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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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Jesus, Josenilton Santos de, and Elias Santiago de Assis. "Aprendizagem de Geometria Esférica Por Meio do Geogebra." Jornal Internacional de Estudos em Educação Matemática 16, no. 3 (February 26, 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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Yıldırım, Abdurrahman, and 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, no. 4 (October 15, 2014): 364–79. http://dx.doi.org/10.12739/nwsa.2014.9.4.1c0624.
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Larke, Patricia J. "Geometric Extravaganza: Spicing Up Geometry." Arithmetic Teacher 36, no. 1 (September 1988): 12–16. http://dx.doi.org/10.5951/at.36.1.0012.
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If we can have science fairs, why not geometry fairs? They are excellent ways for elementary teachers to add pizzazz to the teaching of geometry. A geometry fair or geometric extravaganza is a display or exhibit of geometry projects representing the students' culminating work in a geometry unit. The purposes of a geometry fair a re (I) to remind students of important geometric terms and concepts; (2) to enable students to explore the world of lines, angles, points, and geometric shapes; (3) to help students identify and construct geome tric shapes and designs; (4) to help students prepare projects using their knowledge of geometry and creativity; and (5) to help students share work with othe rs. thus building pride in their work.
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Mallayya, V. Madhukar. "Geometric series geometry: Sankara's contribution." Arya Bhatta Journal of Mathematics and Informatics 13, no. 2 (2021): 215–26. http://dx.doi.org/10.5958/2394-9309.2021.00027.5.
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Salkov, Nikolay. "Parametric Geometry in Geometric Modeling." Геометрия и графика 2, no. 3 (September 10, 2014): 7–13. http://dx.doi.org/10.12737/6519.
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Сальков and Nikolay Sal'kov. "Geometric Simulation and Descriptive Geometry." Geometry & Graphics 4, no. 4 (December 19, 2016): 31–40. http://dx.doi.org/10.12737/22841.
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Geometric simulation is creation of a geometric model, whose properties and characteristics in a varying degree determine the subject of investigation’s properties and characteristics. The geometric model is a special case of the mathematical model. The feature of the geometric model is that it will always be a geometric figure, and therefore, by its very nature, is visual. If the mathematical model is a set of equations, which says little to an ordinary engineer, the geometric model as representation of the mathematical model and as the geometric figure itself, enables to "see" this set. Any geometric model can be represented graphically. Graphical model of an object is a mapping of its geometric model onto a plane (or other surface). Therefore, the graphical model can be considered as a special case of the geometric model. Graphical models are very various – these are graphics, and graphical structures of immense complexity, reflecting spatial geometric figures. These are drawings of geometric figures, simulating processes of all kinds. The simulation goes on as follows. According to known geometric and differential criteria the geometric model is executed. Then a mathematical model is composed based on the geometric model, finally a computer program is compiled on the mathematical model. As a result of consideration in this paper the process of obtaining the geometric models of surface and linear forms for auto-roads it is possible to make a following conclusion. For geometric simulation and the consequent mathematical one the descriptive geometry involvement is vital. Just the descriptive geometry is used both on the initial and final stages of design.
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Basu, B., S. Dhar, and S. Ghosh. "Noncommutative geometry and geometric phases." Europhysics Letters (EPL) 76, no. 3 (November 2006): 395–401. http://dx.doi.org/10.1209/epl/i2006-10299-9.
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Dress, Andreas W. M., and Timothy F. Havel. "Distance geometry and geometric algebra." Foundations of Physics 23, no. 10 (October 1993): 1357–74. http://dx.doi.org/10.1007/bf01883783.
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Gunn, Charles. "Geometric Algebras for Euclidean Geometry." Advances in Applied Clifford Algebras 27, no. 1 (February 26, 2016): 185–208. http://dx.doi.org/10.1007/s00006-016-0647-0.
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Li, Hongbo. "Hyperbolic geometry with geometric algebra." Chinese Science Bulletin 42, no. 3 (February 1997): 262–63. http://dx.doi.org/10.1007/bf02882454.
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Asnawati, Sri, and Irmawati Liliana Kusuma Dewi. "Pemahaman Konsep Geometri dan Self Confidence Mahasiswa Calon Guru Matematika pada Mata Kuliah Pembelajaran Mikro untuk Persiapan Pelaksanaan PPL Di Sekolah." Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang 3, no. 1 (January 2, 2019): 75. http://dx.doi.org/10.31331/medivesveteran.v3i1.706.
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Penelitian ini bertujuan untuk mengetahui tingkat self confidence mahasiswa, hubungan pemahaman konsep geometri dan self confidence mahasiswa pada mata kuliah Pembelajaran Mikro. Penelitian ini adalah penelitian kuantitatif. Pada mata kuliah Pembelajaran Mikro terdapat 8 keterampilan dasar mengajar, salah satunya adalah keterampilan menjelaskan dimana mahasiswa harus dapat mengorganisasikan konsep geometri transformasi dalam tata urutan yang terencana secara sistematis, sehingga mudah dipahami oleh siswa. Perlu adanya self confidence dalam menyampaikan materi khususnya pemahaman konsep geometri. Hasil penelitian menunjukkan bahwa pada taraf signifikansi 5% diperoleh hubungan yang linier antara pemahaman konsep geometri transformasi dan self confidence mahasiswa calon guru matematika pada mata kuliah Pembelajaran Mikro. Tingkat keeratan hubungan kedua variabel berdasarkan koefisien korelasi berada pada kategori kuat yaitu 0,700. Hubungan kedua variabel tersebut menunjukkan arah positif artinya, peningkatan pemahaman konsep geometri transformasi berbanding lurus dengan self confidence mahasiswa calon guru matematika.
