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Academic literature on the topic '3 Pythagoras'

Author: Grafiati

Published: 4 June 2025

Last updated: 23 June 2025

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Journal articles on the topic "3 Pythagoras"

1

Nurafni, Nurafni, Asih Miatun, and Hikmatul Khusna. "PROFIL PEMAHAMAN KONSEP TEOREMA PYTHAGORAS SISWA BERDASARKAN PERBEDAAN GAYA KOGNITIF FIELD INDEPENDENT DAN FIELD." KALAMATIKA Jurnal Pendidikan Matematika 3, no. 2 (2018): 175–92. http://dx.doi.org/10.22236/kalamatika.vol3no2.2018pp175-192.

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This research is a descriptive qualitative approach which aims to describe profile of understanding of pythagoras theorem concept of students based on the difference of field independent and dependent cognitive style. The subjects of this study are 9th grade students of junior secondary school. Subject determination is done using GEFT instrument and mathematics teacher’s consultation, then continued by giving concept comprehension test on Pythagorean theorem material and interview. Checking the validity of data is done by time’s triangulation. The results showed that student: 1) states the meaning of Pythagoras's theorem given in his own language by noting Pythagorean theorem’s definition; 2) when using the concepts of Pythagoras theorem, students use triangle images as representations to facilitate an interpretation of given sides position. Then the students find the unknown values and use Pythagoras theorem to solve the problem; 3) using the necessary condition or sufficient condition of a concept to determine the area of a triangle using Pythagorean theorem by finding a side. While, the results for field independent cognitive style are student: 1) expresses the meaning of Pythagoras theorem by using their own language and mentioning the symbols; 2) using the concepts of Pythagorean theorem to solve the problem given by using multiplication operations to determine one of unknown sides. Then, student use pythagoras theorem to find the answer of the given problem; 3) using the necessary conditions or sufficient terms a concept of Pythagoras theorem by stating that it must be known two sides or not.

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Zhmud, Leonid. "What is Pythagorean in the Pseudo-Pythagorean Literature?" Philologus 163, no. 1 (2019): 72–94. http://dx.doi.org/10.1515/phil-2018-0003.

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AbstractThis paper discusses continuity between ancient Pythagoreanism and the pseudo-Pythagorean writings, which began to appear after the end of the Pythagorean school ca. 350 BC. Relying on a combination of temporal, formal and substantial criteria, I divide Pseudopythagorica into three categories: 1) early Hellenistic writings (late fourth – late second centuries BC) ascribed to Pythagoras and his family members; 2) philosophical treatises written mostly, yet not exclusively, in pseudo-Doric from the turn of the first century BC under the names of real or fictional Pythagoreans; 3) writings attributed to Pythagoras and his relatives that continued to appear in the late Hellenistic and Imperial periods. I will argue that all three categories of pseudepigrapha contain astonishingly little that is authentically Pythagorean.

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3

Vinoo, Cameron. "Historical Resolution of the Mathematical Structure of Modern Trigonometry at 1:3 Pythagoras (360/19) (Revision of Isaac Newton's Fallacy of Trigonometry.)." Journal of Progressive Research in Mathematics 5, no. 4 (2015): 624–27. https://doi.org/10.5281/zenodo.3979587.

