Academic literature on the topic 'Pythagoras and the Pythagorean school'
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Journal articles on the topic "Pythagoras and the Pythagorean school"
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Zhmud, Leonid. "What is Pythagorean in the Pseudo-Pythagorean Literature?" Philologus 163, no. 1 (May 29, 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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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 (October 31, 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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Duarte, Carlos Lisboa, Hegildo Holanda Gonçalves, and Nádia Pinheiro Nobrega. "Tudo é número: uma análise conceitual da ideia de número em Pitágoras." Revista Principia - Divulgação Científica e Tecnológica do IFPB 1, no. 33 (May 16, 2017): 99. http://dx.doi.org/10.18265/1517-03062015v1n33p99-107.
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<p>This work is an analysis of the number concept based on the thoughts of Pythagoras, well as to seek an approximation of the historical reflections of the Pythagorean School in the Greek context of Classical Antiquity. The guiding objective of the study is to analyze the theory of the integers in the Pythagorean philosophy as ultimate cause of man and matter. From Methodological procedures point of view, the research was the bibliographical type, developed from already published material constituted, primarily, of books and journal articles through which we sought a dialogue with the developed studies concerning the subject in question. Through research it was reached the following findings: First, Pythagoras considered the number as the forming principle of the universe. However, he believed that the number constitutes the agreement between an indeterminate or unlimited element and another determinant or limiting and from there had been origin all things; Second, to the Pythagoreans the structure of numbers started from the assumption that in even numbers in even numbers predominates the indeterminate element and in the odd numbers the limiting element, for this reason they had the odd numbers as perfects, because in their distribution the odd numbers always had a limiting element. In sum, both Pythagoras as the Pythagoreans had in the cult of the number the basis of both his philosophy and his way of life.</p>
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Turenko, Vitalii. "VISION OF WOMEN IN CONTEXT APPEARANCES AND FUNCTIONING OF THE PYPHAGORIAN SCHOOL." Sophia. Human and Religious Studies Bulletin 16, no. 2 (2020): 54–57. http://dx.doi.org/10.17721/sophia.2020.16.11.
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The article, based on classical ancient sources and the most modern fundamental scientific works, explores and reveals the specifics of the existence of women in the early Greek philosophical school, founded by Pythagoras. There are three key reasons that led to the full existence of women along with men in the Pythagorean tradition: socio-political, doctrinal and vital. Accordingly, such a high status of women for the Pythagoreans is due not only to certain socio-political conditions of Greater Greece, or rather even the city of Croton, but also to the fact that the founder of this school, Pythagoras, unlike other early Greek thinkers, received philosophical knowledge from a woman, the Delphic Pythia Themistoclea. The doctrinal reason has been shown to be that Pythagoras himself preached the equality of women. If he had preached the opposite of the socio-political role of women in a given geographical region, he would not only not have been accepted, but even expelled. It is substantiated that the presence of women in this philosophical tradition is not a late Hellenistic fiction, but a real fact, based on the available sources of Aristotle's disciples – Dicaearchus and Aristoxenus, which testify to a rather ramified system of attracting women to the functioning of Pythagoreanism The proposed author's dichotomy of the representatives of this philosophical school known to us: pseudo-epigraphic and agraphic. Accordingly, the agraphic ones are known to us only by mentioning in certain ancient sources, while we know about the pseudo-epigraphic ones not only the names, but also preserved works and letters that are attributed to the Pythagorean thinkers.
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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 (December 31, 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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Wares, Arsalan. "Pythagoras Meets Paper Folding." Mathematics Teacher 111, no. 5 (March 2018): 400. http://dx.doi.org/10.5951/mathteacher.111.5.0400.
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One of the most well-known theorems in mathematics, the Pythagorean theorem and its proof are a standard part of the school mathematics curriculum. The theorem is named for Pythagoras, a Greek mathematician and philosopher, born around 570 BCE. More than 400 proofs of the theorem exist, and this number continues to grow (Maor 2007). A future American president, James Garfield, generated an original proof five years before being elected; another proof is credited to twelve-year-old Einstein.
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Arifn, Muhammad Syamsul. "Misconceptions of student junior high school in Solving Pythagorean Theorem." MATHEdunesa 9, no. 2 (September 17, 2020): 461–67. http://dx.doi.org/10.26740/mathedunesa.v9n2.p461-467.
