruh siswa TK Islam Singajaya yang berjumlah 100 siswa. Saat kegiatan berlangsung siswa mengikuti alur permainan dengan antusias dan gembira. Selain itu kami juga memberikan lima set alat peraga berupa menara geometri serta langkah-langkah penggunaanya dalam pembelajaran kepada pihak sekolah agar bisa dimanfaatkan dikemudian hari.Kata Kunci: Geomerty tower adventure, Usia dini
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Clements, Douglas C., and Michael Battista. "Geometry and Geometric Measurement." Arithmetic Teacher 33, no. 6 (February 1986): 29–32. http://dx.doi.org/10.5951/at.33.6.0029.

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Geometry is the study of objects, motions, and relationships in a spatial environment. We use it to examine containers, buildings, cars, and playgrounds—familiar things that students see, touch, or move. Because students are naturally interested in these things, geometry can be a highly motivating topic.
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Rylov, Yuri A. "Geometry without topology as a new conception of geometry." International Journal of Mathematics and Mathematical Sciences 30, no. 12 (2002): 733–60. http://dx.doi.org/10.1155/s0161171202012243.

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A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two points). Such geometric concepts as dimension, manifold, metric tensor, curve are fundamental in the Riemannian conception of geometry, and they are derivative in the T-geometric one. T-geometry is the simplest geometric conception (essentially, only finite point sets are investigated) and simultaneously, it is the most general one. It is insensitive to the space continuity and has a new property: the nondegeneracy. Fitting the T-geometry metric with the metric tensor of Riemannian geometry, we can compare geometries, constructed on the basis of different conceptions. The comparison shows that along with similarity (the same system of geodesics, the same metric) there is a difference. There is an absolute parallelism in T-geometry, but it is absent in the Riemannian geometry. In T-geometry, any space region is isometrically embeddable in the space, whereas in Riemannian geometry only convex region is isometrically embeddable. T-geometric conception appears to be more consistent logically, than the Riemannian one.
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Ningrum, Mallevi Agustin, and Lailatul Asmaul Chusna. "INOVASI DAKON GEOMETRI DALAM MENSTIMULASI KEMAMPUAN MENGENAL BENTUK GEOMETRI ANAK USIA DINI." Kwangsan: Jurnal Teknologi Pendidikan 8, no. 1 (August 5, 2020): 18. http://dx.doi.org/10.31800/jtp.kw.v8n1.p18--32.

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Children aged 4-5 years need to be introduced to the geometry as a provision for further education. But in reality there are still many children aged 4-5 years who are not yet able to recognize geometric shapes (circles, triangles, and quadrilateral) due to the lack of attractive media use in the learning of children aged 4-5 years, especially in understanding geometric shapes. Therefore, the purpose of this study is to provide a media innovation that is appropriate and effective geometry to stimulate children aged 4-5 years in recognizing geometric shapes (circles, triangles and rectangles). This type of research uses Borg and Gall research and development. Material validation test results showed a score of 87% with a good category, while the product validation test results obtained a score of 80% with a good category so that the geometry taxis are worth testing. The results of large group trials using the mann whitney u-test in the experimental group were 4.6, whereas in the control group it was 3.4 and the average achievement score of the large group trial results reached 90.31%. Therefore, it can be concluded that the innovation of geometry is declared feasible and effective to stimulate the ability of children aged 4-5 years to recognize geometric shapes. AbstrakAnak usia 4-5 tahun perlu dikenalkan bentuk geometri sebagai bekal untuk pendidikan selanjutnya. Namun pada kenyataannya masih banyak anak usia 4-5 tahun yang belum bisa mengenal bentuk geometri (lingkaran, segitiga, dan segiempat) karena kurangnya pemanfaatan media yang menarik pada pembelajaran anak usia 4-5 tahun khususnya dalam memahami bentuk geometri. Oleh karena itu, tujuan dari penelitian ini adalah memberikan inovasi media dakon geometri yang layak dan efektif untuk menstimulasi anak usia 4-5 tahun dalam mengenal bentuk geometri (lingkaran, segitiga, dan segiempat). Jenis penelitian ini menggunakan research and development Borg and Gall. Hasil uji validasi materi menunjukkan skor 87% dengan kategori baik, sedangkan hasil uji validasi produk diperoleh skor 80% dengan kategori baik sehingga dakon geometri layak untuk diujicobakan. Hasil uji coba kelompok besar menggunakan uji mann whitney u-test pada kelompok eksperimen sebesar 4,6 sedangkan pada kelompok kontrol sebesar 3,4 dan rata-rata pencapaian skor hasil uji coba kelompok besar mencapai 90,31%. Oleh karena itu, dapat disimpulkan bahwa inovasi dakon geometri dinyatakan layak dan efektif untuk menstimulasi kemampuan anak usia 4-5 tahun dalam mengenal bentuk geometri.
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Misni, Misni, and Ferry Ferdianto. "Analisis Kesalahan dalam Menyelesaikan Soal Geometri Siswa Kelas XI SMK Bina Warga Lemahabang." Jurnal Fourier 8, no. 2 (October 31, 2019): 73–78. http://dx.doi.org/10.14421/fourier.2019.82.73-78.