Kata kunci: pemahaman konsep geometri, self confidence, pembelajaran mikro.
ABSTRACT
This study aims to determine the level of self-confidence of students and relationship between understanding the concept of geometry and self-confidence of students in the Micro Learning subject. This research is quantitative research. In the Micro Learning subject there are 8 basic teaching skills, one of them is the skill to explain where students must be able to organize the geometry concept of transformation in a systematic order planned so that it is easily understood by students. Self confidence is needed in delivering the material, especially understanding the concept of geometry. At a significance level of 5% a linear relationship was found between the understanding of the geometry concept of transformation and the self confidence of mathematics teacher candidates in the Micro Learning subject. The relationship between the two variables based on the correlation coefficient is in the strong category, 0.700. The relationship between these two variables shows a positive relation, it means that as the understanding of geometric concept gets better, the self confidence of mathematics teacher candidates get higher.
Keywords: understanding of the concept of geometry, self confidence, micro learning subject.
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Rosalina, Venny, and Fabio Yuda. "CREATIVE PROCESS OF CONTEMPORARY DANCE GEOMETRY: A CHOREOGRAPHIC WORK WITH A SOCIAL PSYCHOLOGICAL APPROACH." Ekspresi Seni : Jurnal Ilmu Pengetahuan dan Karya Seni 24, no. 1 (June 30, 2022): 149. http://dx.doi.org/10.26887/ekspresi.v24i1.2090.
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This paper discusses the process of creating Geometry, a dance works by using a psychological approach to express the idea of the Minangkabau body in contemporary dance practice. Geometry dance works as a real picture of the behavior, thoughts, appreciation of human characters through the description of body dialogue and unique experiences as character expressions in dance works. This study resulted in a description of the creative process of contemporary dance creation based on the application of a psychological approach by describing creative values, appreciation values and behavioral values in a geometric creation. The audience's reflection becomes the impetus to feel the sensations of contemporary dancers' bodies. Basik Minang Kabau uses geometry as a critical reflection on the development of contemporary dance in West Sumatra as a form of the body of the Minangkabau tradition towards a contemporary body. Keywords: Geometry; psychology; Audience Reflection; choreography; creative processPROSES KREATIF TARI KONTEMPORER GEOMETRI: SEBUAH KARYA KOREOGRAFI DENGAN PENDEKATAN PSIKOLOGI SOSIAL AbstrakTulisan ini membahas tentang sebuah proses kreatif dalam penciptaan tari kontemporer berjudul Geometri dengan menggunakan pendekatan psikologi sosial. Koreografi tersebut disusun untuk mengungkapkan gagasan tentang ketubuhan Minangkabau dalam praktik tari kontemporer. Karya tari Geometri erupakan gambaran nyata dari perilaku, pemikiran, penghayatan karakter manusia melalui penjabaran dialog tubuh dan pengalaman unik sebagai ekspresi karakter dalam karya tari. Penelitian ini mengahasilkan sebuah uraian proses kreatif penciptaan tari kontemporer yang berbasis pada penerapan pendekatan psikologi dengan menjabarkan nilai-nilai kreatif, nilai penghayatan dan nilai bersikap dalam sebuah penciptaan geometri. Refleksi penonton menjadi dorongan untuk merasakan sensasi ketubuhan penari kontemporer. Basik minang kabau menjadikan karya geometri sebagai refleksi kritis terhadap perkembangan tari kontemporer di Sumatera Barat sebagai wujud tubuh tradisi minangkabau menuju tubuh kontemporer. Kata Kunci: Geometri; psikologi sosial, refleksi penonton; koreografi; proses kreatif
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Sal'kov, N., and Nina Kadykova. "Representation of Engineering Geometry Development in “Geometry and Graphics” Journal." Geometry & Graphics 8, no. 2 (August 17, 2020): 82–100. http://dx.doi.org/10.12737/2308-4898-2020-82-100.
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In the paper "On the Increasing Role of Geometry", published in the electronic "Journal of Natural Science Research" in 2017, it was outspoken a hypothesis that now, at the time of innovative technologies, the importance of geometry is constantly increasing. The significance of geometry is also demonstrated by numerous Ph.D. and doctoral dissertations in the specialty No 05.01.01 - “Engineering Geometry and Computer Graphics”. It can be affirmed that all and everyone dissertations of technical and technological profile contain a geometric component to one degree or another. The "Geometry and Graphics" journal turned 8 (it was founded in June 2012). During this time, on its pages have been published numerous scientific papers, developing namely geometry and its branches: from simplest geometric constructions based on new properties of both lines and surfaces, to imaginary elements. Investigations were conducted in the following areas: “New Directions in Geometry”, “Fractal Geometry”, “Multidimensional Geometry”, “Geometric Constructions”, “Construction and Research of Surfaces”, “Imaginary Geometry”, “Practical Application of Geometry”, “Computer Graphics”, “Descriptive Geometry as Basis of other Branches of Geometry” ,”Geometry of Phase Spaces”. The journal publishes both recognized scientists and candidate for Ph.D. and doctor degrees.
