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Euler and triangle geometry

Published online by Cambridge University Press:  01 August 2016

Gerry Leversha  and
G. C. Smith
Gerry Leversha
Affiliation:
St Paul's School, Lonsdale Road, London SW13 9JT, e-mail: g.leversha@btinternet.com
G. C. Smith
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY e-mail: G.C.Smith@bath.ac.uk
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Extract

There is a very easy way to produce the Euler line, using transformational arguments. Given a triangle ABC, let AʹBʹ'C be the medial triangle, whose vertices are the midpoints of the sides. These two triangles are homothetic: they are similar and corresponding sides are parallel, and the centroid, G, is their centre of similitude. Alternatively, we say that AʹBʹC can be mapped to ABC by means of an enlargement, centre G, with scale factor –2.

Type
Articles
Information
The Mathematical Gazette , Volume 91 , Issue 522 , November 2007 , pp. 436 - 452
Copyright
Copyright © The Mathematical Association 2007

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References

1. Dunham, William Euler, the master of us all, MAA (1999).Google Scholar
2. Euler, Leonhard Solutio facili problematum geometricum difficillimorum, reprinted in Speiser, A. (editor) Opera Omnia, serie prima, Vol. 26, pp. 139–157.Google Scholar
3. Kimberling, Clark Triangle centers and central triangles, Congressum Numerantium, 129, Winnipeg (1998).Google Scholar
4. Guinand, A. P. Tritangent centers and their triangles, American Mathematical Monthly, 91, (1984) pp. 290–300.Google Scholar
5. Weisstein, E. W. http://mathworld.wolfram.com/ Google Scholar
6. Johnson, Roger A. Advanced Euclidean geometry, Dover (1960).Google Scholar
7. Bradley, C. J. Challenges in geometry, Oxford University Press (2005).Google Scholar
8. Bradley, C. J. The algebra of geometry, Highperception (2007).Google Scholar
9. Smith, G. C. Statics and the moduli space of triangles, Forum. Geom., 5 (2005) pp. 181–190.Google Scholar
10. Gardiner, A. D. and Bradley, C. J. Plane Euclidean geometry, UKMT (2005).Google Scholar
11. Posamentier, Alfred S. Advanced Euclidean geometry, Key College Publishing (2002).Google Scholar
12. Stern, J. Euler’s triangle determination problem, Forum. Geom. 7 (2007) pp. 1–9.Google Scholar