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This paper is geared towards the students and admirers of Sir Isaac Newton, to assert by this paper, almost after 400 years; to remind him and them; that it is mathematically imprecise to calculate a curve or area of a circle, without the parity of numbers equations with correct trigonometry and equations of numbers, aligned to the great theorem of Pythagoras, specially Pythagoras 1:3, which is the keel of the universe of mathematics at subtended angle 360/19 degrees. The inverse curvature of the universe of mathematics ( Universe itself) is precisely related to Pythagoras 1:1; 1:3 ; 1:5 as shown in this paper using the correct value of 360/19 degrees at Pythagoras 1:3; is easily mathematically plotted and as herein published, and Newton’s attempt to describe curvatures by linear numbers equation is at best approximate. The horizons and the curvature of the universe are precise based on non-linear equations, not approximate as per the rumination of Newton, as in the proof in the previous published paper (Divestiture of mathematics), 360/19 is the correct value in degrees at 1:3 Pythagoras which should have been suspected by the great master of mathematics Newton. The world of mathematics must come to terms with numbers and trigonometric diversions of Pythagoras. The intent is not to challenge the methods of Sir Isaac Newton, but to assert that on what mathematics he based his apparent logical approximations, that basis of mathematics is flawed; given that degrees as defined in the mathematics are precisely concordant with numbers( (360/2)/3=60 precise), representing the constant factor 6. The author maintains in this paper and the previously published paper the following, and provides ample mathematical proof of the keel value of Pythagoras 1:3. 1.1 Pythagoras=360/8=45 (90/2) degrees subtended 1:2 Pythagoras=360/16=22.5 (90/4) degrees subtended 1:3 Pythagoras=360/19= 18.94736842105(90/4.75) degrees, subtended 1.4 Pythagoras=360/24=15 degrees (90/6), subtended 1:5 Pythagoras=360/30= 12 (90/7.5) degrees, subtended (90/7.5) 1:6 Pythagoras=360/38 degrees subtended For Pythagoras1:1;1:3;1:5, the arithmetic is simple and further proven under methods, as from above a factor of 90 degrees (4.75-2) = (7.5-4.75). Journal of Progressive Research in Mathematics(JPRM) ISSN: 2395-0218 Volume 5, Issue 4 available at www.scitecresearch.com/journals/index.php/jprm 625 The fundamental precise mathematical parity of the above Pythagorean precision is defined by the mathematical premise not understood by the approximation of Isaac Newton’s understanding of mathematics that degrees and numbers as understood currently .The revision is as follows 𝐴 𝐵 𝐴 𝐶 = (𝐴 − 𝐵) (𝐴 − 𝐶) 𝟑. 𝟕𝟓 𝑘: @1: 3 𝑃𝑦𝑡𝑕𝑎𝑔𝑜𝑟𝑎𝑠 (22.5 degrees is the subtended angle at Pythagoras 1:2 :) It is a precise mathematical parity of numbers, that 1 + 2 + 3 3 + 4 + 5 = 0.5, 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑛𝑔 𝑡𝑕𝑒 𝑏𝑎𝑠𝑖𝑐 𝑝𝑎𝑟𝑖𝑡𝑦 𝑜𝑓 1: 3 𝑎𝑠 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 By a simple arithmetic factor of 360 degrees the subtended Pythagoras 1:1; 1:3; 1:5(360/8; 360/19; 360/30): see resolution below in the methods section (3.75). Degrees must be concordant with numbers without exception. 19-8=11 30-19=11 30 &lowast; 19 19 &lowast; 8 = 𝟑. 𝟕�

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Elfariana, Rizma, Nyimas Aisyah, and Ely Susanti. "Development of Interactive Electronic Student Worksheets on Pythagorean Theorem Material to Support Students' Mathematical Reasoning in Junior High Schools." Kreano, Jurnal Matematika Kreatif-Inovatif 15, no. 1 (2024): 306–18. https://doi.org/10.15294/kvzmpe80.

