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# Undergraduate student Juan Fernández González makes math discovery

Published: 20 December 2018

One year ago, the Bulletin AMQ of the Association Mathématique du Québec published the article Le polygone du cercle d’Euler (The Polygon of Euler’s Circle). Written by third-year student Juan Fernández González, it defines and explores a convex polygon that can be associated to any triangle.

The geometry discovery started while drawing different forms for Prof. David Covo’s cardboard chair design project, and evolved while drawing in the Montreal metro and buses, amongst other places. “You should keep your eyes open because inspiration can come from anywhere. However, you should close your eyes from time to time! The weirdest ideas and solutions often came to me while falling asleep. When you are obsessed with a problem, your subconscious can give you an answer when you least expect it,” explains the student.

Juan sees some similarities between a math discovery and his approach to an architecture project: they both start with a very imaginative, dream-like phase, which is followed by a very rational, rigorous phase.

This is Juan’s second published article. The findings from the first article, Chemins homothétiques (Bulletin AMQ, LVI, no 2, May 2016), were illustrated in his entrance portfolio to the School of Architecture. Amongst other things, it shows a way of multiplying the length of a line segment by 0<r/s<1, a rational number, by constructing only midpoints and a straight line. He is currently working on new discoveries.

The images below illustrate the proof of one of the theorems which deals with the triangulation of regular polygons. The article can be read online at the following address: https://www.amq.math.ca/wp-content/uploads/bulletin/vol57/no4/05-Polygone-du-cercle-dEuler-2.pdf