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Geometri mengandung gambar dan simbol-simbol yang abstrak sehingga butuh penalaran yang tinggi. Kebanyakan siswa kurang memahami materi geometri, sehingga ketika siswa dihadapkan dengan soal geometri akan terjadi kesalahan dalam pengerjaannya. Oleh karena itu, perlu adanya identifikasi dari kesalahan-kesalahan siswa dalam menjawab soal-soal geometri. Adapun, tujuan dari penelitian ini adalah untuk mengetahui jenis-jenis kesalahan siswa dalam menyelesaikan soal geometri dan untuk mengetahui faktor-faktor yang menjadi kesalahan siswa dalam menjawab soal geomerti. Penelitian ini menggunakan metode deskriptif kualitatif. Sampel yang digunakan dalam penelitian ini adalah siswa kelas XI AK SMK Bina Warga Lemahabang. Pengambilan sampelnya yaitu dengan teknik purposive sampling berdasarkan hasil tes siswa. Cara dalam menganalisis hasil tes siswa dilakukan dengan mengidentifikasi data yang diperoleh dari hasil tes siswa lalu disimpulkan jenis-jenis kesalahannya. Adapun hasil analisis soal dan jawaban siswa, diketahui bahwa faktor-faktor yang menyebabkan kesalahan adalah (1) kesalahan dalam memahami konsep (2) kurangnya tingkat penalaran siswa untuk mencapai sebuah ruang. (3) kurang teliti (4) kurang menguasai materi (5) kesalahan dalam menuliskan formula. [Geometry contains abstract images and symbols so it needs high reasoning. Most students do not understand geometry material, so that when students are faced with geometric problems there will be errors in the process. Therefore, it is necessary to identify students' mistakes in answering geometry questions. Meanwhile, the purpose of this study is to determine the types of student errors in solving geometry problems and to find out the factors that are the students' mistakes in answering geomechanical questions. This study used descriptive qualitative method. The sample used in this study was class XI AK SMK Bina Warga Lemahabang. Sampling is by purposive sampling technique based on student test results. The way to analyze student test results is done by identifying data obtained from student test results and then concluding the types of errors. The results of the analysis of the questions and answers of students, it is known that the factors that cause errors are (1) errors in understanding the concept (2) the lack of students' level of reasoning to reach a space. (3) inaccurate (4) lack of mastery of material (5) errors in writing formula.]
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Kaldor, S., and P. K. Venuvinod. "Macro-level Optimization of Cutting Tool Geometry." Journal of Manufacturing Science and Engineering 119, no. 1 (February 1, 1997): 1–9. http://dx.doi.org/10.1115/1.2836551.

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A new approach to the macro-level optimization of tool geometro in machining is proposed. Methods for characterizing the tool material, the work material and the optimum tool geometry are proposed and a model describing the interactions between them is developed. Empirical evidence drawn from published literature is presented in support of the new approach. In this approach, the optimum tool geometry is characterized by a geometric entity number which can be explicity calculated in terms of cutting tool angles. Practical benefits derivable from the approach are discussed along with the issues requiring further research.
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Moretti, Méricles Thadeu, and Adalberto Cans. "Releitura das Apreensões em Geometria e a Ideia de Expansão Figural a Partir dos Estudos de Raymond Duval." Jornal Internacional de Estudos em Educação Matemática 16, no. 3 (February 26, 2024): 303–10. http://dx.doi.org/10.17921/2176-5634.2023v16n3p303-310.

