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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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Extract

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.

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

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References

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