Hostname: page-component-7dd5485656-zlgnt Total loading time: 0 Render date: 2025-10-30T16:42:03.798Z Has data issue: false hasContentIssue false
  • English
  • Français

Quadrilaterals of triangle centres

Published online by Cambridge University Press:  01 August 2016

Maria Flavia Mammana  and
Biagio Micale
Maria Flavia Mammana
Affiliation:
Department of Mathematics and Computer Science, University of Catania, Italy
Biagio Micale
Affiliation:
Department of Mathematics and Computer Science, University of Catania, Italy
Get access Rights & Permissions [Opens in a new window]

Extract

Let Q be a convex quadrilateral ABCD. We denote by TA , TB , Tc , TD , the four triangles BCD, CDA, DAB, ABC, respectively

The barycentres (or centroids), orthocentres, incentres and circumcentres of such triangles determine other quadrilaterals in their turn that we call the quadrilateral of the barycentres, of the orthocentres, of the incentres and of the circumcentres, respectively. We denote these quadrilaterals by Qb , Q0 , Qi , Qc , respectively.

Information

Type
Articles
Information
The Mathematical Gazette , Volume 92 , Issue 525 , November 2008 , pp. 466 - 475
Copyright
Copyright © The Mathematical Association 2008

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.)

Article purchase

Temporarily unavailable

References

Further reading

Coxeter, H. S. M. and Greitzer, S. L. Geometry revisited, Washington, DC: Amer. Math. Assoc. (1967).Google Scholar
Wells, D. The Penguin dictionary of curious and interesting geometry, Penguin Books (1991).Google Scholar

References

1. Bradley, C. J. Cyclic quadrilaterals, Math. Gaz. 88, (November 2004) pp. 417–431.Google Scholar
2. Yiu, P. Notes on Euclidean Geometry, (1998). http://math.Edu/yiu/EuclideanGeometryNotes.pdf.Google Scholar
3. Bennet, D. Dynamic geometry renews interest in an old problem, in Geometry turned on, MAA Notes 41 (1997) pp. 25–28.Google Scholar
4. King, J. Quadrilaterals formed by perpendicular bisectors, in Geometry turned on, MAA Notes 41 (1997) pp. 29–32.Google Scholar
5. Robert, G. Le triangle. Champ d’investigation et de découvertes, Mathématique et pédagogie, 1993, 91, pp. 27–41; 1993, 92, pp. 17–26.Google Scholar
6. De Villiers, M. Generalizations involving maltitudes, Int. J. Math. Educ. Sci. Technol., 30 (1999) pp. 541–548.Google Scholar
7. Honsberger, R. Episodes in nineteenth and twentieth century Euclidean geometry, Washington, DC: Math. Assoc. Amer. (1995).Google Scholar
8. Micale, B. and Pennisi, M. On the altitudes of quadrilaterals, Int. J. Math. Educ. Sci. Technol. 36, no. 1 (2005) pp. 15–24.Google Scholar
9. Mammana, C. and Micale, B. Una classificazione affine dei quadrilateri, La Matemàtica e la sua Didattica (1999) no. 3, pp. 323–328.Google Scholar