The considered array of papers clearly confirms the statement of the majority of authors, published in the journal, about geometry continuous development, which knocks out the ground for skeptics who decided that geometry is the science of the past centuries. As long as objects with shapes and surfaces surround us, geometry will be in demand. This, as they say, is unequivocal.
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Maharani, Hevy Risqi, YL Sukestiyarno, St Budi Waluya, and Mulyono Mulyono. "Design of creative thinking test in geometry based on information processing taxonomy." Beta: Jurnal Tadris Matematika 11, no. 2 (December 31, 2018): 144–54. http://dx.doi.org/10.20414/betajtm.v11i2.180.
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[English]: This paper describes how to develop a valid and reliable instrument for geometric creative thinking test based on the information processing taxonomy. Using this model, geometry test can be classified in the level of creative thinking based on the information processing process of the mathematical knowledge they already have to solve problems according to the criteria at each hierarchical level. The development of test instrument refers to Beyers (2011). Quantitative method wasused to validate instruments through experts validation and instrument validation. The results showed that there werefive geometry test that can be used to describe the student’s creative thinking process at a different hierarchical level based on the information processing taxonomy. The results of this study can be a reference for teachers and other researchers to design mathematical test by paying attention to the hierarchical level of student’s thinking abilities so that students with different abilities can solve problemswhich refer to their abilities.
Keywords: Creative thinking,Geometry, Information processing taxonomy, Test design
[Bahasa]: Artikel ini memaparkan tentang bagaimana menghasilkan instrumen yang valid dan reliabel untuk kemampuan berpikir kreatif geometris berdasarkan taksonomi pemrosesan informasi. Dengan menggunakan model ini, soal geometri dapat diklasifikasikan dalam tingkatan berpikir kreatif siswa berdasarkan proses pengolahan informasi dari pengetahuan matematika yang telah mereka miliki untuk menyelesaikan masalah sesuai batas kriteria pada setiap tingkatannya. Pengembangan instrumen tes mengikuti langkah Beyers (2011). Metode kuantitatif digunakan untuk memvalidasi instrumen soal yang melalui tahap validasi ahli dan validasi instrumen. Hasil penelitian menunjukkan bahwa terdapat lima butir soal geometri yang dapat digunakan untuk mendeskripsikan proses berpikir kreatif siswa pada tingkatan hierarki yang berbeda berdasarkan model taksonomi pemrosesan informasi. Hasil penelitian ini dapat menjadi rujukan untuk guru maupun para peneliti lain untuk menyusun soal matematika dengan memperhatikan tingkatan hierarki kemampuan berpikir siswa agar siswa dengan berbagai kemampuan yang berbeda dapat mengerjakan soal sesuai dengan kemampuan yang dimiliki.
Kata kunci: Berpikir kreatif, Geometri, Taksonomi pemrosesan informasi, Desain tes
NB: PDF version of this article will be available in maximum two weeks after this publication
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Baldwin, John T., and Andreas Mueller. "Autonomy of Geometry." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 11 (February 5, 2020): 5–24. http://dx.doi.org/10.24917/20809751.11.1.
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In this paper we present three aspects of the autonomy of geometry. (1) An argument for the geometric as opposed to the ‘geometric algebraic’ interpretation of Euclid’s Books I and II; (2) Hilbert’s successful project to axiomatize Euclid’s geometry in a first order geometric language, notably eliminating the dependence on the Archimedean axiom; (3) the independent conception of multiplication from a geometric as opposed to an arithmetic viewpoint.
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Weiss, Gunter. "GEOMETRY. WHAT ELSE !? - MORE OF “ENVIRONMENTAL GEOMETRY”." Boletim da Aproged, no. 34 (December 2018): 9–20. http://dx.doi.org/10.24840/2184-4933_2018-0034_0001.
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This paper is an addendum to a previous article [01] in which several examples demonstrate that “all natural or artificial objects have a shape or form resulting from a natural (bio-physical) or technical (design) process, and therefore have an intrinsic (immanent) geometric constituent”, focusing on the fact that “reality reveals geometry and geometry creates reality”. Since many objects are metaphors for geometric and mathematical content and the starting point for mathematical abstraction, one can conclude that geometry is simply everywhere. This sort of “Appendix” focuses on the symbiotic terms “grasping via senses” and “meaning” in connection with geometry and its visualisation and interpretation, from objects found in our usual environment. A real object that we see or recognize may even gain spiritual meaning, because it is extraordinary and rare and has, therefore, besides its somehow practical purpose, a symbolic one. Here, simplicity, symmetry, smoothness and regularity play an essential role beyond simple aesthetics. In our mainly secular culture, the aesthetic point of view stands in the foreground. KEYWORDS: elementary geometry, intuitive geometry, right angle, cross and square, proofs without words.
