The vertex centroid of a Van Aubel result involving similar quadrilaterals and its further generalisation

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dc.contributor.authorDe Villiers, Michaelen_ZA
dc.contributor.authorHumenberger, Hansen_ZA
dc.date.accessioned2024-07-18T07:54:29Z
dc.date.available2024-07-18T07:54:29Z
dc.date.issued2024 en_ZA
dc.descriptionThe original publication is available at: https://www.tandfonline.comen_ZA
dc.description.abstractThis paper explores the position of the vertex centroid for a generalisation of Van Aubel’s theorem: specifically we look at what happens to the vertex centroid when directly similar quadrilaterals are placed on the sides of an arbitrary quadrilateral. After giving a simple proof that the position of the vertex centroid remains unchanged, the result is further generalised to directly similar triangles (or other directly similar shapes) on the sides of polygons using vectors. Not only are the results mathematically interesting, but can also provide an appropriate classroom opportunity for dynamic geometry exploration, and to build 2D models with clay and drinking straws (or thin wire) to illustrate and check the theoretical solutions. [ABSTRACT FROM AUTHOR]en_ZA
dc.description.urihttps://www.tandfonline.com/doi/full/10.1080/0020739X.2024.2368607en_ZA
dc.description.versionPublisher’s versionen_ZA
dc.format.extent9 pages : illustrations
dc.identifier.citationDe Villiers M. & Humenberger H. 2024. The vertex centroid of a Van Aubel result involving similar quadrilaterals and its further generalisation. International Journal of Mathematical Education in Science and Technology 2024(2024):9 pages. doi.10.1080/0020739x.2024.2368607en_ZA
dc.identifier.doi10.1080/0020739X.2024.2368607en_ZA
dc.identifier.issn178437140 (online)en_ZA
dc.identifier.urihttps://scholar.sun.ac.za/handle/10019.1/131020
dc.language.isoen
dc.publisherTaylor & Francis Groupen_ZA
dc.rights.holderAuthors retain copyrighten_ZA
dc.subject.lcshCenter of massen_ZA
dc.subject.lcshSimilarity (Geometry)en_ZA
dc.subject.lcshBivectorsen_ZA
dc.subject.lcshGeomaticsen_ZA
dc.subject.lcshGeography -- Data processingen_ZA
dc.subject.lcshGeographic information systemsen_ZA
dc.subject.lcshSpatial data infrastructuresen_ZA
dc.subject.lcshGeometry, Algebraicen_ZA
dc.subject.othervan Aubel's theoremen_ZA
dc.titleThe vertex centroid of a Van Aubel result involving similar quadrilaterals and its further generalisationen_ZA
dc.typePreprinten_ZA
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