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The learning process in the classroom is said to be successful, if most students understand the concepts conveyed by the teacher. But, in the learning process, teacher found stundents has misconception. Misconceptions gotten by students, will affect students in the use of a concept between concepts in the mathematic. Identification misconception is one way to learning process get successful.
The purpose of this research was for describe the misconception and the solution of student’s misconception of class IX Junior High School 2 Sedati Sidoarjo at the solve the problem of Pythagorean Theorem. The qualitative research was used as form of this research, with the type of case study research. The data collection technique which was used were 1) Test methods, 2) interview method. The technique of data validation uses triangulation of method, by comparing test result data and interview. The results of this research can be showed as there were three types of misconceptions experienced by students that was classificational misconceptions, Correlational misconception, and Teoritical misconception; (1) students take types correlational misconception. The indicator is writing units incorrectly. Before learning about concept Pythagoras Theorem, students master about unit concept.; (2) students take types classification misconception. The indicator is students missing determine side figure two and three dimentional to Pythagoras Theorem. In this misconception, students difficult illustration skew right triangle.; (3) students take types teoritic misconceptioan. The indicator is students missing giving the reason of problem. In this misconception is about triple Pythagoras concept. Student determine triple Pythagoras with calculate not with concept giving as multiples or formulas. By knowing the description of misconceptions that occur in students, teachers take the steps of the learning process accurately so student do not misconceptions
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Lenz, Markus Alexander. "A Prophet of Divine Wisdom?—Giambattista Vico and the Construction of the Pythagorean Myth." Philological Encounters 5, no. 1 (March 9, 2020): 50–75. http://dx.doi.org/10.1163/24519197-12340069.
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Abstract In the nineteenth century, the reception of Giambattista Vico’s writings came along with nationalist interpretations of his Scienza Nuova as an ‘Italian Science’. This tendency was based upon an increased examination of the role that the philosopher Pythagoras and his Italian school of Croton played in Vico’s hierarchical conception of the ancient Greek and Italian civilizations. Writers, archaeologists and historians used the New Science as a metonymic reference work for their own nationalist concepts by updating the Pythagorean myth in accordance with relevant narratives of exclusive genealogies concerning an ancient Italian wisdom. These narratives follow tendencies in Vico’s own writings that were quoted strategically and mixed with further interpretations of the Scienza Nuova as reliable testimonial for a glorious Italian history. A theological poet characterized by deeper insight into the secrets of nature and some parts of the divine providence, Pythagoras gains his special position in Vico’s general conception of knowledge.
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Santacroce, Luigi, Ioannis Alexandros Charitos, Skender Topi, and Lucrezia Bottalico. "The Alcmaeon’s School of Croton: Philosophy and Science." Open Access Macedonian Journal of Medical Sciences 7, no. 3 (January 30, 2019): 500–503. http://dx.doi.org/10.3889/oamjms.2019.072.
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Among the first physicians and physiologists at the pre-Hippocratic medicine with contradictions and oscillating doctrines was Alcmaeon from Croton in the 6th century BC. For many, he shared as the father of scientific medicine. Unfortunately, we have only eighteen texts written for him and only five fragments of texts written by him. This saved extracts and testimonies they refer mostly to physiology, epistemology and psychology. Was born in the city of Croton (Κρότων) in Magna Graecia (southern Italy) was a reference point for the activity of physicians and philosophers over the years. Furthermore, Herodotus tells us about the excellent practice quality of the physicians, “compared to all the others known in that period”, among which Alcmaeon. But Croton is also famous as the centre of thought and activity of the philosopher Pythagoras of Samos (Πυθαγόρας ὁ Σάμιος, 580-500 BC) through his Pythagorean school around 530 BC.
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Ericksen, Donna, John Stasiuk, and Martha Frank. "Sharing Teaching Ideas: Bringing Pythagoras to Life." Mathematics Teacher 88, no. 9 (December 1995): 744–47. http://dx.doi.org/10.5951/mt.88.9.0744.
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The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) states that “[o]ne of the most important properties in geometry, the Pythagorean theorem, is introduced in the middle grades” (p. 113). Although the Standards document assigns much prominence to the Pythagorean theorem, our experience teaching at the university level has revealed that students know the theorem by name and can recite a2 + b2 = c2 but that they often cannot handle even simple computations using the formula. Students' experience with the Pythagorean theorem in high school needs to be broadened by their continually using the standard formula as well as applying the formula to geometric figures and special right triangles-in particular, the 30°-60°-90° and the 45°-45°-90° right triangles. The following game was developed to afford high school students more opportunity for practicing the formula in an engaging way. This game was created by the second author of the article, a high school classroom teacher, while he was a student in a class taught by another of the authors.
