PYTHAGOREAN PARABOLOGRAPH FOR REGIONS’ QUADRATURE

Autors/ores

  • Georgios K. Ntontos 9th Lyceum of Patras, 62 Australias 26442 Patras, Greece orcid.org/0009-0004-7244-8637
  • Eugenia Koleza University of Patras, 26504 Patras, Greece orcid.org/0009-0000-8211-1924

DOI:

https://doi.org/10.46827/ejes.v11i11.5569

Paraules clau:

parabola, parabolograph, quadrature of regions, artefacts, mathematical machine

Resum

In this paper an attempt is made to design a mathematical machine based on the Pythagorean theory of fitting an equivalent parallelogram (given angle and side) with another parallelogram. An equivalent square or rhombus is constructed given a rectangle or a parallelogram respectively. It is then proved that this mechanism can simultaneously draw a parabolic arc. The parameters of this mathematical machine are checked. In each case, an attempt is made to find the focus and the directrix of the corresponding parabola. The important help of the GeoGebra software for the initial mechanical design of the machine is highlighted, but also the important differences of this simulation from the physical construction.

 

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Biografies de l'autor/a

  • Georgios K. Ntontos, 9th Lyceum of Patras, 62 Australias 26442 Patras, Greece orcid.org/0009-0004-7244-8637
    Georgios K. Ntontos is a PhD Mathematician teaching at the 9th Lyceum of Patras, Greece.
  • Eugenia Koleza, University of Patras, 26504 Patras, Greece orcid.org/0009-0000-8211-1924
    Ms. Koleza Eugenia is a Professor Mathematician teaching at University of Patras, Greece.

Referències

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Exarhakos, Th., & Dziachristos, E. (2001). Euclid "Elements" (Books I, II, III, IV, V, VI): Vol. II (Science and Education Research Center), (Ed.; 1st). Retrieved from: https://commonmaths.weebly.com/uploads/8/4/0/9/8409495/tomos-1.pdf

Heath T.L., (2001). History of Greek Mathematics, From Aristarchus to Diophantus (cf. Aggelis, A., Vlamou, E., Grammenos, T., Spanou A.). Athens: K.E.EΠ.EK. (1921 is the year of original publication)

Heath, T., Taliaferro, C., & D’Ooge, M. (1952). Great books of the Western World. In Encyclopedia Britannica, Inc. (Vol. 11). Benton William. Retrieved from: https://ia902806.us.archive.org/2/items/encyclopaediabritannicagreatbooksofthewesternworld/Encyclop%C3%A6dia%20Britannica%20-%20Great%20Books%20of%20the%20Western%20World%2C%20Volume%2011%20-%20Euclid%2C%20Archimedes%2C%20Apollonius%2C%20Nicomachus.pdf

Ntontos, G. (2019). Machines for generating parabolic arcs and their application in teaching practice (Master's Τhesis). University of Patras. Retrieved from: https://nemertes.library.upatras.gr/items/4ca4e2e9-7cc6-45b1-99a2-297229060fea

Reeder, M. (2015). Archimedes’ Quadrature of the Parabola. Notes for Math, 1–15. Retrieved from: https://pdfcoffee.com/1103quadparabpdf-pdf-free.html

Sardelis, D. A., & Valahas, T. (2017). A Tangent Line Problem, Experimental Mathematics Series, Note 1. January 2000. Retrieved from: https://arxiv.org/pdf/1210.6842

Descàrregues

Publicat

2024-09-06

Número

Vol. 11 Núm. 11 (2024)

Secció

Articles

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