The vertex centroid of a Van Aubel result involving similar quadrilaterals and its further generalisation
Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
Taylor & Francis Group
Abstract
This 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]
Description
The original publication is available at: https://www.tandfonline.com
Keywords
Citation
De 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.2024.2368607