Dissertations / Theses on the topic "Pythagoras and the Pythagorean school"
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Batal, Jamil, and Daniel Marklund. "Kan du bevisa det? : En enkätstudie av gymnasielärarens förhållningssätt till matematiska bevis." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-15095.
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Practice of mathematical proof increase the understanding of mathematics anddevelop creativity skills, problem solving, communication, logical thinking andreasoning which are all important tools not only within the subject of mathematicsbut also important tools for the society in which we are living. The aim of this projectwas to investigate whether it is accurate that proof and proving has a subordinate rolein mathematic education in the upper secondary school in Sweden. This was done byconstructing of a digital survey that was sent to approximately 100 practicingmathematics teachers in a normal size city located in the middle of Sweden. Theresults of the survey show that the teachers consider themselves comfortable withtheir own skills in teaching proof. Paradoxically, the results also show that there is alack of teaching of proof and proving in the upper secondary school, although the newcurriculum puts more focus on proof and proving.Matematiska bevis ger eleven en ökad förståelse för matematiken och utvecklarförmågor som kreativitet, problemlösning, kommunikation, logiskt tänkande ochresonemang, vilka alla är viktiga även utanför matematiken och för det samhälle vilever i. Syftet med detta arbete var att undersöka om det stämmer att bevis ochbevisföring har en underordnad roll i matematikundervisningen i den svenskagymnasieskolan vilket gjordes med hjälp av en enkät som skickades digitalt till cirka100 gymnasiematematiklärare i en medelstor stad i Mellansverige. Det visade sig attlärarna själva anser sig tillräckligt kunniga för att undervisa i bevis men det förefallerinte som att undervisningen är tillräcklig trots att dagens läroplaner sätter bevis istörre fokus än tidigare.
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Nordheimer, Swetlana. "Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht der Sekundarstufe I." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014. http://dx.doi.org/10.18452/16922.
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Die Notwendigkeit einer Untersuchung über Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht ergibt sich einerseits aus den aktuellen bildungspolitischen Forderungen, andererseits aus den reichhaltigen bildungsphilosophischen Traditionen im deutschsprachigem Raum(KMK 2012, 11). Das Ziel der vorliegenden Arbeit besteht vor allem in der Reflexion von Beziehungshaltigkeit und Vernetzungen im Mathematikunterricht. Diese Reflexion ist durch drei Fragen bestimmt: Was kann man als Lehrer über Beziehungshaltigkeit wissen? Wie kann man als Lehrer handeln, so dass die Schüler Beziehungen zwischen mathematischen Inhalten erkennen bzw. selbständig herstellen? Um handeln zu können, muss man die Wirklichkeit oder die Praxis (bzw. Empirie) kennen, in der man handelt. In diesem Sinne ist die vorliegende Arbeit aufgebaut. Dabei wird ein Versuch unternommen, die klassische Aufteilung zwischen Theorie und Empirie bzw. Praxis des Mathematikunterrichts aufzubrechen, um eine Verzahnung zwischen diesen zu verstärken. Das Herzstück der Arbeit bilden zwei ausgearbeitete und in der schulischen Arbeit erprobte Aufgabennetze (Pythagorasbaum und Rund ums Sechseck), die den Rahmen zur Reflexion bieten.The need for a study on relations sustainability and networks in mathematics stems, on the one hand, from current education policy requirements, and, on the other, from the rich philosophical traditions of education in the German-speaking countries (KMK 2012, 11). The goal of the present work consists, above all, in reflecting on relations sustainability and networks in mathematics lessons. This reflection is guided by three questions: What can one know, as a teacher, about relations sustainability? How can one act a teacher to ensure that students recognise relationships between mathematical content, or independently produce such relations? In order to act, one must know the reality or practice (e.g. empiricism) in which one acts. The project is focused on the development and testing of worked examples of concrete task networks ("Pythagoras’ tree" and "Around the hexagon").
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Viltanioti, Irini Fotini. "De l'omphalos de la Terre à la cité céleste d'Apollon: études sur la doctrine de la Tétractys dans le pythagorisme ancien." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210038.
