Artisan procedures to generate uniform tilings

Fernández Cabo, Miguel Carlos (2014). Artisan procedures to generate uniform tilings. "International Mathematical Forum", v. 9 (n. 23); pp. 1109-1130. ISSN 1314-7536. https://doi.org/10.12988/imf.2014.45103.

Description

Title: Artisan procedures to generate uniform tilings
Author/s:
  • Fernández Cabo, Miguel Carlos
Item Type: Article
Título de Revista/Publicación: International Mathematical Forum
Date: 2014
ISSN: 1314-7536
Volume: 9
Subjects:
Freetext Keywords: Tessellations, tilings, ornament, regular polygons, ornamental patterns, ornamental geometry
Faculty: E.T.S. Arquitectura (UPM)
Department: Construcción y Tecnología Arquitectónica
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

This paper try to prove how artisans c ould discover all uniform tilings and very interesting others us ing artisanal combinatorial pro cedures without having to use mathematical procedures out of their reac h. Plane Geometry started up his way through History by means of fundamental drawing tools: ruler and co mpass. Artisans used same tools to carry out their orna mental patterns but at some point they began to work manually using physical representations of fi gures or tiles previously drawing by means of ruler and compass. That is an important step for craftsman because this way provides tools that let him come in the world of symmetry opera tions and empirical knowledge of symmetry groups. Artisans started up to pr oduce little wooden, ceramic or clay tiles and began to experiment with them by means of joining pieces whether edge to edge or vertex to vertex in that way so it can c over the plane without gaps. Economy in making floor or ceramic tiles could be most important reason to develop these procedures. This empiric way to develop tilings led not only to discover all uniform tilings but later discovering of aperiodic tilings.

More information

Item ID: 36143
DC Identifier: http://oa.upm.es/36143/
OAI Identifier: oai:oa.upm.es:36143
DOI: 10.12988/imf.2014.45103
Official URL: http://www.m-hikari.com/imf.html
Deposited by: Memoria Investigacion
Deposited on: 08 Jul 2015 08:00
Last Modified: 08 Jul 2015 08:00
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