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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: [email protected]
G. C. Smith
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY e-mail: [email protected]
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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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