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La doctrine pythagoricienne de la Tétractys est sans doute une des questions les plus délicates de l’histoire de la philosophie. Elle représente non seulement une des théories essentielles de l’arithmologie, mais aussi, ainsi que la doxographie ancienne en témoigne, « le plus grand secret et le fondement de la philosophie pythagoricienne ». Armand Delatte, dans ses classiques Etudes sur la littérature pythagoricienne, a souligné l’importance véhiculée par ce philosophème. Dans la première partie, « méthodologique », de notre étude, nous traitons du lien entre Platon et la pensée pythagoricienne, en prenant comme fil conducteur trois notions essentielles: le silence voué des initiés de l’ordre et la pratique du secret ;l’expression énigmatique et « symbolique » ;la pratique de l’allégorie (hyponoia), indissolublement associée, elle, à celle du mythe. La deuxième partie de notre travail est centrée sur le témoignage le plus ancien au sujet de la Tétractys, à savoir sur la fameuse maxime des Acousmatiques :« Qu’est-ce que l’oracle des Delphes ?La Tétractys, c'est-à-dire l’harmonie où se trouvent les Sirènes ». En outre, en modérant, d’une certaine manière, l’ « ésotérisme historique » de l’Ecole de Tübingen, dont nous nous prenons des distances quant à certains points (comme, par exemple, l’importance de la méthode allégorique), nous tentons, dans la troisième et dernière partie de notre étude, de lire certains passages mythiques de Platon comme des allégories susceptibles d’être comprises et de trouver leur cohérence à la lumière de la tradition indirecte, voire de la théorie platonicienne sur les nombres, théorie intimement liée à la doctrine pythagoricienne de la Tétractys. Dans cet ordre d’idées, à partir de la République et du Timée jusqu’au Phèdre et au Gorgias, la mathématisation platonicienne de la réalité se verrait intégrée aux mythes, dont la somptuosité poétique ne serait qu’une image de l’enchantement philosophique entraînant l’élévation de l’âme vers l’Un – Bien. Bien qu’ayant toujours présents à l’esprit les dangers auxquels notre étude s’expose, nous n’avons pas toujours su les éliminer. Nous ne méconnaissons aucunement ses lacunes et ses faiblesses. Nous considérons en revanche que son avantage réside en ce qu’elle tente de contribuer à éclairer d’une lumière nouvelle certains aspects méconnus. C’est sans doute là que se situe le danger, mais aussi son intérêt.
Doctorat en Philosophie
info:eu-repo/semantics/nonPublished
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Spyrou, Panagiotis, Andreas Moutsios-Rentzos, and Dimos Triantafyllou. "Teaching for the objectification of the Pythagorean Theorem." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80973.
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This study concerns a teaching design with the purpose to facilitate the students’ objectification of the Pythagorean Theorem. Twelve 14-year old students (N=12) participated in the study before the theorem was introduced to them at school. The design incorporated
ideas from the ‘embodied mind’ framework, history and realistic mathematics, linking ‘embodied verticality’ with ‘perpendicularity’. The qualitative analyses suggested that the participants were led to the conquest of the ‘first level of objectification’ (through numbers)
of the Pythagorean Theorem, showing also evidence of appropriate ‘fore-conceptions’ of the ‘second level of objectification’ (through proof) of the theorem. The triangle the sides of which are associated with the Basic Triple (3,4,5) served as a primary instrument for the
students’ objectification, mainly, by facilitating their ‘generic abstraction’ of the Pythagorean Triples.
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Cornelli, Gabriele. "Em busca do pitagorismo: o pitagorismo como categoria historiográfica." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/8/8133/tde-25022011-104305/.
