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The Critical Fortunes of Pythagoras’ Probes

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The Palgrave Handbook of Educational Thinkers

Abstract

Pythagoras is one of the most important scholars of all time. He made vital discoveries that continue to be applied today in various educational fields. His most influential contribution is the Pythagorean theorem, which was named after him and attained applicability in mathematical areas. He also made essential discoveries in music and astronomy, which scholars continue to explore and expand on today. This chapter examines the life of Pythagoras, especially zeroing in on the contributions that his discoveries have had on contemporary education. The study follows an in-depth historical account of Pythagoras’ discoveries and influences on early thinkers, especially Plato. Also, the chapter focuses on how Pythagoras’ theories continue to influence a variety of current educational and professional fields. A critical portrayal rests on primary and secondary sources such as history books, original writings, and academic journals. This chapter presents the need for school students to learn mathematics from a historical stance of events surrounding Pythagoras and how he developed knowledge. A cultural and contextual approach situates the learner in meaningful mathematics teaching rather than merely using the famous theorem and equation for rule-based or anecdotal problem-solving.

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References

  • Adelstein, I. M., & Ashline, G. L. (2019). Reframing the Pythagorean theorem. The College Mathematics Journal, 50(1), 28–35. https://doi.org/10.1080/07468342.2019.1557983

    Article  Google Scholar 

  • Ambarsari, E. W., Awaludin, A. A. R., Suryana, A., Hartuti, P. M., & Rahim, R. (2019). Basic concept Pythagoras tree for constructing data visualization on decision tree learning. Journal of Applied Engineering Science, 17(4). https://doi.org/10.5937/jaes17-21960

  • Andrew, G. (2014). Parmenides, cosmology and sufficient reason. Apeiron, 47(1), 16–47.

    Article  Google Scholar 

  • Benakis, L. G. (2018). Byzantine musical theory (harmonics). Wisdom, 10(1), 98–104.

    Article  Google Scholar 

  • Bigelow, J., & Leckey, M. (2020). Raphael’s platonic vision. Journal of the American Philosophical Association, 6(4), 410–430. https://doi.org/10.1017/apa.2019.46

    Article  Google Scholar 

  • Bronowski, J. (2019). The music of the spheres (pp. 61–71). Chapman and Hall/CRC.

    Google Scholar 

  • Caiazzo, I. (2021). “Pythagoras’ mistake”: The transmigration of souls in the latin middle ages and beyond. In Brill’s companion to the reception of Pythagoras and Pythagoreanism in the middle ages and the renaissance (pp. 322–349). Brill. https://doi.org/10.1163/9789004499461_012

  • Chapple, C. K. (2018). Animals, vegetarianism, and nonviolence. In The Routledge handbook of pacifism and nonviolence (pp. 343–354). Routledge.

    Google Scholar 

  • Colas, G., & Colas-Chauhan, U. (2017). An 18th century Jesuit “refutation of metempsychosis” in Sanskrit. Religion, 8(9), 192.

    Article  Google Scholar 

  • David, C. A., & Coan, P. G. (2018). The implicit stress of eating meat. Life Research, 1(1), 9–17. https://doi.org/10.12032/life2018-0711-003

    Article  Google Scholar 

  • Deutsch, D. (2019). Psychology and music. In Psychology and its allied disciplines (pp. 155–194). Psychology Press.

    Google Scholar 

  • Dillon, J. (2021). C. Huffman Aristoxenus of Tarentum: The Pythagorean precepts (how to live a Pythagorean life). Cambridge: Cambridge University Press; 2019. Pp. xii+ 636.₤ 130. 9781108425315. The Journal of Hellenic Studies, 141, 291–292. https://doi.org/10.1017/S0075426921000604

  • Dolgert, S. (2018). Vegetarian republic: Pythagorean themes in Plato’s republic. Proceedings of the XXIII World Congress of Philosophy, 2(2), 83–88. https://doi.org/10.5840/wcp232018221288

    Article  Google Scholar 

  • Edwards, G. F. (2018). Reincarnation. Rationality, and Temperance: Platonists on not eating animals: A History, 27–55.

    Google Scholar 

  • El Naschie, M. S. (2019). On the fractal counterpart of C. Vafa’s twelve-dimensional F-theory and the A. Schoenberg twelve-tone music implicit in the standard model of high energy elementary particles. International Journal of Innovation in Science and Mathematics, 7(5), 222–230.

