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Variations of the Vecten configurations

Published online by Cambridge University Press:  20 June 2025

Hans Humenberger  and
Michael de Villiers
Hans Humenberger
Affiliation:
University of Vienna, Austria e-mail: hans.humenberger@univie.ac.at
Michael de Villiers
Affiliation:
University of Stellenbosch, South Africa e-mail: profmd1@mweb.co.za
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We present some less known variations of the the Vecten configuration and give purely geometric proofs for them. It is unlikely that these variations (and even proofs?) are new, probably just well-hidden in the literature. If a reader happens to know references for the variations discussed (or other geometric proofs), please let the authors know. At [1] the reader can find a dynamic webpage on our topic.

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Type
Articles
Information
The Mathematical Gazette , Volume 109 , Issue 575 , July 2025 , pp. 265 - 272
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provieded the original work is properly cited.
Copyright
© The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association

References

de Villiers, M., Some variations of Vecten configuration (updated 2024), accessed January 2025 at http://dynamicmathematicslearning.com/vecten-variations.htmlGoogle Scholar
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Alsina, C. and Nelsen, R. B., Charming proofs: a journey into Elegant Mathematics, Mathematical Association of America (2010).CrossRefGoogle Scholar
de Villiers, M., Dual generalizations of Van Aubel’s theorem, Math. Gaz. 82 (November 1998) pp. 405–412.CrossRefGoogle Scholar
Silvester, J. R., Extensions of a theorem of Van Aubel, Math. Gaz. 90 (March 2006) pp. 2–12.CrossRefGoogle Scholar
https://www.cut-the-knot.org/Curriculum/Geometry/GeoGebra/PropertiesOfFlankTriangles.shtmlGoogle Scholar
Pellegrinetti, D. and de Villiers, M., Forgotten properties of the Van Aubel and bride’s chair configurations, Int. J. Geom. 10(3) (2021), pp. 5–10. https://ijgeometry.com/wp-content/uploads/2021/07/1.-5-10.pdf Google Scholar