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Procurou-se neste trabalho revisitar a noção de apreensão na aprendizagem da geometria com objetivo de renomear apreensões de forma a atribuir, a cada uma delas, o papel que toma na resolução de problemas em geometria com figuras. A partir dessa busca, identificou-se um tipo de expansão discursiva fortemente presente e que tem o papel de listar as regras ou resultados matemáticos oriundos da identificação de elementos geométricos na figura. Pretendeu-se, portanto, neste estudo deixar bastante visível essas operações semiocognitivas presentes na resolução de problemas em geometria. Palavras-chave: Apreensões em Geometria. Expansão Discursiva. Resolução de Problemas. AbstractThis paper sought to revisit the notion of apprehension in geometry learning with the goal of renaming apprehensions in order to assign to, each of them, the role it takes in solving problems in geometry with figures. From this search, it was identified a type of discursive expansion strongly present and that has the role of listing the rules or mathematical results arising from the identification of geometric elements in the figure. It was intended, therefore, in this study to make quite visible these semiocognitive operations present in geometry problem solving. Keywords: Apprehensions in Geometry. Discursive Expansion. Problem Solving.
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Dissertations / Theses on the topic "Geometry"

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Jadhav, Rajesh. "Geometric Routing Without Geometry." Kent State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=kent1178080572.

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Scott, Phil. "Ordered geometry in Hilbert's Grundlagen der Geometrie." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/15948.

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The Grundlagen der Geometrie brought Euclid’s ancient axioms up to the standards of modern logic, anticipating a completely mechanical verification of their theorems. There are five groups of axioms, each focused on a logical feature of Euclidean geometry. The first two groups give us ordered geometry, a highly limited setting where there is no talk of measure or angle. From these, we mechanically verify the Polygonal Jordan Curve Theorem, a result of much generality given the setting, and subtle enough to warrant a full verification. Along the way, we describe and implement a general-purpose algebraic language for proof search, which we use to automate arguments from the first axiom group. We then follow Hilbert through the preliminary definitions and theorems that lead up to his statement of the Polygonal Jordan Curve Theorem. These, once formalised and verified, give us a final piece of automation. Suitably armed, we can then tackle the main theorem.
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Liu, Yang, and 劉洋. "Optimization and differential geometry for geometric modeling." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40988077.

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Greene, Michael Thomas. "Some results in geometric topology and geometry." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.397717.

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Liu, Yang. "Optimization and differential geometry for geometric modeling." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B40988077.

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Hidalgo, García Marta R. "Geometric constraint solving in a dynamic geometry framework." Doctoral thesis, Universitat Politècnica de Catalunya, 2013. http://hdl.handle.net/10803/134690.

