Using Direct and Contructive Methods for the Existence of Origami Models with Given Boundary Conditions
Whenever a unit square is folded to create an origami model in threedimensional space, the edge of the paper forms a closed curve in space with a total length equal to four units. In this paper, some of the restrictions applicable to such resulting closed curves are derived in the case of classic or...
Guardado en:
Autores principales: | , |
---|---|
Formato: | info:eu-repo/semantics/article |
Lenguaje: | spa |
Publicado: |
Universidad Antonio Nariño
2023
|
Materias: | |
Acceso en línea: | https://revistas.uan.edu.co/index.php/espaciomatematico/article/view/1626 https://repositorio.uan.edu.co/handle/123456789/11569 |
Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
_version_ | 1812671671945920512 |
---|---|
author | Geretschläger, Robert Keeling, Stephen L. |
author_facet | Geretschläger, Robert Keeling, Stephen L. |
author_sort | Geretschläger, Robert |
collection | DSpace |
description | Whenever a unit square is folded to create an origami model in threedimensional space, the edge of the paper forms a closed curve in space with a total length equal to four units. In this paper, some of the restrictions applicable to such resulting closed curves are derived in the case of classic origami models, in which none of the sections of the folded paper is curvedin any way. This allows us to restrict the methods applied to those of classic euclidean geometry. Noting that it is of interest to determine origami models whose edges coincide with a polyline fullling the required conditions, we then proceed to show some methods for reconstructing the origami model if the boundary is known. Finally, some concrete reconstructions are demonstrated. |
format | info:eu-repo/semantics/article |
id | repositorio.uan.edu.co-123456789-11569 |
institution | Repositorio Digital UAN |
language | spa |
publishDate | 2023 |
publisher | Universidad Antonio Nariño |
record_format | dspace |
spelling | repositorio.uan.edu.co-123456789-115692024-10-11T20:03:51Z Using Direct and Contructive Methods for the Existence of Origami Models with Given Boundary Conditions Uso de métodos directos y constructivos para la existencia de modelos de origami con condiciones límite dadas Geretschläger, Robert Keeling, Stephen L. origami reconstrucción problema inverso origami reconstruction inverse problem Whenever a unit square is folded to create an origami model in threedimensional space, the edge of the paper forms a closed curve in space with a total length equal to four units. In this paper, some of the restrictions applicable to such resulting closed curves are derived in the case of classic origami models, in which none of the sections of the folded paper is curvedin any way. This allows us to restrict the methods applied to those of classic euclidean geometry. Noting that it is of interest to determine origami models whose edges coincide with a polyline fullling the required conditions, we then proceed to show some methods for reconstructing the origami model if the boundary is known. Finally, some concrete reconstructions are demonstrated. Siempre que una unidad cuadrada se pliega para crear un modelo de origami en un espacio tridimensional, el borde del papel forma una curva cerrada en el espacio con una longitud total igual a cuatro unidades. En este trabajo, algunas de las restricciones aplicables a estas curvas cerradas resultantes se derivan en el caso de los modelos clásicos de origami, en los que ninguna de las secciones del papel plegado está curvada de ninguna manera. Esto nos permite restringir los métodos aplicados a los de la geometría clásica euclídea. Observando que es de interés determinar modelos de origami cuyos bordes coincidan con una polilínea que cumpla con las condiciones requeridas, procedemos a mostrar algunos métodos para reconstruir el modelo de origami si se conocen los límites. Finalmente, se muestran algunas reconstrucciones concretas. 2023-09-25 2024-10-11T20:03:51Z 2024-10-11T20:03:51Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Artículo revisado por pares https://revistas.uan.edu.co/index.php/espaciomatematico/article/view/1626 10.48082/espmat-v01n01a20p05 https://repositorio.uan.edu.co/handle/123456789/11569 spa https://revistas.uan.edu.co/index.php/espaciomatematico/article/view/1626/1246 Derechos de autor 2023 Espacio Matemático application/pdf Universidad Antonio Nariño ESPACIO MATEMÁTICO Journal; Vol. 1 No. 1 (2020); 54-71 Espacio Matemático; Vol. 1 Núm. 1 (2020); 54-71 ESPACIO MATEMÁTICO; Vol. 1 No 1 (2020); 54-71 Revista Espacio Matemático; v. 1 n. 1 (2020); 54-71 2711-1792 10.48082/em.v1i1 |
spellingShingle | origami reconstrucción problema inverso origami reconstruction inverse problem Geretschläger, Robert Keeling, Stephen L. Using Direct and Contructive Methods for the Existence of Origami Models with Given Boundary Conditions |
title | Using Direct and Contructive Methods for the Existence of Origami Models with Given Boundary Conditions |
title_full | Using Direct and Contructive Methods for the Existence of Origami Models with Given Boundary Conditions |
title_fullStr | Using Direct and Contructive Methods for the Existence of Origami Models with Given Boundary Conditions |
title_full_unstemmed | Using Direct and Contructive Methods for the Existence of Origami Models with Given Boundary Conditions |
title_short | Using Direct and Contructive Methods for the Existence of Origami Models with Given Boundary Conditions |
title_sort | using direct and contructive methods for the existence of origami models with given boundary conditions |
topic | origami reconstrucción problema inverso origami reconstruction inverse problem |
url | https://revistas.uan.edu.co/index.php/espaciomatematico/article/view/1626 https://repositorio.uan.edu.co/handle/123456789/11569 |
work_keys_str_mv | AT geretschlagerrobert usingdirectandcontructivemethodsfortheexistenceoforigamimodelswithgivenboundaryconditions AT keelingstephenl usingdirectandcontructivemethodsfortheexistenceoforigamimodelswithgivenboundaryconditions AT geretschlagerrobert usodemetodosdirectosyconstructivosparalaexistenciademodelosdeorigamiconcondicioneslimitedadas AT keelingstephenl usodemetodosdirectosyconstructivosparalaexistenciademodelosdeorigamiconcondicioneslimitedadas |