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Madang, Septina, Irvinia Ariesti, Maria Apriani, Sesilia Dea Lestari, Alviyani Masrifah, Kezia Kezia, and Fachrul Rozie. "Stimulating Early Children’s Knowledge about Shape Using the Geometry Board." GENIUS Indonesian Journal of Early Childhood Education 3, no. 1 (June 30, 2022): 81–90. http://dx.doi.org/10.35719/gns.v3i1.84.
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This study aims to describe the use of learning media products in the form of geometric boards to develop children's cognitive abilities aged 4-5 years. Using the geometric board as media, children can easily recognize geometric shapes such as triangles, rectangles, circles, semicircles, rectangles, and parallelograms. This type of research uses an approach with a descriptive analysis model. The data analysis stage uses the Miles and Huberman model, including compaction, data presentation, and concluding. In this study, the the researcher chose to conduct research in kindergarten. The informants observed were children aged between 4 to 5 years who were in early childhood education and their parents. To check the validity of the data, using the triangulation technique. The results of the study found that using the geometry board was very helpful for parents in introducing geometry to their children. The media is made of simple materials that are easy to find, so it is not difficult to make. Children also become more interested in learning and are willing to learn various shapes of objects. Abstrak Penelitian ini bertujuan untuk mendeskripsikan tentang pemanfaatan produk media pembelajaran berupa papan geometri untuk mengembangkan kemampuan kognitif anak usia 4-5 tahun. Manfaat dari penggunaan media papan geometri ini agar anak dapat mengenal bentuk-bentuk geometri seperti bentuk segitiga, segi empat, lingkaran, setengah lingkaran, persegi panjang, dan jajaran genjang. Jenis penelitian ini menggunakan pendekatan kualitatif dengan model analisis deskriptif. Tahap analisis data menggunakan model Miles dan Huberman yang meliputi pemadatan data, penyajian data, dan penarikan kesimpulan. dalam penelitian ini peneliti memilih untuk melakukan penelitian di taman kanak-kanak. Informan yang diamati adalah anak-anak berusia antara 4 sampai 5 tahun yang berada dalam masa pendidikan anak usia dini serta orang tuanya. Untuk mengecek keabsahan data, peneliti menggunakan teknik triangulasi. Hasil penelitian menemukan bahwa penggunaan papan geometri sangat membantu orang tua dalam mengenalkan geometri kepada anak-anak. Media terbuat dari bahan-bahan sederhana yang mudah ditemukan sehingga tidak sulit pembuatannya.anak-anak juga menjadi lebih tertarik belajar dan memiliki kemauan untuk mempelajari ragam bentuk benda.
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Saputra, Paulus Roy. "Pembelajaran Geometri Berbantuan Geogebra dan Cabri Ditinjau dari Prestasi Belajar, Berpikir Kreatif dan Self-Efficacy." PYTHAGORAS: Jurnal Pendidikan Matematika 11, no. 1 (June 10, 2016): 59. http://dx.doi.org/10.21831/pg.v11i1.9680.
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Penelitian ini bertujuan untuk mendeskripsikan dan membandingkan keefektifan pembelajaran geometri berbantuan Cabri dan pembelajaran geometri berbantuan Geogebra ditinjau dari prestasi belajar, berpikir kreatif, dan self-efficacy siswa SMP. Penelitian ini adalah penelitian eksperimen semu desain pretest-posttest non equivalent group design. Penelitian ini menggunakan dua kelompok eksperimen tanpa kelompok kontrol. Populasi penelitian ini mencakup seluruh siswa kelas VII SMP Santa Maria Banjarmasin. Sampel terdiri dari dua kelas, yaitu kelas VIIA dan kelas VIIB yang dipilih secara acak. Kelas VIIA menggunakan pembelajaran geometri berbantuan Cabri dan kelas VIIB menggunakan pembelajaran geometri berbantuan Geogebra. Hasil penelitian ini menunjukkan bahwa ditinjau dari prestasi belajar, berpikir kreatif, dan self-efficacy siswa (1) pembelajaran geometri berbantuan Cabri efektif; (2) pembelajaran geometri berbantuan Geogebra efektif; (3) terdapat perbedaan keefektifan pembelajaran geometri berbantuan Geogebra dan Cabri; (4) pembelajaran geometri berbantuan Geogebra lebih efektif dari pada pembelajaran geometri berbantuan Cabri.Kata Kunci: Cabri, Geogebra, prestasi belajar, berpikir kreatif, dan self-efficacy Geometry Instruction Using Cabri and Geogebra in Terms of Achievement, Creative Thinking, and Self-Efficacy AbstractThis study aimed to describe and to compare the effectiveness geometry instruction using Cabri and Geogebra in terms of the achievement, creative thinking, and self-efficacy of the students junior high schools. This research was a quasi-experimental research with the pretest-posttest non-equivalent group design. This study used two experimental groups without control groups. The population of the study was all grade VII students of Junior High School Saint Mary Banjarmasin. The sample of two classes (class VIIA, and class VIIB) was established randomly. Class VIIA got geometry instruction with Cabri and class VIIB got geometry instruction with Geogebra. The results show that in terms of students’ academic achievement, creative thinking, and self-efficacy: (1) geometry instruction using by Cabri was effective; (2) geometry instruction using by Geogebra was effective; (3) there was a difference in the instruction using Cabri and that using Geogebra; (4) geometry instruction using Geogebra was more effective than geometry instruction using Cabri.Keywords: Cabri, Geogebra, academic achievement, creative thinking, and self – efficacy
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Geng, Runshi, and Joseph M. Landsberg. "On the geometry of geometric rank." Algebra & Number Theory 16, no. 5 (August 16, 2022): 1141–60. http://dx.doi.org/10.2140/ant.2022.16.1141.