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Geometric constraint solving is a central topic in many fields such as parametric solid modeling, computer-aided design or chemical molecular docking. A geometric constraint problem consists of a set geometric objects on which a set of constraints is defined. Solving the geometric constraint problem means finding a placement for the geometric elements with respect to each other such that the set of constraints holds. Clearly, the primary goal of geometric constraint solving is to define rigid shapes. However an interesting problem arises when we ask whether allowing parameter constraint values to change with time makes sense. The answer is in the positive. Assuming a continuous change in the variant parameters, the result of the geometric constraint solving with variant parameters would result in the generation of families of different shapes built on top of the same geometric elements but governed by a fixed set of constraints. Considering the problem where several parameters change simultaneously would be a great accomplishment. However the potential combinatorial complexity make us to consider problems with just one variant parameter. Elaborating on work from other authors, we develop a new algorithm based on a new tool we have called h-graphs that properly solves the geometric constraint solving problem with one variant parameter. We offer a complete proof for the soundness of the approach which was missing in the original work. Dynamic geometry is a computer-based technology developed to teach geometry at secondary school, which provides the users with tools to define geometric constructions along with interaction tools such as drag-and-drop. The goal of the system is to show in the user's screen how the geometry changes in real time as the user interacts with the system. It is argued that this kind of interaction fosters students interest in experimenting and checking their ideas. The most important drawback of dynamic geometry is that it is the user who must know how the geometric problem is actually solved. Based on the fact that current user-computer interaction technology basically allows the user to drag just one geometric element at a time, we have developed a new dynamic geometry approach based on two ideas: 1) the underlying problem is just a geometric constraint problem with one variant parameter, which can be different for each drag-and-drop operation, and, 2) the burden of solving the geometric problem is left to the geometric constraint solver. Two classic and interesting problems in many computational models are the reachability and the tracing problems. Reachability consists in deciding whether a certain state of the system can be reached from a given initial state following a set of allowed transformations. This problem is paramount in many fields such as robotics, path finding, path planing, Petri Nets, etc. When translated to dynamic geometry two specific problems arise: 1) when intersecting geometric elements were at least one of them has degree two or higher, the solution is not unique and, 2) for given values assigned to constraint parameters, it may well be the case that the geometric problem is not realizable. For example computing the intersection of two parallel lines. Within our geometric constraint-based dynamic geometry system we have developed an specific approach that solves both the reachability and the tracing problems by properly applying tools from dynamic systems theory. Finally we consider Henneberg graphs, Laman graphs and tree-decomposable graphs which are fundamental tools in geometric constraint solving and its applications. We study which relationships can be established between them and show the conditions under which Henneberg constructions preserve graph tree-decomposability. Then we develop an algorithm to automatically generate tree-decomposable Laman graphs of a given order using Henneberg construction steps.
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Chuang, Wu-yen. "Geometric transitions, topological strings, and generalized complex geometry /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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Villa, E. "Methods of geometric measure theory in stochastic geometry." Doctoral thesis, Università degli Studi di Milano, 2007. http://hdl.handle.net/2434/28369.

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All the results of the present thesis have been obtained facing problems related to the study of the so called birth-and-growth stochastic processes, relevant in several real applications, like crystallization processes, tumour growth, angiogenesis, etc. We have introduced a Delta formalism, à la Dirac-Schwartz, for the description of random measures associated with random closed sets in R^d of lower dimensions, such that the usual Dirac delta at a point follows as particular case, in order to provide a natural framework for deriving evolution equations for mean densities at integer Hausdorff dimensions in terms of the relevant kinetic parameters associated to a given birth-and-growth process. In this context connections with the concepts of hazard functions and spherical contact distribution functions, together with local Steiner formulas at first order have been studied and, under suitable general conditions on the resulting random growing set, we may write evolution equations of the mean volume density in terms of the growing rate and of the mean surface density. To this end we have introduced definitions of discrete, continuous and absolutely continuous random closed set, which extend the standard well known definitions for random variables. Further, since in many real applications such as fibre processes, n-facets of random tessellations several problems are related to the estimation of such mean densities, in order to face such problems in the general setting of spatially inhomogeneous processes, we have analyzed an approximation of mean densities for sufficiently regular random closed sets, such that some known results in literature follow as particular cases.
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Persson, Aron. "On the Existence of Electrodynamics on Manifold-like Polyfolds." Thesis, Umeå universitet, Institutionen för fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-155488.

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This essay examines the question whether the classical theory of electrodynamics can be extended to a spacetime which locally changes dimension and if such an endeavour is mathematically possible. Recent research has developed a new generalisation of smooth manifolds, the so called M-polyfolds, which constitutes a sufficient foundation to make this endeavour a physical plausibility. These M-polyfolds then facilitate the capability to define the velocity of a curve going through a dimensionally shifting spacetime. Moreover, necessary extensions to the theory of M-polyfolds is developed in order to tailor the theory to a more physically focused framework. Concluding the essay, Maxwell’s equations on M-polyfolds are defined.
Den här uppsatsen betraktar huruvida klassisk elektrodynamik kan generaliseras till en rumtid som lokalt byter dimension samt om detta är matematiskt möjligt. Nyligen har forskningen utvecklat en generalisering av släta mångfalder, så kallade M-polyfolds, vilka ger oss en tillräcklig grund för att göra detta till en fysikalisk möjlighet. Dessa M-polyfolds möjliggör förmågan att definiera hastigheten av en kurva som går igenom en dimensionellt varierande rumtid. Därutöver utvecklas vissa nödvändiga förlängningar av teorin om M-polyfolds, detta för att skräddarsy teorin till ett mer fysikaliskt ramverk. Därefefter avslutas uppsatsen genom att definiera Maxwells ekvationer på M-polyfolds.
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Lokteva, Elizaveta. "On Smooth Knots and Tangent Lines." Thesis, Uppsala universitet, Algebra och geometri, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354484.