    Google Scholar 

  • Fachrudin, A. D., Ekawati, R., Kohar, A. W., Widadah, S., Kusumawati, I. B., & Setianingsih, R. (2019). Ancient China history-based task to support students’ geometrical reasoning and mathematical literacy in learning Pythagoras. Journal of Physics: Conference Series, 1417(1), 012042. https://doi.org/10.1088/1742-6596/1417/1/012042

    Article  Google Scholar 

  • Fehér, A., Gazdecki, M., Véha, M., Szakály, M., & Szakály, Z. (2020). A comprehensive review of the benefits of and the barriers to the switch to a plant-based diet. Sustainability, 12(10), 4136.

    Article  Google Scholar 

  • Fischer, M. M. (2020). Ethnicity and the post-modern arts of memory (pp. 194–233). University of California Press.

    Google Scholar 

  • Garrido, S., & Davidson, J. W. (2019). Music, nostalgia, and memory: Historical and psychological perspectives. Springer.

    Book  Google Scholar 

  • Guthrie, W. K. (1969). A history of Greek philosophy. III, the fifth-century enlightenment. Cambridge University Press.

    Google Scholar 

  • Haley, G. J. (2018). The Pragmatism of food porn: Modern media as a mode of Zen perpetuation (Publication No. 10814302) [Doctoral dissertation, The University of North Carolina at Charlotte].

    Google Scholar 

  • Heath, T. L. (1991). Greek astronomy. Courier Corporation.

    Google Scholar 

  • Hodges, D. A. (2019). Music in the human experience: An introduction to music psychology. Routledge.

    Book  Google Scholar 

  • Hodson, G., & Earle, M. (2018). Conservatism predicts lapses from vegetarian/vegan diets to meat consumption (through lower social justice concerns and social support). Appetite, 120, 75–81. https://doi.org/10.1016/j.appet.2017.08.027

    Article  Google Scholar 

  • Katkar, L. N. (2019). Extensions of the theorem of Pythagoras. At Right Angles, 5, 11–16.

    Google Scholar 

  • Katopodis, C. (2021). The Music of the Spheres in Emerson, Fuller, and Thoreau: Lyell’s Principles and Transcendental Listening. ISLE: Interdisciplinary Studies in Literature and Environment, 28(3), 839–867. https://doi.org/10.1093/isle/isz113

  • Kostelnik, K. M. (2019). Greek Music Theory vs. the Bible. Cedarville University, The Research and Scholarship 2019 Symposium.

    Google Scholar 

  • Laks, A. (2014). Diogenes Laertius’ life of Pythagoras. In Huffman (Ed.), pp. 360–380.

    Google Scholar 

  • Lentz, G., Connelly, S., Mirosa, M., & Jowett, T. (2018). I am gauging attitudes and behaviors: Meat consumption and potential reduction. Appetite, 127, 230–241.

    Article  Google Scholar 

  • Li, C. (2020). Bring back harmony in philosophical discourse: A confucian perspective. Journal of Dharma Studies, 2(2), 163–173. https://doi.org/10.1016/j.appet.2018.04.015

    Article  Google Scholar 

  • Linzey, A., & Linzey, C. (2018). Introduction: Vegetarianism as an ethical protest. In Ethical vegetarianism and veganism (pp. 1–16). Routledge.

    Google Scholar 

  • Mahmud, S. (2019). A new long proof of the Pythagorean theorem. International Journal of Scientific and Innovative Mathematical Research, 7(9), 3–7. https://doi.org/10.20431/2347-3142.0709002

    Article  Google Scholar 

  • Maniatis, Y. N. (2009). Pythagorean Philolaus pyrocentric universe. Schole. Философское антиковедение и классическая традиция, 3(2), 401–415.

    Google Scholar 

  • Maor, E. (2019). The Pythagorean theorem: A 4,000-year history. Princeton University Press.

    Book  Google Scholar 

  • McKirahan, R. D. (2011). Philosophy before Socrates: An introduction with texts and commentary. Hackett Publishing.

    Google Scholar 

  • Mojsik, T. O. M. A. S. Z. (2017). Dicearchus (fr. 41 Mirhady) on Pythagoras’ death. Eos, 104, 47–69.

