An interpretation of a Nguyen perspector

David Nguyen is an optometrist from Sydney who is very fruitful in discovering concurrences in the also fruitful world of Triangle Geometry. We give an interpretation to one of his recent findings.

An interpretation of a Nguyen perspector

Another relationship between Napoleon cubic and Neuberg cubic

The world of Triangle Geometry is very intrincate. There are many paths that lead to the same place.

In this case a problem from proposed by Benjamin L. Warren at  Euclid 8052 and later expanded by Antreas Hatzipolakis lead to a relationship between these two cubics.

Another relationship between Napoleon cubic and Neuberg cubic

 

La página web de Triángulos Cabri

El Laboratorio Virtual de Triángulos con Cabri fue un sitio web dedicado a la resolución de problemas relacionados con el triángulo.

Estaba dirigida por el profesor Ricardo Barroso Campos y estuvo activa desde 2000 a 2023.

Aunque el sitio ha desaparecido, queda una copia de seguridad en un archivo comprimido. Me tomado, con mucho agrado, la molestia de editar los enlaces que apuntaban a direcciones de la web original a archivos que pueden verse localmente.

Naturalmente habrá errores, algún archivo que falte, etc. Si ves alguno, comunícamelo a 'garciacapitan arroba gmail punto com' para intentar subsanarlo.

Dedicado al profesor Ricardo Barroso Campos y a la gran cantidad de entusiastas que disfrutamos y aprendimos durante todos esos años.

NTC20250219.zip (636 Mb)

Constant angles from the vertices to two cubics

 This is an ancient question that easily can call your attention (Journal de Mathématiques Élémentaires, 1893, p. 254):

We solve it by using barycentric coordinates. Any of the points describe a cubic.

Read the details here. Calculations with barycentric coordinates and Mathematica and comments in Spanish are here.

Triangle with integer sides

 A misunderstanding of a problem lead to this study of tangents to an excircle

Triangle with integer sides

Trilinear Polars of Brocardians Revisited

Fifteen years ago (in 2009) my article Trilinear Polars of Brocardians was published in Forum Geometricorum. We now give a general construction for the case when the two trilinear polars are perpendicular to each oher and some new properties of the configuration.

PDF: Trilinear Polars of Brocardians Revisited

Jean-Pierre Ehrmann

Es triste escribir que el gran geómetra Jean-Pierre Ehrmann falleció en enero de 2024.

Estos son sus artículos en Forum Geometricorum. Los puedes descargar todos aquí

•  (with B. Gibert) A Morley configuration, 1 (2001) 51--58.
• (with B. Gibert) The Simson cubic, 1 (2001) 107--114.
• A pair of Kiepert hyperbolas, 2 (2002) 1--4.
• Congruent inscribed rectangles, 2 (2002) 15--19.
• (with F. M. van Lamoen) The Stammler circles, 2 (2002) 151--161.
• (with F. M. van Lamoen) Some similarities associated with pedals, 2 (2002) 163--166.
• Similar pedal and cevian triangles, 3 (2003) 101--104.
• Steiner's theorems on the complete quadrilateral, 4 (2004) 35--52.
• (with F. M. van Lamoen) A projective generalization of the Droz-Farny line theorem, 4 (2004) 225--227.
• Some geometric constructions, 6 (2006) 327--334.
• (with H. Connelly and N. Dergiades) Construction of triangle from a vertex and the feet of two angle bisectors, 7 (2007) 103--106.
• Constructive solution of a generalization of Steinhaus' problem on partition of a triangle, 7 (2007) 187--190.
• An affine variant of a Steinhaus problem, 8 (2008) 1--5.
• (with F. J. García Capitán and A. Myakishev) Construction of circles through intercepts to paralells to cevians, 11 (2011) 261--268.