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Books on the topic "Geometry"

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Sal'kov, Nikolay. Geometry in education and science. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1158751.

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This monograph consists of the author's articles on geometry, geometric education, and the formation of the teaching staff. Various problems concerning the development of geometric science itself, as well as those that periodically arise in the pedagogical environment of universities, are considered. It is intended for a wide range of readers: not only geometers and those interested in geometry, but also those related to pedagogy and science.
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Collezione Maramotti (Gallery : Reggio Emilia, Italy), ed. Geometria figurativa: Figurative geometry. Cinisello Balsamo, Milano: Silvana editoriale, 2017.

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Pedoe, Daniel. Geometry: A comprehensive course. New York: Dover, 1988.

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Pedoe, Daniel. Geometry, a comprehensive course. New York: Dover Publications, 1988.

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Jost, Jürgen. Riemannian geometry and geometric analysis. 3rd ed. New York: Springer, 2002.

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W, Henderson David. Differential geometry: A geometric introduction. Upper Saddle River, N.J: Prentice Hall, 1998.

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Quinto, Eric, Fulton Gonzalez, and Jens Christensen, eds. Geometric Analysis and Integral Geometry. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/conm/598.

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Jost, Jürgen. Riemannian Geometry and Geometric Analysis. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-662-03118-6.

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Jost, Jürgen. Riemannian Geometry and Geometric Analysis. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61860-9.

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Elkadi, Mohamed, Bernard Mourrain, and Ragni Piene, eds. Algebraic Geometry and Geometric Modeling. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-33275-6.

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Book chapters on the topic "Geometry"

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Pütz, Ralph, and Ton Serné. "Geometrie Geometry." In Rennwagentechnik - Praxislehrgang Fahrdynamik, 105–41. Wiesbaden: Springer Fachmedien Wiesbaden, 2017. http://dx.doi.org/10.1007/978-3-658-16102-6_5.

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Pütz, Ralph, and Ton Serné. "Geometrie Geometry." In Rennwagentechnik - Praxislehrgang Fahrdynamik, 127–69. Wiesbaden: Springer Fachmedien Wiesbaden, 2019. http://dx.doi.org/10.1007/978-3-658-26704-9_5.

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Vince, John. "Geometry Using Geometric Algebra." In Imaginary Mathematics for Computer Science, 229–36. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94637-5_10.

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Wattenhofer, Mirjam, Roger Wattenhofer, and Peter Widmayer. "Geometric Routing Without Geometry." In Structural Information and Communication Complexity, 307–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11429647_24.

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Wu, Wen-tsün. "Orthogonal geometry, metric geometry and ordinary geometry." In Mechanical Theorem Proving in Geometries, 63–113. Vienna: Springer Vienna, 1994. http://dx.doi.org/10.1007/978-3-7091-6639-0_3.

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Jost, Jürgen. "Geometry." In Geometry and Physics, 1–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00541-1_1.

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Stillwell, John. "Geometry." In Numbers and Geometry, 37–67. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0687-3_2.

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Bronshtein, Ilja N., Konstantin A. Semendyayev, Gerhard Musiol, and Heiner Muehlig. "Geometry." In Handbook of Mathematics, 128–250. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05382-9_3.

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Bronshtein, I. N., K. A. Semendyayev, Gerhard Musiol, and Heiner Mühlig. "Geometry." In Handbook of Mathematics, 129–268. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-46221-8_3.

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Hurlbert, Glenn H. "Geometry." In Undergraduate Texts in Mathematics, 59–72. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-79148-7_3.