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This study aims to develop Electronic Learner Worksheets (LKPD) or interactive E-LKPD on Pythagorean theorem material that meets valid, practical, and effective criteria. This development research was conducted at SMP Negeri 1 Parittiga with the research subjects of class VIII B students totaling 22 people. This research uses the RnD method with the Tessmer model which consists of two stages, namely preliminary studies and formative evaluation. This research is since there are still many secondary school students who have low mathematical reasoning skills on geometry topics, including the Pythagorean theorem. The results of this study indicate that the development of interactive E-LKPD on Pythagorean theorem material is categorized as valid and practical. The average validity value obtained was 89.46% with a very valid category. The characteristics of valid interactive E-LKPD on Pythagorean theorem material are (1) Presenting contextual problems that are close to the lives of students; (2) E-LKPD reflects the principles and characteristics of interactive E-LKPD; (3) E-LKPD guides students in constructing their own knowledge. Interactive E-LKPD on Pythagorean theorem exercise material is reviewed in terms of ease and benefits of use, time efficiency, and presentation attractiveness. The average practicality score obtained was 83.748% with a very practical category. The characteristics of the practicality of interactive E-LKPD are (1) Interactive E-LKPD is easy to use because the instructions provided are complete, clear, and the language is easy to understand; (2) E-LKPD processing time is efficient; (3) Commands and questions on E-LKPD are clear and easy to understand; (4) The appearance and color combination on E-LKPD is attractive; (5) Students are helped in understanding the concepts and material of the pythagorean theorem. Based on the results of interviews with teachers and students, interactive E-LKPD on Pythagorean theorem material facilitates students in learning and arouses students' interest in learning. Interactive E-LKPD on pythagorean theorem material can facilitate teachers and parents in conducting student learning activities anywhere and anytime. This research can be a meaningful experience and learning resource for students in learning geometry, especially about the Pythagorean theorem. Penelitian ini bertujuan untuk mengembangkan Elektronik Lembar Kerja Peserta Didik (LKPD) atau E-LKPD interaktif pada materi teorema Pythagoras yang memenuhi kriteria valid, praktis dan efektif. Penelitian pengembangan ini dilaksanakan di SMP Negeri 1 Parittiga dengan subjek penelitian siswa kelas VIII B yang berjumlah 22 orang. Penelitian ini menggunakan metode RnD dengan model Tessmer yang terdiri dari dua tahap, yaitu studi pendahuluan dan evaluasi formatif. Penelitian ini dilandasi karena masih banyak siswa sekolah menengah yang memiliki kemampuan penalaran matematis yang rendah pada topik geometri, termasuk teorema Pythagoras. Hasil penelitian ini menunjukkan bahwa pengembangan E-LKPD interaktif pada materi teorema Pythagoras dikategorikan valid dan praktis. Nilai rata-rata kevalidan yang diperoleh sebesar 89,46% dengan kategori sangat valid. Karakteristik E-LKPD interaktif yang valid pada materi teorema Pythagoras adalah (1) Menyajikan masalah kontekstual yang dekat dengan kehidupan peserta didik; (2) E-LKPD mencerminkan prinsip-prinsip dan karakteristik E-LKPD interaktif; (3) E-LKPD menuntun peserta didik dalam mengkonstruksi pengetahuannya sendiri. E-LKPD interaktif pada materi latihan soal teorema Pythagoras ditinjau dari segi kemudahan dan manfaat penggunaan, efisiensi waktu, dan kemenarikan penyajian. Rata-rata nilai kepraktisan yang diperoleh sebesar 83,748% dengan kategori sangat praktis. Karakteristik kepraktisan E-LKPD interaktif yaitu (1) E-LKPD interaktif mudah digunakan karena petunjuk yang diberikan lengkap, jelas, dan bahasanya mudah dipahami; (2) Waktu pengerjaan E-LKPD efisien; (3) Perintah dan pertanyaan pada E-LKPD jelas dan mudah dimengerti; (4) Tampilan dan perpaduan warna pada E-LKPD menarik; (5) Peserta didik terbantu dalam memahami konsep dan materi teorema pythagoras. Berdasarkan hasil wawancara dengan guru dan peserta didik, E-LKPD interaktif pada materi teorema Pythagoras memudahkan peserta didik dalam belajar dan membangkitkan minat belajar peserta didik. E-LKPD interaktif pada materi teorema pythagoras dapat memudahkan guru dan orang tua dalam melakukan kegiatan belajar siswa dimanapun dan kapanpun. Penelitian ini dapat menjadi pengalaman dan sumber belajar yang bermakna bagi peserta didik dalam mempelajari geometri khususnya mengenai teorema Pythagoras.

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Farman, Farman, and Chairuddin Chairuddin. "PENGEMBANGAN MEDIA E-LEARNING BERBASIS EDMODO PADA MATERI TEOREMA PYTHAGORAS." AKSIOMA: Jurnal Program Studi Pendidikan Matematika 9, no. 4 (2020): 872. http://dx.doi.org/10.24127/ajpm.v9i4.3114.

