{"id":13859,"date":"2021-05-01T07:00:00","date_gmt":"2021-05-01T11:00:00","guid":{"rendered":"https:\/\/mathemalchemy.org\/2021\/05\/01\/proyecciones-estereograficas\/"},"modified":"2025-05-03T08:07:37","modified_gmt":"2025-05-03T12:07:37","slug":"proyecciones-estereograficas","status":"publish","type":"post","link":"https:\/\/mathemalchemy.org\/es\/2021\/05\/01\/proyecciones-estereograficas\/","title":{"rendered":"Proyecciones estereogr\u00e1ficas"},"content":{"rendered":"\n<h2 class=\"has-large-font-size wp-block-heading\">Vea la cr\u00f3nica en v\u00eddeo de Henry Segerman<\/h2>\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"900\" height=\"507\" src=\"https:\/\/www.youtube.com\/embed\/8QQywzbGAU8?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=es-ES&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n<h2 class=\"wp-block-heading\">Lea la transcripci\u00f3n del v\u00eddeo<\/h2>\n\n<h3 class=\"has-large-font-size wp-block-heading\">Sobre Mathemalchemy<\/h3>\n\n<p>Hola, soy Henry Segerman,<\/p>\n\n<p>Durante el \u00faltimo a\u00f1o y pico, he estado trabajando con un equipo de <a href=\"https:\/\/mathemalchemy.org\/team-23-mathematicians-artists-of-mathemalchemy\/\">otros 24 matem\u00e1ticos y artistas matem\u00e1ticos<\/a> para crear una gran instalaci\u00f3n art\u00edstica multimedia que celebre la creatividad y la belleza de las matem\u00e1ticas. El proyecto est\u00e1 dirigido por <a href=\"https:\/\/mathemalchemy.org\/team-23-mathematicians-artists-of-mathemalchemy\/#Ingrid-Daubechies\">Ingrid Daubechies<\/a>, matem\u00e1tica de la Universidad de Duke, y <a href=\"https:\/\/mathemalchemy.org\/team-23-mathematicians-artists-of-mathemalchemy\/#Dominique-Ehrmann\">Dominique Ehrmann<\/a>, artista textil residente en Canad\u00e1. <\/p>\n\n<p>Todo empez\u00f3 cuando Ingrid vio la instalaci\u00f3n de Dominique<a href=\"http:\/\/dominiquehrmann.com\/en\/timetobreakfree\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u00abTime to Break Free<\/a>\u00ab, en la que una especie de \u00abm\u00e1quina\u00bb convierte figuras planas sobre un quilt en personajes totalmente tridimensionales.<\/p>\n\n<p>Esto inspir\u00f3 a Ingrid a preguntarse si algo as\u00ed podr\u00eda dar vida de forma similar a la belleza y la creatividad de las ideas matem\u00e1ticas.<\/p>\n\n<p>Ingrid y Dominique hicieron una presentaci\u00f3n en la <a href=\"https:\/\/jointmathematicsmeetings.org\/jmm\">Reuni\u00f3n Conjunta de Matem\u00e1ticas<\/a> en enero de 2020, y se form\u00f3 un grupo en torno a la idea, llamado \u00abMathemalchemy\u00bb, que ahora cuenta con <a href=\"https:\/\/mathemalchemy.org\/team-23-mathematicians-artists-of-mathemalchemy\/\">24 matem\u00e1ticos y artistas<\/a> involucrados.<\/p>\n\n<figure class=\"wp-block-image size-large coblocks-animate\" data-coblocks-animation=\"fadeIn\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"499\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/tour-67-e1601858479125-1024x568.jpg?resize=900%2C499&#038;ssl=1\" alt=\"\" class=\"wp-image-694\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/tour-67-e1601858479125.jpg?resize=1024%2C568&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/tour-67-e1601858479125.jpg?resize=300%2C166&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/tour-67-e1601858479125.jpg?resize=768%2C426&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/tour-67-e1601858479125.jpg?resize=1536%2C852&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/tour-67-e1601858479125.jpg?resize=1200%2C666&amp;ssl=1 1200w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/tour-67-e1601858479125.jpg?w=1564&amp;ssl=1 1564w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption>Maqueta final de Mathemalchemy<\/figcaption><\/figure>\n\n<p>\u00c9sta es la <a href=\"https:\/\/mathemalchemy.org\/2020\/11\/12\/the-maquettes-creation-process\/\">maqueta actual a escala 1\/4<\/a> de la pieza: una isla m\u00e1gica llena de escenas caprichosas, hecha de :<\/p>\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<ul class=\"wp-block-list\"><li>ganchillo,<\/li><li>tejido de punto,<\/li><li>quilting,<\/li><li>costura,<\/li><li>tejido en telar,<\/li><li>trabajo con cuentas,<\/li><li>lana fieltrada con aguja,<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<ul class=\"wp-block-list\"><li>bordado,<\/li><li>carpinter\u00eda,<\/li><li>cer\u00e1mica,<\/li><li>arcilla polim\u00e9rica,<\/li><li>Impresi\u00f3n 3D,<\/li><li>pintura,<\/li><li>vitrales,<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<ul class=\"wp-block-list\"><li>soldadura de acero,<\/li><li>acr\u00edlico,<\/li><li>doblado de alambre,<\/li><li>origami,<\/li><li>temari,<\/li><li>cuero,<\/li><li>luz.