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Berger, Melvyn S. "Book Review: Modern geometry (Sovremennaya geometriya)." Bulletin of the American Mathematical Society 13, no. 1 (July 1, 1985): 62–66. http://dx.doi.org/10.1090/s0273-0979-1985-15366-2.
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Tyurin, N. A. "Algebraic Lagrangian geometry: three geometric observations." Izvestiya: Mathematics 69, no. 1 (February 28, 2005): 177–90. http://dx.doi.org/10.1070/im2005v069n01abeh000527.
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Bhatia, Rajendra, and John Holbrook. "Riemannian geometry and matrix geometric means." Linear Algebra and its Applications 413, no. 2-3 (March 2006): 594–618. http://dx.doi.org/10.1016/j.laa.2005.08.025.
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Ehm, Werner, and Jiří Wackermann. "Geometric–optical illusions and Riemannian geometry." Journal of Mathematical Psychology 71 (April 2016): 28–38. http://dx.doi.org/10.1016/j.jmp.2016.01.005.
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Leok, Melvin, and Jun Zhang. "Connecting Information Geometry and Geometric Mechanics." Entropy 19, no. 10 (September 27, 2017): 518. http://dx.doi.org/10.3390/e19100518.
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Yong-ping, Zhang, and Xie He-ping. "Fractal geometry derived from geometric inversion." Applied Mathematics and Mechanics 11, no. 11 (November 1990): 1075–79. http://dx.doi.org/10.1007/bf02015691.
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Dinh, Trung Hoa, Sima Ahsani, and Tin-Yau Tam. "Geometry and inequalities of geometric mean." Czechoslovak Mathematical Journal 66, no. 3 (September 2016): 777–92. http://dx.doi.org/10.1007/s10587-016-0292-8.
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Goto, Shin-itiro. "Affine geometric description of thermodynamics." Journal of Mathematical Physics 64, no. 1 (January 1, 2023): 013301. http://dx.doi.org/10.1063/5.0124768.
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Thermodynamics provides a unified perspective of the thermodynamic properties of various substances. To formulate thermodynamics in the language of sophisticated mathematics, thermodynamics is described by a variety of differential geometries, including contact and symplectic geometries. Meanwhile, affine geometry is a branch of differential geometry and is compatible with information geometry, where information geometry is known to be compatible with thermodynamics. By combining above, it is expected that thermodynamics is compatible with affine geometry and is expected that several affine geometric tools can be introduced in the analysis of thermodynamic systems. In this paper, affine geometric descriptions of equilibrium and nonequilibrium thermodynamics are proposed. For equilibrium systems, it is shown that several thermodynamic quantities can be identified with geometric objects in affine geometry and that several geometric objects can be introduced in thermodynamics. Examples of these include the following: specific heat is identified with the affine fundamental form and a flat connection is introduced in thermodynamic phase space. For nonequilibrium systems, two classes of relaxation processes are shown to be described in the language of an extension of affine geometry. Finally, this affine geometric description of thermodynamics for equilibrium and nonequilibrium systems is compared with a contact geometric description.
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Wong, Wing-Kwong, Sheng-Kai Yin, and Chang-Zhe Yang. "Drawing dynamic geometry figures online with natural language for junior high school geometry." International Review of Research in Open and Distributed Learning 13, no. 5 (November 15, 2012): 126. http://dx.doi.org/10.19173/irrodl.v13i5.1217.
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<p>This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the help of the knowledge base engine InfoMap, geometric concepts are extracted from an input text. The concepts are then used to output a multistep JavaSketchpad script, which constructs the dynamic geometry figure on a web page. Finally, the system outputs the script as an HTML document that can be visualized and read with an internet browser. Furthermore, a preliminary evaluation of the tool showed that it produced correct dynamic geometric figures for over 90% of problems from textbooks. With such high accuracy, the system produced by this study can support distance learning for geometry students as well as distance learning in producing geometry content for instructors.<br /><br /></p>
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Burger, William F. "Geometry." Arithmetic Teacher 32, no. 6 (February 1985): 52–56. http://dx.doi.org/10.5951/at.32.6.0052.