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Penelitian ini bertujuan untuk menyusun dan memperoleh media e-learning berbasis edmodo pada materi pythagoras yang valid, praktis dan efektif bagi peserta didik kelas VIII SMP-TQ Muadz Bin Jabal Kendari. Pembelajaran matematika berbasis e-learning menggunakan edmodo dipilih sebagai media alternatif dalam meningkatkan minat dan hasil belajar pada materi pythagoras. Pengembangan e-learning ini dikembangkan dengan model ADDIE yang terdiri atas beberapa langkah, yaitu: (1) analysis (2) design (3) development, (4) implementation dan (5) evaluation. Subyek uji coba dalam penelitian pengembangan ini adalah peserta didik Kelas VIII SMP Mu’adz Bin Jabal Kendari pada Tahun Ajaran 2019/2020 yang berjumlah 31 peserta didik.Uji kevalidan media pembelajaran digunakan lembar validasi dan untuk menguji keefektifan media pembelajaran digunakan angket respon peserta didik. Sedangkan uji keefektifan media pembelajaran digunakan tes hasil belajar materi teorema pythagoras. Berdasarkan penilaian oleh ahli dan pelaksanaan uji coba, diperoleh hasil bahwa media e-learning berbasis edmodo materi teorema Pythagoras memenuhi kriteria valid, praktis dan efektif. E-learning berbasis edmodo dapat dimanfaatkan untuk meningkatkan minat dan memfasilitasi pembelajaran interaktif yang mendukung pemahaman peserta didik SMP Kelas VIII pada materi Pythagoras. Abstract This study aims to compile and obtain edmodo-based e-learning media on pythagorean material which is valid, practical, and effective for grade VIII students of SMP-TQ Muadz Bin Jabal Kendari. E-learning based mathematics learning using edmodo was chosen as an alternative media in increasing interest and learning outcomes of Pythagorean material. This e-learning development is developed with the ADDIE model, which consists of several steps, namely: (1) analysis, (2) design, (3) development, (4) implementation, and (5) evaluation. The subjects in this development research were 31 students of grade VIII SMP Mu'adz Bin Jabal Kendari in the 2019/2020 academic year. The learning media's validity test used a validation sheet, and to test the effectiveness used student response questionnaire. At the same time, the test of the learning media's effectiveness used the learning outcomes test of the Pythagorean theorem. The experts' assessment and the implementation of trials found that the mathematics learning media of the Edmodo-based Pythagorean theorem met the valid, practical, and effective criteria. Edmodo-based e-learning can be used to increase interest and facilitate interactive learning that supports the understanding of grade VIII junior high school students on the pythagorean theorem material.

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Konovalova, N. R. "The philosophy of music of Pythagoras." Mathematics in Modern Technical University 2021, no. 1 (2021): 47–59. http://dx.doi.org/10.20535/mmtu-2021.1-047.

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The article reproduces the image of the great thinker Pythagoras - one of the most popular scientists and the most mysterious personality, the philosopher. Pythagoras created the brightest and most modern "religion": he nurtured in humanity a belief in the power of reason, the belief that the key to the mysteries of the worldview is mathematics. Music for Pythagoras became not only a means of inspiration but also a subject of scientific research, it was in music that Pythagoras found direct proof of his statement: "Everything is a number." 2,500 years ago, Pythagoras guided people on the path of triumph of the Mind. The whole world, Pythagoras argued, is a harmonious number. And these numbers form the ratio as well as the intervals between different degrees of scale. From time immemorial, numbers seemed to people to be something mysterious. Any object could be seen. The number cannot be touched and, at the same time, numbers really exist, because all objects can be counted... Pythagoras and his followers believed that everything in nature is measured, everything is subject to numbers, and to know the world means to know the numbers that control them. If before Pythagoras, music was understood magically and understood as the embodiment of the forces of nature, used mainly in ritual and religious rites, it is Pythagoras who became the progenitor of the mathematization of the musical phenomenon. The main grain of Pythagorean world harmony is the idea of harmony in a mathematically ordered whole. Pythagoras came to this idea when he discovered that the basic harmonic intervals: octave, pure fifth and pure fourth - occur when the lengths of the strings are 2:1, 3:2 and 4:3. Drawing analogies between the orderliness of the material world and the orderly mathematical relationship in music, he suggested that each planet in its rotation around the Earth emits a tone of a certain height, passing through the clean upper air - the ether. All the celestial sounds of all the planets, merging, form what is called "harmony of the spheres" or "music of the spheres." The laws of music and mathematics are the basic essence of natural existence, according to which the universe is not only built, but also moves and develops.The teachings of Pythagoras showed the unity of everything in the set, and the main purpose of man was expressed in the fact that through self-development man must achieve a connection with the cosmos.

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Vinoo, Cameron. "-3 As the created root of all mathematics by numbers, Prime number 5 as the created template of all Prime number and pseudo-prime numbers(Mathematical Proof)." Journal of Progressive Research in Mathematics 14, no. 1 (2018): 2318–23. https://doi.org/10.5281/zenodo.3981236.

