A simple proof is presented of a famous, and difficult, theorem by Jakob Steiner. By means of a straightforward transformation of the triangle, the proof of the theorem is reduced to the case of the equilateral triangle. Several relations of the Steiner deltoid with the Feuerbach circle and the Morley triangle appear then as obvious.
Se presenta una demostración sencilla de un teorema famoso, y difícil, de Jakob Steiner. Mediante una transformación muy directa del triángulo, la demostración del teorema se reduce al caso del triángulo equilátero. Diversas relaciones de la deltoide de Steiner con la circunferencia de Feuerbach y con el triángulo de Morley aparecen entonces como obvias.
@article{urn:eudml:doc:41600,
title = {The envelope of the Wallace-Simpson lines of a triangle. A simple proof of the Steiner problem on the deltoid.},
journal = {RACSAM},
volume = {95},
year = {2001},
pages = {57-64},
zbl = {1022.51014},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41600}
}
Guzmán, Miguel de. The envelope of the Wallace-Simpson lines of a triangle. A simple proof of the Steiner problem on the deltoid.. RACSAM, Tome 95 (2001) pp. 57-64. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41600/