<\/li><\/ul>\n<\/div>\n<\/div>\n\n<div class=\"wp-block-cover alignfull has-parallax\" style=\"background-image:url(https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/04\/mathemalchemy-techniques-gallery.jpg);min-height:900px;aspect-ratio:unset;\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-primary-color has-background-background-color has-text-color has-background has-huge-font-size\">All\u00ed donde cabe una idea o referencia matem\u00e1tica, la hemos ido encajando.<\/p>\n<\/div><\/div>\n\n<p><br\/>La instalaci\u00f3n permanente de MatemAlquimia estar\u00e1 en <a href=\"https:\/\/www.duke.edu\/\" target=\"_blank\" rel=\"noreferrer noopener\">la Universidad de Duke<\/a>, pero tambi\u00e9n saldr\u00e1 de gira, con paradas previstas en la <a href=\"http:\/\/www.nasonline.org\/\" target=\"_blank\" rel=\"noreferrer noopener\">Academia Nacional de Ciencias<\/a> de Washington DC, as\u00ed como en otros lugares internacionales (todo ello pendiente de posibles trastornos debidos a la pandemia).<\/p>\n\n<h2 class=\"has-huge-font-size wp-block-heading\">Proyecci\u00f3n estereogr\u00e1fica<\/h2>\n\n<p>Una de las escenas matem\u00e1ticas en las que he participado es el faro. La parte superior del faro tendr\u00e1 dos luces: una proyect\u00e1ndose horizontalmente desde el interior de un <a href=\"https:\/\/mathemalchemy.org\/2021\/01\/19\/dodecahedral-trajectory\/\">dodecaedro de<\/a> vitral realizado por <a href=\"https:\/\/mathemalchemy.org\/team-23-mathematicians-artists-of-mathemalchemy\/#Bronna-Butler\">Bronna Butler<\/a>, y la otra proyect\u00e1ndose hacia el techo. <\/p>\n\n<p>Esto reutilizar\u00e1 un antiguo proyecto m\u00edo que ilustra algo llamado proyecci\u00f3n estereogr\u00e1fica. La proyecci\u00f3n estereogr\u00e1fica es un mapa de la esfera al plano. As\u00ed que, al igual que la proyecci\u00f3n de Mercator es una forma de obtener los continentes del globo terr\u00e1queo en un trozo de papel plano; la proyecci\u00f3n estereogr\u00e1fica es otra forma de hacerlo.  <\/p>\n\n<figure class=\"wp-block-image size-large coblocks-animate\" data-coblocks-animation=\"fadeIn\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"663\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/04\/stereographic-projection-mathemalchemy-art-project.jpg?resize=900%2C663&#038;ssl=1\" alt=\"\" class=\"wp-image-2555\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/04\/stereographic-projection-mathemalchemy-art-project.jpg?w=1000&amp;ssl=1 1000w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/04\/stereographic-projection-mathemalchemy-art-project.jpg?resize=300%2C221&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/04\/stereographic-projection-mathemalchemy-art-project.jpg?resize=768%2C566&amp;ssl=1 768w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption>Proyecci\u00f3n estereogr\u00e1fica<\/figcaption><\/figure>\n\n<p>En el modelo, lo que ocurre es que el rayo de luz comienza en el polo norte de la esfera, se dirige al interior de la esfera, golpea la esfera desde el interior en alguna parte y luego contin\u00faa hasta golpear el plano en alguna parte.<\/p>\n\n<p>Y \u00e9se es el mapeo. Lo hacen los rayos de luz. El punto donde la luz incide en la esfera se mapea al punto donde incide en el plano.<\/p>\n\n<p>Y puede ver lo que hace la proyecci\u00f3n estereogr\u00e1fica con s\u00f3lo mirar la sombra. Por ejemplo, los tri\u00e1ngulos del centro tienen aproximadamente el mismo tama\u00f1o que los tri\u00e1ngulos de la esfera, pero a medida que se aleja, empiezan a ser mucho m\u00e1s grandes. Y hay muchas otras caracter\u00edsticas interesantes de la proyecci\u00f3n estereogr\u00e1fica, por ejemplo: los \u00e1ngulos se conservan, todos los \u00e1ngulos de noventa y sesenta grados de la esfera aparecen como de noventa y sesenta grados en la sombra. Adem\u00e1s, c\u00edrculos se mapean a c\u00edrculos. Todos los c\u00edrculos de la esfera se mapean a c\u00edrculos en el plano.    <\/p>\n\n<p>La sombra es muy sensible a d\u00f3nde est\u00e1 la luz con respecto a la esfera, pero no es demasiado sensible a d\u00f3nde est\u00e1 la mesa. Por tanto, si muevo la esfera y la luz hacia arriba, alej\u00e1ndolas de la mesa, lo \u00fanico que ocurre es que la sombra aumenta de tama\u00f1o, no cambia en nada la imagen. Esto nos viene bien porque en el faro la luz apuntar\u00e1 hacia arriba proyectando la sombra sobre el techo y como la instalaci\u00f3n estar\u00e1 en muchos lugares distintos no hay forma de saber a qu\u00e9 altura estar\u00e1 el techo.  <\/p>\n\n<p>Tenemos prevista una segunda versi\u00f3n por si fuera necesario. Si el techo es demasiado alto en alg\u00fan local, puede que el patr\u00f3n se crezca demasiado y la mayor parte se proyecte en las paredes. El patr\u00f3n seguir\u00eda siendo visible, pero la sombra en las paredes no tendr\u00e1 todas las bonitas propiedades de la proyecci\u00f3n estereogr\u00e1fica. Nuestro plan en este caso es utilizar un patr\u00f3n de sombra diferente que proyecte el modelo de disco de Poincar\u00e9 del plano hiperb\u00f3lico sobre un disco. Este modelo s\u00f3lo utiliza un cono de luz de 90 grados que se proyectar\u00e1 sobre un parche m\u00e1s peque\u00f1o, en lugar de los 180 grados que se utilizan en la esfera completa de la proyecci\u00f3n estereogr\u00e1fica.    <\/p>\n\n<figure class=\"wp-block-image size-large coblocks-animate\" data-coblocks-animation=\"fadeIn\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"669\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/04\/poincare-stereographic-projection-mathemalchemy-art-project.jpg?resize=900%2C669&#038;ssl=1\" alt=\"\" class=\"wp-image-2557\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/04\/poincare-stereographic-projection-mathemalchemy-art-project.jpg?w=1000&amp;ssl=1 1000w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/04\/poincare-stereographic-projection-mathemalchemy-art-project.jpg?resize=300%2C223&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/04\/poincare-stereographic-projection-mathemalchemy-art-project.jpg?resize=768%2C571&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/04\/poincare-stereographic-projection-mathemalchemy-art-project.jpg?resize=200%2C150&amp;ssl=1 200w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption>Modelo de disco de Poincar\u00e9<\/figcaption><\/figure>\n\n<p>Muy bien, \u00e9sa es la esfera de la parte superior del faro. El plan es que el montaje de todas las partes de la instalaci\u00f3n construidas de forma independiente tenga lugar en julio de este a\u00f1o, as\u00ed que \u00a1esperamos que haya m\u00e1s que contar! <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mire la cr\u00f3nica en v\u00eddeo de Henry Segerman. <\/p>\n<p>Una de las escenas matem\u00e1ticas en las que he participado es el faro. La parte superior del faro tendr\u00e1 dos luces: una proyect\u00e1ndose horizontalmente desde el interior de un dodecaedro de vidrieras realizado por Bronna Butler, y la otra proyect\u00e1ndose hacia el techo. <\/p>\n<p>Esto reutilizar\u00e1 un antiguo proyecto m\u00edo que ilustra algo llamado proyecci\u00f3n estereogr\u00e1fica. La proyecci\u00f3n estereogr\u00e1fica es un mapeo de la esfera al plano. As\u00ed que, al igual que el mapeo de Mercator es una forma de obtener los continentes del globo terr\u00e1queo en un trozo de papel plano; la proyecci\u00f3n estereogr\u00e1fica es otra forma de hacerlo.  <\/p>\n","protected":false},"author":44503789,"featured_media":13860,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[6325],"tags":[],"class_list":["post-13859","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-non-classe","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Proyecciones estereogr\u00e1ficas - Mathemalchemy<\/title>\n<meta name=\"description\" content=\"Mire la cr\u00f3nica en v\u00eddeo de Henry Segerman sobre su asombrosa proyecci\u00f3n estereogr\u00e1fica. 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