A Curious Property of Octagons

  • Rogério César dos Santos University of Brasília, Brazil
  • Ana Clara Oliveira Comby University of Brasília, Brazil
  • Ramires Vargas da Silva State University of Goiás, Brazil
DOI: https://doi.org/10.32350/sir.32.01
Keywords: octagon, plane geometry, Van Aubel theorem

Abstract

Abstract Views: 133

The famous theorem of Van Aubel for quadrilaterals postulates that if squares are built externally on the sides of any quadrilateral, then the two segments that join the opposing centers of these squares are congruent and orthogonal. Inspired by this result and also by the results of Krishna, in this article we will prove the following result of plane geometry: each octagon is associated with a parallelogram, in some cases the parallelogram in question can be degenerate at a point or a segment. This is possible because of complex numbers and basics of analytical geometry.

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Published
2019-06-05
How to Cite
1.
Rogério César dos Santos, Ana Clara Oliveira Comby, Ramires Vargas da Silva. A Curious Property of Octagons. Sci Inquiry Rev. [Internet]. 2019Jun.5 [cited 2024Nov.21];3(2):01-7. Available from: https://journals.umt.edu.pk/index.php/SIR/article/view/293
Issue
Vol 3 No 2: June 2019
Section
Orignal Article

Copyright (c) 2019 Rogério César dos Santos, Ana Clara Oliveira Comby, Ramires Vargas da Silva

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.