Geometry

   

Continuidad Limitada en el Cubo (Limited Continuity in the Cube)

Authors: Carlos Alejandro Chiappini

He intentado construir una antena con forma de cubo. La idea era construirla con un alambre continuo, sin cortes ni interrupciones, que recorriese las aristas una a una. Me sorprendió el hecho siguiente. Sin cortar el alambre y sin pasar más de una vez por alguna arista me resultó imposible formar más de 9 aristas. Muchos intentos me convencieron de la imposibilidad práctica. Eso despertó el interés por averiguar algo respecto a eso en términos teóricos, sea por geométría, por topología o por combinación de ambas.Mis habilidades en geometría son escasas y en topología nulas. Me gustaría recibir la noticia de una demostración teórica del hecho mencionado. Por eso he redactado esta nota y porque puede brindar entretenimiento a personas amantes de la geometría y de la topología.

I have tried to build a cube shaped antenna. The idea was to build it with a continuous wire, without cuts or interruptions, that ran through the edges one by one. I was surprisedthe following fact. Without cutting the wire and without going over any edge more than once, was impossible to form more than 9 edges. Many attempts convinced me of thepractical impossibility. That aroused interest in finding out something about it intheoretical terms, either by geometry, by topology or by a combination of both.My skills in geometry are poor and in topology null. I would like to receive the news of a theoretical proof of the mentioned fact. That is why I have written this note and because it can provide entertainment for people who love geometry and topology.

Comments: 2 Pages. Email: carloschiappini@gmail.com

Download: PDF

Submission history

[v1] 2022-11-29 03:00:57

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