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The elementary school mathemalics curriculum contains no substitute for the study of informal concepts in geometry. in geometry, children organize and structure their spatial experiences. Also, geometry provides a vehicle for developing mathematical reasoning abilities about visual concepts, for example, through the study of planar shapes. In this article, I shall focus on how reasoning can be developed through the study of two-dimensional shapes, their properties, and the relationships among them. Additional topics, such as tessellations with shapes, motions and symmetry, congruence, similarity, geometric constructions, and measurement, are also highly useful in developing reasoning in geometry. The Bibliography includes many materials that teachers have recommended on these topics.
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NEDOMOVÁ, Š., and J. BUCHAR. "Goose eggshell geometry." Research in Agricultural Engineering 60, No. 3 (September 12, 2014): 100–106. http://dx.doi.org/10.17221/80/2012-rae.
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The paper presents a new approach of the eggshell geometry determination using and analysing the egg digital image and edge detection techniques. The detected points on the eggshell contour were fitted by the Fourier series. The obtained equations describing an egg profile were used to calculate the egg volume, surface area, and radius of curvature with much higher degree of precision in comparison with previously published approaches. The paper shows and quantifies the limitations of the common and frequent procedures.
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Tyurin, A. N. "Special Lagrangian geometry as slightly deformed algebraic geometry (geometric quantization and mirror symmetry)." Izvestiya: Mathematics 64, no. 2 (April 30, 2000): 363–437. http://dx.doi.org/10.1070/im2000v064n02abeh000287.
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Kock, Anders. "Differential Calculus and Nilpotent Real Numbers." Bulletin of Symbolic Logic 9, no. 2 (June 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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YOUSSEF, NABIL L., and A. M. SID-AHMED. "EXTENDED ABSOLUTE PARALLELISM GEOMETRY." International Journal of Geometric Methods in Modern Physics 05, no. 07 (November 2008): 1109–35. http://dx.doi.org/10.1142/s0219887808003235.
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In this paper, we study Absolute Parallelism (AP-) geometry on the tangent bundle TM of a manifold M. Accordingly, all geometric objects defined in this geometry are not only functions of the positional argument x, but also depend on the directional argument y. Moreover, many new geometric objects, which have no counterpart in the classical AP-geometry, emerge in this different framework. We refer to such a geometry as an Extended Absolute Parallelism (EAP-) geometry. The building blocks of the EAP-geometry are a nonlinear connection (assumed given a priori) and 2n linearly independent vector fields (of special form) defined globally on TM defining the parallelization. Four different d-connections are used to explore the properties of this geometry. Simple and compact formulae for the curvature tensors and the W-tensors of the four defined d-connections are obtained, expressed in terms of the torsion and the contortion tensors of the EAP-space. Further conditions are imposed on the canonical d-connection assuming that it is of Cartan type (resp. Berwald type). Important consequences of these assumptions are investigated. Finally, a special form of the canonical d-connection is studied under which the classical AP-geometry is recovered naturally from the EAP-geometry. Physical aspects of some of the geometric objects investigated are pointed out and possible physical implications of the EAP-space are discussed, including an outline of a generalized field theory on the tangent bundle TM of M.
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Crompton, Helen, and Sarah Ferguson. "An analysis of the essential understandings in elementary geometry and a comparison to the common core standards with teaching implications." European Journal of Science and Mathematics Education 12, no. 2 (April 1, 2024): 258–75. http://dx.doi.org/10.30935/scimath/14361.
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Geometry and spatial reasoning form the foundations of learning in mathematics. However, geometry is a subject often ignored by curriculum writers and teachers until high school, leading to students lacking in critical skills in geometric reasoning. As the United States moves into a new curriculum epoch, heralding the commencement of the national common core standards (CCS), one could question if CCS in geometry align with the essential understandings children need to be successful geometric thinkers. This paper begins with an examination of the essential understandings of geometric reasoning leading to an interpretation and critique of the elementary geometry CCS. Finally, the instructional implications are discussed, considering the common core progression through what we know about how children learn geometry.
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Sholihah, Silfi Zainatu, and Ekasatya Aldila Afriansyah. "Analisis Kesulitan Siswa dalam Proses Pemecahan Masalah Geometri Berdasarkan Tahapan Berpikir Van Hiele." Mosharafa: Jurnal Pendidikan Matematika 6, no. 2 (August 24, 2018): 287–98. http://dx.doi.org/10.31980/mosharafa.v6i2.317.