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The author has published several papers with JPRM which were unorthodox, but led to the acceptance of a major book on created mathematics , this small paper validates JPRM, and is a challenge to the entire current numbers theory if understood correctly .This small paper is the basic proof of the base of numbers in the created mathematics of the cone of Pythagoras 1:3 as Published at JPRM  , with the spiral arrangement of the Prime numbers and their multiples by the template of prime number 5, as the basis as shown separately in an upcoming book on created mathematics. The table entered in this paper is the precise cardinal proof of numbers, to validate the premise of created mathematics at Pythagoras 1:3 and to refute current numbers theory.

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Meika, Ika, Risma Berliana, and Nenden Suciyati Sartika. "DESAIN DIDAKTIS PEMAHAMAN KONSEP SISWA SEKOLAH MENENGAH PERTAMA (SMP) PADA MATERI TEOREMA PYTHAGORAS." Teorema: Teori dan Riset Matematika 7, no. 2 (2022): 411. http://dx.doi.org/10.25157/teorema.v7i2.8332.

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Penelitian ini dilatar belakangi oleh pentingnya kemampuan pemahaman konsep siswa terhadap materi teorema pythagoras yang bertujuan untuk mengidentifikasi learning obstacle siswa pada materi teorema pythagoras dengan membuat desain didaktis (bahan ajar) berupa modul teorema pythagoras. Penelitian dilaksanakan dengan menggunakan metode Didactical Design Research (DDR). Metode ini dilakukan dengan tiga tahap, yaitu analisis situasi didaktis sebelum pembelajaran, analisis metapedadidaktik, dan analisis retrospektif. Berdasarkan hasil studi pendahuluan yang dilakukan melalui tes identifikasi learning obstacle pada materi teorema pythagoras terhadap 25 siswa kelas VIII G SMP Negeri 1 Saketi, terdapat hambatan yang dialami siswa terkait pemahaman konsep diantaranya: 1) hambatan dalam memahami konsep segitiga siku-siku; 2) hambatan dalam menerapkan teorema pythagoras, 3) hambatan dalam menentukan jenis segitiga 4) hambatan dalam memahami tripel pythagoras; dan 5) hambatan dalam menerapkan teorema pythagoras dalam kehidupan sehari-hari. Untuk mengatasi hambatan siswa pada materi teorema pythagoras diperlukan rancangan pembelajaran yang dikembangkan berdasarkan analisis learning obstacle sehingga menghasilkan desain didaktis hipotesis yang memuat berbagai aktifitas siswa dan prediksi respon siswa beserta dengan antisipasinya serta menghasilkan modul pembelajaran. Hasil penelitian menunjukkan bahwa desain didaktis yang diberikan dapat mengantisipasi kesulitan siswa terhadap kemampuan pemahaman konsep siswa pada materi teorema pythagoras, hal tersebut dapat terlihat dari hasil kerja siswa pada modul.

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Siska Nurfadilah Sri Kusumah and Uba Umbara. "Penerapan Didactical Design Research (DDR) Pada Materi Teorema Pythagoras di Kelas VIII SMP Negeri 3 Kuningan." Didactical Mathematics 7, no. 1 (2024): 58–72. https://doi.org/10.31949/dm.v7i1.12464.

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Penelitian ini adalah penelitian Didactical Design Research (DDR) dengan pendekatan kualitatif. Subjek pada penelitian ini adalah sebanyak 33 (tiga puluh tiga) orang siswa kelas VIII A SMP Negeri III. Penelitian ini bertujuan untuk: 1) mengetahui kesulitan belajar dan lintasan belajar siswa dalam proses belajar matematika pada materi teorema Pythagoras; 2) mengetahui desain didaktis yang dikembangkan guna mengatasi kesulitan belajar dalam proses belajar matematika pada materi teorema Pythagoras; 3) mengetahui respon siswa saat implementasi desain didaktis dalam proses belajar matematika pada materi teorema Pythagoras; dan 4) mengetahui gambaran desain didaktis empirik yang dihasilkan dari penerapan desain didaktis pada konsep teorema Pythagoras. Hasil dari penelitian ini menunjukan bahwa: 1) teridentifikasi tiga kategori learning obstacle yang dialami siswa yakni: hambatan ontogenik (ontogenical obstacle), hambatan epistemologis (epistemological obstacle), dan hambatan didaktis (didactical obstacle); 2) desain didaktis dirancang kedalam empat desain didaktis, dengan menerapkan pendekatan teori APOS; 3) learning obstacle dapat diatasi dengan implementasi desain didaktis; 4) desain empirik merupakan gabungan dari keempat desain yang telah melalui tahapan revisi dan berhasil diimplementasikan secara optimal