    Google Scholar 

  • National Research Council. (2011). Climate stabilization targets: emissions, concentrations, and impacts over decades to millennia. National Academies Press.

    Google Scholar 

  • Olney, J. (2020). The rhizome and the flower. University of California Press.

    Google Scholar 

  • Olsen, S., Marek-Crnjak, L., He, J. H., & El Naschie, M. S. (2020). A grand unification of the sciences, art & consciousness: Rediscovering the Pythagorean Plato’s golden mean number system. Journal of Progressive Research in Mathematics, 16(2).

    Google Scholar 

  • O’Meara, D. J. (2019). The music of philosophy in late antiquity (pp. 131–147). Routledge.

    Google Scholar 

  • Peddie, M., Ranasinghe, C., Scott, T., Heath, A. L., Horwath, C., Gibson, R., … & Haszard, J. (2020). Dietary intake nutritional status and lifestyle of adolescent vegetarian and nonvegetarian girls in New Zealand (The SuNDiAL Project): Protocol for a clustered, cross-sectional survey. JMIR Research Protocols, 9(5), e17310. https://doi.org/10.2196/17310

  • Pellò, C. (2018). The lives of Pythagoras: A proposal for reading Pythagorean metempsychosis. Rhizomatic, 6(2), 135–156.

    Article  Google Scholar 

  • Riedweg, C. (2012). Pythagoras. Cornell University Press.

    Book  Google Scholar 

  • Salowey, C. A. (2004). Great Lives from History: The Ancient World, Prehistory-476 CE. Salem Press.

    Google Scholar 

  • Schorn, S. (2018). Chapter 13: Pythagoras in the historical tradition: From Herodotus to Diodorus Siculus. In Studien zur hellenistischen Biographie und Historiographie (pp. 409–430). De Gruyter.

    Google Scholar 

  • Teresi, D. (2010). Lost discoveries: The ancient roots of modern science – from the baby. Simon and Schuster.

    Google Scholar 

  • Williamson, K., Satre-Meloy, A., Velasco, K., & Green, K. (2018). Climate change needs behavior change: Making a case for behavioral solutions to reduce global warming. Rare.

    Google Scholar 

  • Wilson, R. (2018). Astronomy through the ages: The story of the human attempt to understand the universe. CRC Press.

    Book  Google Scholar 

  • Wirnitzer, K. C. (2018). Vegan nutrition: The latest boom in health and exercise. In Therapeutic, probiotic, and unconventional foods (pp. 387–453). Academic.

    Google Scholar 

  • Yongdan, L. (2018). An exploration of a Tibetan lama’s study of the Pythagorean theorem in the mid-18th century. Études mongoles et sibériennes, centrasiatiques et tibétaines, 49. https://doi.org/10.4000/emscat.3565

  • Zhmud, L. (2012). Pythagoras and the early Pythagoreans. Oxford University Press.

    Book  Google Scholar 

  • Zhmud, L. (2018). Physis in the Pythagorean tradition. Philologia classica, 13(1), 50–68.

    Article  Google Scholar 

Further Reading

  • Bamford, C. (Ed.). (1994). Homage to Pythagoras: Rediscovering sacred science. SteinerBooks.

    Google Scholar 

  • Fauvel, J., Flood, R., & Wilson, R. J. (Eds.). (2006). Music and mathematics: From Pythagoras to fractals. Oxford University Press on Demand.

    Google Scholar 

  • Morrison, J. S. (1956). Pythagoras of Samos. The Classical Quarterly, 6(3/4), 135–156. http://www.jstor.org/stable/636906

    Article  Google Scholar 

  • Phelps, N. (2007). The longest struggle: Animal advocacy from Pythagoras to PETA. Lantern Books.

    Google Scholar 

  • Zubkova, A., & Nani, H. (2012). Dialogues with Pythagoras. New Atlanteans.

    Google Scholar 

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Correspondence to Manasseh Cudjoe .

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Cudjoe, M., Ebenezer, J. (2022). The Critical Fortunes of Pythagoras’ Probes. In: Geier, B.A. (eds) The Palgrave Handbook of Educational Thinkers . Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-81037-5_14-1

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  • DOI: https://doi.org/10.1007/978-3-030-81037-5_14-1

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