Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T10:32:34.131Z Has data issue: false hasContentIssue false
  • English
  • Français

Some more properties of the bisect-diagonal quadrilateral

Published online by Cambridge University Press:  13 October 2021

Michael de Villiers
Michael de Villiers*
Affiliation:
Mathematics Education (RUMEUS), University of Stellenbosch, South Africa, e-mail: profmd@mweb.co.za
Get access Rights & Permissions [Opens in a new window]

Extract

Martin Josefsson [1] has coined the term ‘bisect-diagonal quadrilateral’ for a quadrilateral with at least one diagonal bisected by the other diagonal, and extensively explored some of its properties. This quadrilateral has also been called a ‘bisecting quadrilateral’ [2], a ‘sloping-kite’ or ‘sliding-kite’ [3], or ‘slant kite’ [4]. The purpose of this paper is to explore some more properties of this quadrilateral.

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 564 , November 2021 , pp. 474 - 480
Check for updates
Copyright
© The Mathematical Association 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Josefsson, M., Properties of bisect-diagonal quadrilaterals, Math. Gaz. 101 (July 2017) pp. 214-226.CrossRefGoogle Scholar
de Villiers, M., Some adventures in Euclidean geometry, Dynamic Mathematics Learning (2009).Google Scholar
Graumann, G., Investigating and ordering quadrilaterals and their analogies in space – problem fields with various aspects, ZDM 37 (3) (2005) pp. 190-198, also available at: http//subs.emis.de/journals/ZDM/zdm053a8.pdfGoogle Scholar
Ramachandran, A., The four-gon family tree, At Right Angles 1 (1) (2012) pp. 53-57, also available at http://www.teachersofindia.org/sites/default/files/12_four_gon_family_tree.pdfGoogle Scholar
Coxeter, H. S. M. & Greitzer, S. L., Geometry revisited, Math. Ass. Amer. (1967).CrossRefGoogle Scholar
Pillay, S. & Pillay, P., Equipartitioning and balancing points of polygons, Pythagoras, 71 (July 2010) pp. 13-21.Google Scholar
Gilbert, G. T., Krusemeyer, M. and Larson, L. C., The Wohascum County problem book, Dolciani Mathematical Expositions, 14 (10), Math. Ass. Amer. (1993).Google Scholar
Johnson, R. A., Advanced Euclidean geometry, Dover Publications (1960).Google Scholar
De Villiers, M., A cyclic Kepler quadrilateral & the Golden Ratio, At Right Angles, March 2018, pp. 91-94. (Accessed on 16 August 2020 at: https://azimpremjiuniversity.edu.in/SitePages/resources-ara-march-2018-cyclic-kepler-quadrilateral.aspx).Google Scholar