Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-30T17:35:58.533Z Has data issue: false hasContentIssue false
  • English
  • Français

Yet more characterisations of parallelograms

Published online by Cambridge University Press:  03 July 2023

Mowaffaq Hajja  and
Panagiotis T. Krasopoulos
Mowaffaq Hajja
Affiliation:
P. O. Box 388 (Al-Husun), 21510 Irbid – Jordan e-mail: [email protected], [email protected]
Panagiotis T. Krasopoulos
Affiliation:
Department of Informatics, KEAO Electronic National Social Security Fund 12 Patision St. 10677 Athens – Greece e-mail: [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This article, like our previous one [1], combines known and new characterisations of parallelograms. Both can be thought of as additions to Martin Josefsson’s series on ‘characterisations of’ and ‘properties of’ various types of quadrilaterals – a series that does not include parallelograms. Josefsson’s publications can be found listed in [2], [3] and [4]. For the importance of characterisations in geometry, see [5].

Type
Articles
Information
The Mathematical Gazette , Volume 107 , Issue 569 , July 2023 , pp. 225 - 233
Check for updates
Copyright
© The Authors, 2023. Published by Cambridge University Press on behalf of The Mathematical Association

References

Hajja, M. and Krasopoulos, P. T., More characterisations of parallelograms, Math. Gaz. 107 (March 2023) pp. 76–83.Google Scholar
https://forumgeom.fau.edu/FGAuthorsJ.htmlGoogle Scholar
https://ijgeometry.com/search/martin+josefsson/Google Scholar
https://www.cambridge.org/core/search?filters%5BauthorTerms%5D=Martin%20Josefsson&eventCode=SE-AUGoogle Scholar
Josefsson, M., The importance of characterisations in geometry, Math. Gaz. 102 (July 2018) pp. 302–307.CrossRefGoogle Scholar
Viglione, R., The Thébault configuration keeps on giving, Math. Gaz. 104 (March 2020) pp. 74–81.CrossRefGoogle Scholar
Viglione, R., An extension of the Thébault second problem, Math. Gaz. 103 (July 2019) pp. 343–346.CrossRefGoogle Scholar
Hahn, L-s, Complex numbers & geometry, MAA, Washington (1994).Google Scholar
Andreescu, T. and Andrica, D., Complex numbers from A to … Z, Birkhäuser (2006).Google Scholar
Needham, T., Visual complex analysis, Clarendon (1997).Google Scholar
Van Aubel, M. H., Note concernant les centres de carrés construits sur le côtés d’un polygone quelqonque, Nouvelles Corresp. Math. 4 (1878) pp. 40–44.Google Scholar
Finney, R. L., Dynamical proofs of Euclidean theorems, Math. Mag. 43 (1970) pp. 177–185.CrossRefGoogle Scholar
Engel, A., Problem-solving strategies, Springer (1998).Google Scholar
Al-Afifi, Gh., Hajja, M., and Hamdan, A., Another n-dimensional generalization of Pompeiu’s theorem, Amer. Math. Monthly 125 (2018) pp. 612–622.CrossRefGoogle Scholar
Al-Afifi, Gh., Hajja, M., Hamdan, A. and Krasopoulos, P. T., Pompeiulike theorems for the medians of a simplex, Math. Ineq. Appl., 21 (2018) pp. 539–552.Google Scholar
Barbara, R., Problem 90F, Math. Gaz. 90 (July 2006) p. 354.Google Scholar
McCartin, B. J., Mysteries of the equilateral triangle, Hikari Ltd (2010).Google Scholar
Fomin, D., Genkin, S. and Itenberg, I., Mathematical circles (Russian experience), Amer. Math. Society (1996).CrossRefGoogle Scholar
Pop, O. T., Minculete, N. and Bencze, M., An introduction to quadrilateral geometry, Editura Dedicata si Pedagigica, Romania (2013).Google Scholar
Melzak, Z. A., Invitation to geometry, John Wiley (1983).Google Scholar
Silvester, J. R., Geometry, ancient and modern, Oxford University Press (2001).Google Scholar
Andreescu, T. and Crişan, V., Mathematical induction, XYZ Press (2017).Google Scholar