My solution to Euclid 2066

 This is my solution to Problem Euclid 2066 by Antreas Hatzipolakis. The solution contains a conic and a cubic and several new triangle centers.

Solution

The conic:

The cubic:

Revista Escolar de la Olimpiada Iberoamericana de Matemáticas

Pongo aquí enlaces a mis artículos publicados en la desaparecida Revista Escolar de la Olimpiada Iberoamericana de Matemáticas dirigida durante años por el profesor Francisco Bellot Rosado:

• Inversión en Olimpiadas (Aplicación de la inversión a la resolución de problemas)
• Lectura atenta del Court:
  • Catorce Problemas del Court
  • El triángulo órtico
  • La recta de Simson en el Court
• Ángulos e inversión
• Un problema del Sidler
• Algunas homografías en el triángulo
• Máximos sin derivadas

(22/07/2022) ¡Novedad! Todos los archivos de la la Revista pueden descargarse aquí: REOIM.ZIP (100 Mb).

Coordenadas baricéntricas

Barycentric coordinates allow you easily make calculations in triangle geometry. A document on barycentric coordinates (Spanish). cb.pdf This document come from a reading of the book Introduction to the Geometry of the Triangle by Paul Yiu. We solve some of the proposed exercises and we include some examples of other sources. Some Mathematica routines to work on barycentric coordinates.  baricentricas.nb Installation: Copy the notebook into a directory where Mathematica can find it, such as the AddOns\ExtraPackages. In a standard Windows installation this can be the directory C:\Archivos de programa\Wolfram Research\Mathematica\5.2\AddOns\ExtraPackages Open and execute the notebook on that location. A file baricentricas.m will be generated Now you can call the routines in baricentricas.nb from any other notebook by entering the command <<Baricentricas`;

Links related to Triangle Geometry

Encyclopedia of Triangle Centers

https://faculty.evansville.edu/ck6/encyclopedia/

Laboratorio Virtual de Triángulos con Cabri (cerrado) (ZIP, 636 Mb)

Forum Geometricorum (Almost closed, closed)

http://forumgeom.fau.edu/ Download the archives here

Catalogue of Triangle Cubics

http://bernard-gibert.fr

euclid

https://groups.io/g/euclid

Hyacinthos (Closed):

Link to archive: Hyacinthos.rar

ADGEOM (Closed):

Link to archive: ADGEOM.rar

Sites by Cesar Lozada:

ADGEOM: http://adgeom.epizy.com/ ANOPOLIS: http://anopolis.epizy.com/ HYACINTHOS : http://hyacinthos.epizy.com/ QUADRI-FIGURES: http://qfg.epizy.com/ Triangles relations: http://cesarlozada.epizy.com/

A locus of triangles

 We study the set of all triangles such that $a^2 = b(b+c)$.

Download: A locus of triangles

About the Parallel-Side Projected Triangle

 Let $ABC$ be a triangle and call $A'$ the intersection of the circumcircle and the line through $A$ parallel to BC. Define $B'$, $C'$ cyclically. We call $A'B'C'$ the parallel-side projected triangle and study some of their properties.

Download: About the Parallel-Side Projected Triangle

Problemas y Soluciones - Volumen 1

Descarga: Problemas y Soluciones - Volumen 1

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