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AbstrakMatematika memiliki peranan penting dalam kehidupan. Namun, dalam praktik pembelajarannya sebagian siswa masih menganggap matematika sebagai mata pelajaran yang sulit. Bukti-bukti di lapangan menunjukkan bahwa hasil belajar geometri masih rendah. Kesulitan pada materi geometri dapat berdampak pada kesulitan-kesulitan bagian lain dalam materi geometri itu sendiri, karena banyak pokok bahasan dalam geometri yang saling berhubungan. Penelitian ini bertujuan untuk mengetahui faktor penyebab kesulitan siswa dalam proses pemecahan masalah geometri berdasarkan tahapan berpikir Van Hiele serta untuk melihat ketercapaian siswa dalam pemahaman geometri berdasarkan tahapan berpikir geometri Van Hiele. Metode penelitian yang digunakan adalah metode penelitian kualitatif dengan jenis penelitian studi kasus. Subjek penelitian yang diambil sebanyak 6 siswa dari kelas VII C SMP Negeri 6 Garut. Hasil penelitian menunjukkan bahwa ketercapaian siswa pada proses pemecahan masalah geometri berdasarkan tahapan berpikir Van Hiele paling banyak adalah pada tahap 0 (visualisasi). Hal ini ditunjukkan dengan tingginya persentase pencapaian siswa pada tahap visualisasi yaitu sebanyak 96,87 %. Ketercapaian tahapan berpikir Van Hiele yang paling baik dicapai sebesar 3,13% pada tahap 1 (Analisis). Untuk tahap 2 (deduksi informal) dan tahap 3 (deduksi) belum ada siswa yang mampu mencapai tahapan tersebut. Faktor yang menjadi penyebab kesulitan siswa dalam materi segiempat disebabkan karena beberapa hal, yaitu pemahaman mengenai konsep dan sifat-sifat segiempat yang kurang, pemahaman sebelumnya mengenai materi bangun datar segiempat yang masih kurang kuat, kurangnya keterampilan menggunakan ide-ide geometri dalam memecahkan masalah matematika yang berkaitan dengan bangun segiempat, serta kondisi kelas yang kurang kondusif untuk belajar.Kata Kunci: Kesulitan siswa pada geometri, tahapan berpikir Van Hiele, Kualitatif, Studi Kasus.AbstractMathematics has an important role in life. However, in the practice of learning some students still regard mathematics as a difficult subject. The evidence in the field shows that the geometry learning result is still low. Difficulties in geometrical matter can affect the difficulties of other parts of the material itself, since many of the subjects in the geometry are interconnected. This study aims to determine the factors causing student difficulties in the process of solving geometry problems based on the stages of thinking Van Hiele and to see students' achievement in understanding geometry based on the stages of thinking geometry Van Hiele. The research method used is qualitative research method with case study research type. Research subjects taken as many as 6 students from class VII C SMP Negeri 6 Garut. The results showed that students' achievement in the process of solving geometry problems based on the stage of thinking Van Hiele at most is at stage 0 (visualization). This is indicated by the high percentage of student achievement in the visualization stage that is as much as 96.87%. The achievement of the best stage of Van Hiele thinking was achieved at 3.13% in stage 1 (Analysis). For stage 2 (informal deduction) and stage 3 (deduction) no students have been able to reach that stage. Factors that cause student difficulties in rectangular material caused by several things, namely the understanding of the concept and the characteristics of the rectangle is lacking, previous understanding of the material wake rectangular flat that is still less strong, the lack of skills to use geometric ideas in solving math problems Relating to wake up quadrilateral, as well as class conditions that are less conducive to learning.Keyword: Student difficulties on geometry, Van Hiele thinking stages, Qualitative, Case Studies.
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Sabirova, Dildora, Mirzayor Inoyatov, Kamola Aripova, and Dildora Alimova. "Algorithms and 3D visualization tools to bring geometric data to life, facilitating immersive experiences and interactive storytelling." E3S Web of Conferences 548 (2024): 03011. http://dx.doi.org/10.1051/e3sconf/202454803011.
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The fusion of measurement geometry and computer graphics has ushered in a realm where geometric principles intersect with visual representation, creating a dynamic landscape of spatial analysis, visualization, and digital creativity. This article explores the synergies between measurement geometry and computer graphics, delving into the essence of geometric data, rendering techniques, 3D modeling, and virtual reality applications in a digitized world. Within the realm of measurement geometry, the precision of spatial relationships, dimensional analysis, and geometric computations forms the foundation for accurate measurements and analysis across diverse domains. On the other hand, computer graphics technologies harness geometric transformations, rendering algorithms, and 3D visualization tools to bring geometric data to life, facilitating immersive experiences and interactive storytelling. The abstract navigates through the realms of polygonal modeling, computational geometry, virtual reality, and spatial mapping, unveiling the intricate ways in which geometric data shapes visual content, simulations, and augmented reality applications. By exploring the integration of geometric algorithms, visualization techniques, and geometric precision, this research bridges the gap between theoretical geometry and practical visual representation in the digital domain.
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Wahyudi, Erwin Eko, Janoe Hendarto, Nur Rokhman, and Andika Rahim Darusalam. "Konstruksi Pola Fraktal Berdasarkan Bentuk Dasar Persegi Menggunakan Transformasi Affine." Jurnal Ilmiah ILKOMINFO - Ilmu Komputer & Informatika 6, no. 1 (January 31, 2023): 87–97. http://dx.doi.org/10.47324/ilkominfo.v6i1.159.