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Conference papers on the topic "Geometry"

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Qing, Ni, and Wang Zhengzhi. "Geometric invariants using geometry algebra." In 2011 IEEE 2nd International Conference on Computing, Control and Industrial Engineering (CCIE 2011). IEEE, 2011. http://dx.doi.org/10.1109/ccieng.2011.6008094.

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Caticha, Ariel. "Geometry from information geometry." In TECHNOLOGIES AND MATERIALS FOR RENEWABLE ENERGY, ENVIRONMENT AND SUSTAINABILITY: TMREES. Author(s), 2016. http://dx.doi.org/10.1063/1.4959050.

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Ivic, Aleksandar. "Number of digital convex polygons inscribed into an (m,m)-grid." In Vision Geometry II. SPIE, 1993. http://dx.doi.org/10.1117/12.165003.

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Allili, Madjid. "A deformable model with topology analysis and adaptive clustering for boundary detection." In Vision Geometry XIV. SPIE, 2006. http://dx.doi.org/10.1117/12.642353.

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Nguyen, Hung, Rolf Clackdoyle, and Laurent Desbat. "Automatic geometric calibration in 3D parallel geometry." In Physics of Medical Imaging, edited by Hilde Bosmans and Guang-Hong Chen. SPIE, 2020. http://dx.doi.org/10.1117/12.2549568.

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Plauschinn, Erik. "Non-geometric fluxes and non-associative geometry." In Proceedings of the Corfu Summer Institute 2011. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.155.0061.

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Lima, Guilherme. "In-memory Geometry Converter." In In-memory Geometry Converter. US DOE, 2023. http://dx.doi.org/10.2172/2204991.

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Fernández, M., A. Tomassini, L. Ugarte, R. Villacampa, Fernando Etayo, Mario Fioravanti, and Rafael Santamaría. "On Special Hermitian Geometry." In GEOMETRY AND PHYSICS: XVII International Fall Workshop on Geometry and Physics. AIP, 2009. http://dx.doi.org/10.1063/1.3146230.

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Szabo, Richard. "Higher Quantum Geometry and Non-Geometric String Theory." In Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity". Trieste, Italy: Sissa Medialab, 2018. http://dx.doi.org/10.22323/1.318.0151.

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Lai, Y. K., S. M. Hu, D. X. Gu, and R. R. Martin. "Geometric texture synthesis and transfer via geometry images." In the 2005 ACM symposium. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1060244.1060248.

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Reports on the topic "Geometry"

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Chuang, Wu-yen, and /SLAC /Stanford U., Phys. Dept. Geometric Transitions, Topological Strings, and Generalized Complex Geometry. Office of Scientific and Technical Information (OSTI), June 2007. http://dx.doi.org/10.2172/909289.

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Heath, Daniel, and Joshua Jacobs. Geometry Playground. Washington, DC: The MAA Mathematical Sciences Digital Library, November 2010. http://dx.doi.org/10.4169/loci003567.

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Foster, Karis. Exposed Geometry. Ames: Iowa State University, Digital Repository, 2014. http://dx.doi.org/10.31274/itaa_proceedings-180814-975.

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Ungar, Abraham A. Hyperbolic Geometry. GIQ, 2014. http://dx.doi.org/10.7546/giq-15-2014-259-282.

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Ungar, Abraham A. Hyperbolic Geometry. Jgsp, 2013. http://dx.doi.org/10.7546/jgsp-32-2013-61-86.

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Earnshaw, Connie. Overgrown geometry. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.5380.

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Butler, Lee A., and Clifford Yapp. Adaptive Geometry Shader Tessellation for Massive Geometry Display. Fort Belvoir, VA: Defense Technical Information Center, March 2015. http://dx.doi.org/10.21236/ada616646.

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Hansen, Mark D. Results in Computational Geometry: Geometric Embeddings and Query- Retrieval Problems. Fort Belvoir, VA: Defense Technical Information Center, November 1990. http://dx.doi.org/10.21236/ada230380.

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CONCEPT ANALYSIS CORP PLYMOUTH MI. Missile Geometry Package. Fort Belvoir, VA: Defense Technical Information Center, March 1989. http://dx.doi.org/10.21236/ada253181.

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Zhanchun Tu, Zhanchun Tu. Geometry of Membranes. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-24-2011-45-75.

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