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A presente tese explora, como solução para o controvertido quadro geral da moderna história da crítica sobre Pitágoras e seu movimento, a definição do pitagorismo como categoria historiográfica. Superando tanto o dilema entre ceticismo e confiança nas fontes, como a pretensão de alcançar uma única chave hermenêutica que permita resolver a questão pitagórica, procura percorrer a história da tradição em busca de uma imagem suficientemente plural a ponto de possibilitar a compreensão do pitagorismo em sua irredutível articulação de bíos e theoría e não apesar dela. A configuração da comunidade e de seu bíos é percebida como elemento central de identificação do pitagorismo. A análise das duas teorias que mais decididamente contribuíram para a definição do pitagorismo ao longo da história, a transmigração da alma imortal e a doutrina dos números, procura definir as condições de possibilidade de atribuí-las ao pitagorismo mais antigo e as formas pelas quais ambas teriam contribuído, ao longo da história, para a definição do pitagorismo como categoria historiográfica. As fontes pré-socráticas, a platonização do pitagorismo, o testemunho aristotélico sobre os assim chamados pitagóricos, a literatura pseudoepigráfica helenística e o pitagorismo de época imperial são entendidos como momentos de um percurso histórico que resulta em uma imagem poliédrica de um dos maiores fenômenos intelectuais da história ocidental.This thesis explores the definition of Pythagoreanism as historiographical category, seen as solution for the controversial general framework of modern history of criticism about Pythagoras and his movement. Overcoming both the dilemma between skepticism and faith in the sources and the claim to achieve a single hermeneutical key to solve the Pythagorean question, in it searches are made throughout the history of tradition looking for an image sufficiently plural in order to understand Pythagoreanism in accordance with its irreducible articulation of bíos and theoría, not despite it. The setting of the community and its bíos is understood as central element for Pythagorean identification. An analysis of the two theories that more decisively contributed to the definition of Pythagoreanism throughout history, the transmigration of the immortal soul and the doctrine of numbers, attempts to define the conditions of possibility to assign them to the earlier Pythagoreanism and the ways in which these have contributed throughout history to the definition of Pythagoreanism as historiographical category. Presocratic sources, the platonization of Pythagoreanism, Aristotle\'s testimony about the \"so-called\" Pythagoreans, the hellenistic Pseudoepigrapha and Pythagoreanism in imperial age are understood as moments of an historical route resulting in a polyhedral image of one of the greatest intellectual phenomena in Western history.
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"Progress towards the synthesis of Indolizidine alkaloid 223AB." Thesis, 2008. http://hdl.handle.net/10413/167.
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It has been shown that alkaloids from various sources are vital as lead compounds in medicinal research and thus also the efficient synthesis of these. With the goal of developing a general synthetic route that can potentially access pyrrolizidine, indolizidine, quinolizidine and possibly lehmizidine alkaloid skeletons, a modified route that has been shown to produce pyrrolizidines was employed towards the synthesis of indolizidine alkaloid 223AB. Within this synthesis, a 6-endo-dig hydroamination-cyclization step was attempted for construction of the bicyclic system. For this purpose, a selection of titanium-based catalysts were synthesized in order to determine their regiochemical outcome. For the purpose of investigating ab initio the mechanism of regioselective hydroamination, the skills and methods involved in computational chemistry were acquired through a study into amide rotational barriers:
A range of novel 2-oxo-2H-chromen-7-yl dimethylcarbamates were synthesised containing either an oxygen or sulphur in the α-position to the carbonyl or thiocarbonyl group of the amide moiety. Microwave synthesis was essential for the successful synthesis of some of the sulphur containing carbamates. The barriers to internal rotation of each of these compounds were investigated as follows. Variable Temperature and Exchange Spectroscopy NMR was performed on these compounds and the barrier to free amide rotation was calculated. Each of these compounds were also modeled ab initio and the gas phase barrier to rotation calculated. These three sets of data were compared and the influence of the α-heteroatom on rotation for amides and thioamides evaluated.Thesis (M.Sc.) - University of KwaZulu-Natal, Pietermaritzburg, 2008.
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LIN, HUA-CHIEN, and 林華倩. "Effects of a Step-Prompting with E-Learning on Junior High School Students’ Math Learning Performances-Pythagorean Theorem for Example." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/ny3zks.
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碩士國立臺北教育大學
數學暨資訊教育學系碩士班
107
Nowadays, integrating information technology into education draws more and more attention. The courses of information technology even became a core course in the curriculum guidelines 108. To help students integrate with this information based society, have the capability to apply information technology to problem solving, and promote their learning effectiveness , more and more teachers gradually start integrating technology into their instructional strategies and the curriculum. Some researchers claim that among lots of learning strategies, giving clues has played a supplementary role that helps learners gain enough key information and allow them to achieve their learning goal. With that being said, how to give clues also affects if the learners understand the concept comprehensively. As a result, this research focuses on utilizing a digital learning system of Step-Prompting to guide students solve the problems and achieve their learning goal. Therefore, this study applied a Step-Prompting-Based e-Learning System for students learning Pythagorean theorem.In order to assess benefits of the learning model, this study targeted at 36 eighth grade students as research objects in Taipei City. The Experiment group used Step-Prompting-Based e-Learning System, and the Control group used the general Prompting-Based e-Learning System. Collect and analyze the experiment data of learning achievement, learning motivation, self-efficiency, cognitive load.