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Abstrak: Geometri fraktal, juga dikenal sebagai "geometri alam", adalah jenis geometri yang mempelajari geometri tidak beraturan. Karakteristik utama dari geometri fraktal adalah self-similarity, yaitu bagian lain dari fraktal memiliki bentuk yang serupa pada skala yang berbeda. Penelitian ini bertujuan untuk membangun pola fraktal berdasarkan bentuk dasar persegi dan menggunakan dua jenis transformasi affine, yaitu dilatasi dan translasi. Parameter yang dapat diubah untuk transformasi adalah skala. Implementasi pembuatan program dilakukan dengan menggunakan bahasa pemrograman Python. Dengan membandingkan hasil dari enam iterasi untuk skala 0,5 dan 0,45, diperoleh perbedaan secara visual baru terlihat jelas dari iterasi 3.Kata kunci: geometri fraktal, transformasi, persegiAbstract: Fractal geometry, also known as "natural geometry", is a type of geometry that studies irregular geometries. The main characteristic of fractal geometry is self-similarity, i.e. other parts of the fractal have a similar shape at different scales. This study aims to build a fractal pattern based on a basic shape of a square and use two types of affine transformations, which are dilation and translation. The parameter that can vary for the transformation is the scale. The implementation of making the program is carried out using the Python programming language. By comparing the results of the six iterations for a scale of 0.5 and 0.45, the visual differences are only clearly visible from iteration 3.Keywords: fractal geometry, transformation, square
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Freidel, Laurent, and Jonathan Ziprick. "Spinning geometry = Twisted geometry." Classical and Quantum Gravity 31, no. 4 (January 22, 2014): 045007. http://dx.doi.org/10.1088/0264-9381/31/4/045007.
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Jupri, Al, and Ernawulan Syaodih. "BETWEEN FORMAL AND INFORMAL THINKING: THE USE OF ALGEBRA FOR SOLVING GEOMETRY PROBLEMS FROM THE PERSPECTIVE OF VAN HIELE THEORY." Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam 21, no. 2 (October 25, 2016): 108–13. http://dx.doi.org/10.18269/jpmipa.v21i2.44254.
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This study investigated primary education master program students’ problem solving strategies and their for-mal and informal thinking ability when dealing with geometry problems that require the use of algebra in its solution processes. In order to do so, an explorative study through individual written test, observation, and field notes, involving 47 primary education master program students was carried out. The perspective of Van Hiele theory on the development of geometric thought was used to interpret student formal and informal thinking strategy when dealing with geometry problems. The results showed that more than half of the stu-dents used informal rather than formal algebraic strategies in solving geometry problems; when students used algebraic strategies, their work were imperfect as they still made mistakes in applying the strategies. In the light of Van Hiele theory, it can be concluded that students’ level of thinking are still in between formal and informal thinking when dealing with geometry problems.ABSTRAKPenelitian ini menyelidiki strategi pemecahan masalah mahasiswa program magister pendidikan dasar serta ke-mampuan berpikir formal dan informal mereka ketika menyelesaikan soal geometri yang memerlukan peng-gunaan aljabar dalam proses penyelesaiannya. Untuk mencapai tujuan ini, studi eksploratif melalui tes indi-vidu tertulis, observasi dan catatan lapangan dilakukan dengan melibatkan 47 mahasiswa program magister pendidikan dasar. Teori Van Hiele digunakan untuk menginterpretasi kemampuan berpikir formal dan infor-mal mahasiswa dalam menyelesaikan soal-soal geometri. Hasil penelitian menunjukkan bahwa lebih dari sepa-ruh mahasiswa menggunakan strategi-strategi informal ketimbang strategi-strategi aljabar formal dalam proses penyelesaian soal-soal geometri; ketika mahasiswa menggunakan strategi-strategi aljabar, proses penyelesaian yang mereka lakukan tidak sempurna dan masih melakukan kekeliruan-kekeliruan dalam menerapkan strategi tersebut. Berdasarkan tinjauan teori Van Hiele, dapat disimpulkan bahwa kemampuan berpikir mahasiswa ma-sih berada pada kemampuan antara formal dan informal ketika menyelesaikan soal-soal geometri.How to cite: Jupri, A., Syaodih, E. (2016). Between Formal and Informal Thinking: The Use of Algebra for Solving Geometry Problems from the Perspective of Van Hiele Theory, Jurnal Pengajaran MIPA, 21(2), 108-113.
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Mahmudati, Rina, and Ragil Tri Indrawati. "Penerapan Rainbow Geometry dalam Pembentukan Konsep Keruangan Sejak Usia Dini." Jurnal Penelitian dan Pengabdian Kepada Masyarakat UNSIQ 6, no. 1 (January 30, 2019): 16–20. http://dx.doi.org/10.32699/ppkm.v6i1.494.
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Mis-konsep dalam pemahaman geometri terjadi pada setiap jenjang pendidikan. Oleh karena itu, pemahaman konsep harus ditanamkan sejak usia dini. Tujuan dari kegiatan ini untuk meningkatkan pemahaman konsep geometri dengan menggunakan rainbow geometry. Metode pelaksanaan dilakukan dengan cara menciptakan media kreatif sebagai alat pembelajaran berupa rainbow geometry. Kegiatan ini dilaksanakan di RA Hj Maryam, dengan memberi pelatihan kepada guru dan menerapkan media tersebut kepada siswa. Hasil dari kegiatan ini terlihat bahwa terjadi peningkatan terhadap pemahaman geometri secara signifikan pada siswa RA Hj Maryam yaitu sebesar 49 %. Hal ini membuktikan bahwa media yang dikembangkan berupa rainbow geometry memiliki dampak positif terhadap pemahaman keruangan siswa.