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De Campos, Rogério G. "Unwritten Doctrine of Pythagoras in Hermias of Alexandria." Peitho. Examina Antiqua 13, no. 1 (2022): 185–98. http://dx.doi.org/10.14746/pea.2022.1.9.

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In Hermias’ commentary on Phaedrus (In Platonis Phaedrum Scholia), it is possible to identify several direct references to the philosophers and pre-Socratic doctrines, including Pythagoras. We point out to three references to Pythagoras in Hermias: (1) Pythagoras is characterized as an unwritten philosopher, (2) there is a special connection with the divinities and Muses, and (3) there is a special connection with the Phaedrus dialogue, revealed by the affinity between Pythagoras and Socrates. We show how the explicit references to Pythagoras in Hermias constitute a certain method of interpreting Platonism: as a philosophy manifested in writing, but which, at the same time, values the unwritten tradition, represented especially by Pythagoras and Socrates. We also demonstrate how the references translated and examined here reveal the image of this Neoplatonic Pythagoras of Hermias, an image which is not necessarily in tune with the oldest doxography, and which permits the reevaluation of Plato’s position as a philosopher who sought to combine unwritten doctrines with his explicit activity as a writer.

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Books on the topic "3 Pythagoras"

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Paul, Dietrich. PISA, Bach, Pythagoras. Vieweg+Teubner Verlag, 2005. http://dx.doi.org/10.1007/978-3-322-95319-3.

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Schreiber, Alfred, ed. Die Leier des Pythagoras. Vieweg+Teubner, 2010. http://dx.doi.org/10.1007/978-3-8348-9352-9.

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Agarwal, Ravi P. Mathematics Before and After Pythagoras. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-74224-8.

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Schüffler, Karlheinz. Pythagoras, der Quintenwolf und das Komma. Springer Fachmedien Wiesbaden, 2017. http://dx.doi.org/10.1007/978-3-658-15186-7.

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Schüffler, Karlheinz. Pythagoras, der Quintenwolf und das Komma. Vieweg+Teubner Verlag, 2012. http://dx.doi.org/10.1007/978-3-8348-8667-5.

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Gerwig, Mario. Der Satz des Pythagoras in 365 Beweisen. Springer Berlin Heidelberg, 2021. http://dx.doi.org/10.1007/978-3-662-62886-7.

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Valtonen, Mauri, Joanna Anosova, Konstantin Kholshevnikov, Aleksandr Mylläri, Victor Orlov, and Kiyotaka Tanikawa. The Three-body Problem from Pythagoras to Hawking. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-22726-9.

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Rothe, Jennifer. Flipped Classroom im Mathematikunterricht der Sekundarstufe I am Beispiel der Satzgruppe des Pythagoras. Springer Fachmedien Wiesbaden, 2025. https://doi.org/10.1007/978-3-658-47480-5.

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McDonnell, Jane. The Pythagorean World. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-40976-4.

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Takloo-Bighash, Ramin. A Pythagorean Introduction to Number Theory. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02604-2.

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Book chapters on the topic "3 Pythagoras"

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Herrmann, Dietmar. "Pythagoras and the Pythagoreans." In Ancient Mathematics. Springer Berlin Heidelberg, 2022. http://dx.doi.org/10.1007/978-3-662-66494-0_4.

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Gorman, Peter. "The Philosophers." In Pythagoras. Routledge, 2025. https://doi.org/10.4324/9781003656852-3.

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Dudley, Underwood. "Pythagoras." In Die Macht der Zahl. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-5086-5_1.

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Habermehl, Peter. "Pythagoras." In Metzler Philosophen Lexikon. J.B. Metzler, 1995. http://dx.doi.org/10.1007/978-3-476-03642-1_231.