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Liu, Tsung-Yun, and 劉從雲. "Integrating Multi-media and E-learning Platform to the Remedy Teaching for Mathematic: Taking “Pythagorean Theorem” in Junior High School as an Example." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/r896y4.
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碩士育達科技大學
資訊管理所
103
The government has started to promote the “Hand-in-Hand Project- After-School Remedial Program” since 2006, aiming to provide diverse and adaptive learning opportunities for the elementary and junior high school students with poor academic performance. Besides, to respond to Twelve-year National Fundamental Education to be officially launched in August, 2014, it has fully promoted the remedial teaching screening and growth test since 2011, to reduce the gap of the students with poor academic performance. Remedial teaching requires much manpower during the teaching process. Moreover, since the regular classes almost take up all time of the students and the teachers at school, the remedial teaching in limited spare time will not only impose burdens on the students, but also increase the workload of teachers. This study will build e-learning platform to resolve above problems. If the teaching materials and network are combined together in this era of computer and network popularization, students will be able to study at school and review at home. For the teachers, they could supplement or revise the teaching materials via the network at any time. In this way, it will not only extend the time for remedial teaching, but also make the students more interested in learning through network. Based on the quasi-experimental method, this study conducts experimental teaching among the research samples of 20 students from Grade Two of a Junior High School in Miaoli County by taking the Technology Acceptance Model as the theoretical foundation of the research structure, and taking remedial teaching behavior scale and learning effectiveness scale which were integrated with multi-media and e-learning platform for teachings as the study tools. In this way, it is to explore the acceptance degree and learning effectiveness of the students towards the remedial teaching by using the e-learning platform. The experiment results showed that students’ acceptance for the integrating multi-media and e-learning platform in junior high school was much better after the teaching. For the learning achievement, the usage of integrating multi-media and e-learning platform was better than the usage of traditional educational environment.
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LIU, JEN-TI, and 劉仁棣. "A study on the Learning Achievement of Using MOODLE Digital Learning Platform on Junior High School --- take an example of Pythagorean theorem unit Teaching." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/95465933901802356932.
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碩士中華大學
科技管理學系碩士在職專班
100
The purpose of this study was to integrate the strategic teaching with “MOODLE Digital Learning Platform”, assessing the learning achievement and attitude of Junior High School 2th grade students on the units of Pythagorean Theorem. The study adopted “quasi- experimental research”: applying a five-classes (225 minutes) group teaching on the 2th grade Junior High School students, and implementing the “Pythagorean Theorem Achievement Tests” and “Survey of Students’ Attitude toward Mathematical Learning” as a research tool, which consisted of pre-test and post-test. Then the collected data was analyzed by means of ANCOVA, the analysis of covariance. The finding of this study are: 1. There are significant difference (P &;lt; 0.05) between the experimental group and control group ; besides, the former students’ achievement scores are higher than the latter students’ ones, which showed that the experimental teaching is better than the traditional one. 2. The experimental group and control group on average of mathematical attitudes were over the control group. But no significant difference, which may be caused by the common usage and generalization of internet. 3. According to the data from the students’ achievement test and learning attitude, the post-test average scores of the experimental group are higher than the pre-test ones, which inferred that “MOODLE Digital Learning Platform” is helpful for students’ learning, both on achievement and motivation. The study can be applied to the relationship between the teaching model and the learners with different learning styles, genders, and information attainments, and to differentiate the learning achievement with the motivation and feelings; moreover, to judge the effect of students’ problem-solving capability and meta-cognition. Keywords：MOODLE digital learning platform、Mathematics Learning Achievement、Mathematics Learning attitude、Pythagorean theorem
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Moledina, Amreen. "Should the Pythagorean Theorem Actually be Called the 'Pythagorean' Theorem." Thesis, 2013. http://hdl.handle.net/1807/43260.
