PYTHAGOREAN PARABOLOGRAPH FOR REGIONS’ QUADRATURE

Authors

  • 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

Keywords:

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

Abstract

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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Author Biographies

  • 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.

References

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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

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Published

2024-09-06

Issue

Vol. 11 No. 11 (2024)

Section

Articles

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