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Michalos, Alex C. "Pythagoras." In Encyclopedia of Quality of Life and Well-Being Research. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-17299-1_3933.

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Habermehl, Peter. "Pythagoras." In Philosophen. J.B. Metzler, 2004. http://dx.doi.org/10.1007/978-3-476-02949-2_45.

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Naylor, John. "Pythagoras’ Hammers." In Now Hear This. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89877-9_2.

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Agrò, Maurizio. "Everything Is Number. Pythagoras and the Pythagoreans." In Music and Astronomy. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-41524-1_3.

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Prokhorov, Vladimir V. "PYTHAGORAS: Multienvironment software." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60614-9_10.

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Ostermann, Alexander, and Gerhard Wanner. "Thales and Pythagoras." In Geometry by Its History. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29163-0_1.

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Conference papers on the topic "3 Pythagoras"

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Magnaghi-Delfino, Paola, Giampiero Mele, and Tullia Norando. "Il pentagono come strumento per il disegno delle fortezze." In FORTMED2020 - Defensive Architecture of the Mediterranean. Universitat Politàcnica de València, 2020. http://dx.doi.org/10.4995/fortmed2020.2020.11324.

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The pentagon as a tool for fortresses’ drawingStarting from the fifteenth century, the diagram of many fortresses has a pentagonal shape. Among the best known fortresses, in Italy we find the Fortezza da Basso of Florence, the Cittadella of Parma, the Cittadella of Turin, Castel Sant’Angelo in Rome. The aim of this article is to analyze the reasons that link form and geometry to the planning of the design and the layout of pentagonal fortresses. The pentagon is a polygon tied to the golden section and to the Fibonacci sequence and it is possible to construct it starting from the golden triangle and its gnomon. This construction of the pentagon is already found in the book De Divina Proportione by Luca Pacioli and is particularly convenient for planning pentagonal fortresses. If one wants to draw the first approximated golden triangle, one can just consider the numbers of the Fibonacci sequence, for example 5 and 8, which establish the relationship between the sides: 5 units is the length of the base and 8 units the length of the equal sides. In the second isosceles triangle, which is the gnomon of the first, the base is 8 units long and equal sides are 5 units long; half of this isosceles triangle is the Pythagorean triangle (3, 4, 5). This characteristic of the golden triangles, that was already known by the Pythagoreans and, in a certain sense, contained in the symbol of their School, allows to build a pentagon with only the use of the ruler and the set square. The distinctive trait of the construction just described makes preferable to use the pentagon in the layout of the military architectures in the fieldworks. We have verified the relationship between numbers, shape and size in the layout of Castel Sant’Angelo (1555-1559) in which the approximate pentagon was the instrument for the generation of its form.

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Reports on the topic "3 Pythagoras"

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ธรรมบุตร, ณรงค์ฤทธิ์. ซิมโฟนีแห่งสกลจักรวาล : รายงาน. จุฬาลงกรณ์มหาวิทยาลัย, 2002. https://doi.org/10.58837/chula.res.2002.52.

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ซิมโฟนีแห่งสกลจักรวาล เป็นบทเพลงซิมโฟนีสำหรับวงออร์เคสตราขนาดมาตรฐานความยาวของการบรรเลงประมาณ 25 นาที ลักษณะของบทเพลงจะเป็นโปรแกรมซิมโฟนี ที่ได้รับแรงบันดาลใจจากปรัชญากรีกของไพธากอรัส (Pythagoras) และโบเอเธียส (Boethius) ที่ได้อธิบายเปรียบเทียบว่า ระบบของระดับเสียงในดนตรีจะสอดคล้องกับสัดส่วน ระเบียบ และความกลมกลืนของดาวต่างๆ ในจักรวาล ดังนั้น ความเป็นไปของดวงดาว (เกิด-โคจร-ดับสูญ) จะทำให้เกิด “ดนตรีแห่งสกลจักรวาล” (Music of the Spheres) อันเป็นที่มาของชื่อบทเพลงนี้ ซิมโฟนีแห่งสกลจักรวาลประกอบด้วย 3 กระบวนดังต่อไปนี้ 1. มูซิกา มุนดานา (Musica Mundana) 2. มูซิกา ฮูมานา (Musica Humana) 3. มูซิกา อินสทรูเมนทาลิส (Musica Instrumentalis)

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