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This paper investigates whether it is reasonable to bestow credit to one person or group for the famed theorem that relates to the side lengths of any right-angled triangle, a theorem routinely referred to as the “Pythagorean Theorem”. The author investigates the first-documented occurrences of the theorem, along with its first proofs. In addition, proofs that stem from different branches of mathematics and science are analyzed in an effort to display that credit for the development of the theorem should be shared amongst its many contributors rather than crediting the whole of the theorem to one man and his supporters.
Books on the topic "Pythagoras and the Pythagorean school"
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Guthrie, Kenneth Sylvan. The Pythagorean Sourcebook and Library: An Anthology of Ancient Writings Which Relate to Pythagoras and Pythagorean Philosophy. Edited by David Fideler. Grand Rapids: Phanes Press, 1987.
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Pythagoras: His life, teaching, and influence. Ithaca: Cornell University Press, 2005.
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1948-, Wasserman James, ed. Pythagoras: His life and teachings : a compendium of classical sources. Lake Worth, FL: Ibis Press, 2010.
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Opsopaus, John. Guide to the Pythagorean tarot: An interpretation based on Pythagorean & alchemical principles. St. Paul, Minn: Llewellyn Publications, 2001.
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Pythagoras in der Spätantike: Studien zu De vita Pythagorica des Iamblichos von Chalkis. München: Saur, 2002.
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Cecilia, Accademia di Santa, ed. L' arte della fuga di Johann Sebastian Bach: Un'opera pitagorica e la sua realizzazione. Milano: Skira, 2000.
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Capparelli, Vincenzo. Il messaggio di Pitagora: Il pitagorismo nel tempo. Roma: Edizione mediterranee, 1990.
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Stanley, Thomas. Pythagoras: His life and teachings : a compendium of classical sources. Lake Worth, FL: Ibis Press, 2010.
Find full textBook chapters on the topic "Pythagoras and the Pythagorean school"
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Anglin, W. S., and J. Lambek. "Pythagoras and His School." In The Heritage of Thales, 33–36. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0803-7_8.
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Allen, G. Donald. "Pythagorean Triples Plus One." In Pedagogy and Content in Middle and High School Mathematics, 67–71. Rotterdam: SensePublishers, 2017. http://dx.doi.org/10.1007/978-94-6351-137-7_17.
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Carlson, Philip. "Area and the Pythagoras Theorem." In Solutions Manual for Geometry: A High School Course, 27–37. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0861-7_3.
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Svetlikova, Ilona. "The Moscow “School”: P. A. Nekrasov." In The Moscow Pythagoreans, 50–89. New York: Palgrave Macmillan US, 2013. http://dx.doi.org/10.1057/9781137338280_3.
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Svetlikova, Ilona. "Some Other Members of the “School”." In The Moscow Pythagoreans, 114–33. New York: Palgrave Macmillan US, 2013. http://dx.doi.org/10.1057/9781137338280_5.
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Svetlikova, Ilona. "The Pythagoreanism of the Moscow “School”." In The Moscow Pythagoreans, 134–60. New York: Palgrave Macmillan US, 2013. http://dx.doi.org/10.1057/9781137338280_6.
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Svetlikova, Ilona. "Origins of the Moscow “School”: N. V. Bugaev." In The Moscow Pythagoreans, 14–49. New York: Palgrave Macmillan US, 2013. http://dx.doi.org/10.1057/9781137338280_2.
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Danesi, Marcel. "The Pythagorean theorem." In Pythagoras' Legacy, 1–21. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198852247.003.0001.
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The Pythagorean theorem constitutes one of the first great ideas of mathematics. Its importance is evident in the fact that it has been taught in schools throughout human history; it has had many applications in science and engineering; it has cropped up in numerous other mathematical ideas; it has led to discoveries, such as Fermat’s last theorem; and the list could go on and on. In a phrase, the theorem is one of those ideas that have mattered to mathematics and to human history. This chapter looks at the theorem and at why it is so profoundly important. It also deals with some key concepts that the theorem has introduced, including irrational numbers.
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"Pythagorean triples." In Understanding Numbers in Elementary School Mathematics, 487–89. Providence, Rhode Island: American Mathematical Society, 2011. http://dx.doi.org/10.1090/mbk/079/37.
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"The Archytan Alternative in the Pythagorean School." In Plato’s Timaeus and the Missing Fourth Guest, 305–7. BRILL, 2019. http://dx.doi.org/10.1163/9789004389922_013.
Full textConference papers on the topic "Pythagoras and the Pythagorean school"
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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. Valencia: 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.