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Generalisation of a quadrilateral duality theorem

Published online by Cambridge University Press:  15 June 2017

Martin Josefsson
Martin Josefsson*
Affiliation:
Västergatan 25d, 285 37 Markaryd, Sweden e-mail: martin.markaryd@hotmail.com

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We will prove a generalisation to our Theorem 10 about duality between orthodiagonal quadrilaterals and equidiagonal quadrilaterals in [1, p. 134]. These are quadrilaterals with perpendicular diagonals and diagonals of equal lengths respectively. Unfortunately we made a careless mistake in the proof of Theorem 10 (ii) in [1], which was found by Zoltán Szilasi at the University of Debrecen in Hungary. When reviewing that theorem, we realised that it's just a special case of a more general theorem. The equilateral triangles in Theorem 10 can be replaced by almost any regular polygons.

Information

Type
Articles
Information
The Mathematical Gazette , Volume 101 , Issue 551 , July 2017, pp. 208 - 213
Copyright
Copyright © Mathematical Association 2017 

References

1. Josefsson, M., Properties of equidiagonal quadrilaterals, Forum Geom. 14 (2014) pp. 129–144.Google Scholar
2. Olson, A. T., Exploring skewsquares, Mathematics Teacher 69(7) (1976) pp. 570–573.CrossRefGoogle Scholar
3. Contreras, J. N., Pose and solve Varignon converse problems, Mathematics Teacher 108(2) (2014) pp. 98–106.CrossRefGoogle Scholar
4. Nishiyama, Y., The beautiful geometric theorem of van Aubel, Int. J. Pure Appl. Math. 66 (1) (2011) pp. 71–80.Google Scholar
5. Oxman, V. and Stupel, M., Elegant special cases of Van Aubel's theorem, Math. Gaz. 99 (July 2015) pp. 256–262.CrossRefGoogle Scholar
6. Josefsson, M., Characterizations of orthodiagonal quadrilaterals, Forum Geom. 12 (2012) pp. 13–25.Google Scholar
7. Djukič, D., Jankovič, V., Matič, I. and Petrovič, N., The IMO Compendium, Springer (2006).Google Scholar
8. Crux Mathematicorum 21 (February 1995), available at https://cms.math.ca/crux/backfile/Crux_v21n02_Feb.pdf Google Scholar
9. Solutions to reader investigations: May 2004, AMESA KZN Mathematics Journal (December 2004), available at: http://dynamicmathematicslearning.com/readersol04.pdf Google Scholar
10. Reader investigations, AMESA KZN Mathematics Journal 9 (2005), available at http://mysite.mweb.co.za/residents/profmd/readerinvest05.pdf Google Scholar
11. Solutions to reader investigations, AMESA KZN Mathematics Journal 9 (2005), available at http://mysite.mweb.co.za/residents/profmd/readersol05.pdf Google Scholar