{"id":13899,"date":"2021-01-19T10:05:00","date_gmt":"2021-01-19T15:05:00","guid":{"rendered":"https:\/\/mathemalchemy.org\/2021\/01\/19\/trayectoria-dodecaedrica\/"},"modified":"2026-01-16T20:15:47","modified_gmt":"2026-01-17T01:15:47","slug":"trayectoria-dodecaedrica","status":"publish","type":"post","link":"https:\/\/mathemalchemy.org\/es\/2021\/01\/19\/trayectoria-dodecaedrica\/","title":{"rendered":"Trayectoria dodeca\u00e9drica"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-normal-font-size\">Presentado por Bronna Butler<\/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\/DwdGau6jIqs?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 has-large-font-size\">Transcripci\u00f3n del v\u00eddeo de la Trayectoria Dodeca\u00e9drica<\/h2>\n\n<h3 class=\"wp-block-heading\">Sobre Bronna Butler<\/h3>\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<p>Hola, me llamo <a href=\"https:\/\/mathemalchemy.org\/team-23-mathematicians-artists-of-mathemalchemy\/#Bronna-Butler\">Bronna Butler<\/a>. Soy artista profesional desde hace 23 a\u00f1os. Tengo una licenciatura en arte y un m\u00e1ster en contabilidad\/finanzas, por la Universidad de Missouri. Trabajo con vitrales, pinturas al \u00f3leo y al pastel, grafito, acero inoxidable y, recientemente, un poco de electr\u00f3nica. He dise\u00f1ado y pintado m\u00e1s de <g id=\"gid_1\">900 pies cuadrados de vitrales<\/g> en varios edificios. Dise\u00f1\u00e9 y dirig\u00ed la fabricaci\u00f3n e instalaci\u00f3n de un monumento de acero inoxidable de 6 metros de altura con 4 paneles de fotomontaje de titanio coloreado, y he pintado cientos de \u00f3leos y pasteles grandes y peque\u00f1os por encargo; el \u00f3leo m\u00e1s grande era de 8 x 12 pies, que pint\u00e9 de pie sobre un andamio.     <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"900\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/bronna-butler-mathmalchemy-art-project-collaboration-mathematics.jpg?resize=900%2C900&#038;ssl=1\" alt=\"Bronna Butler\" class=\"wp-image-490\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/bronna-butler-mathmalchemy-art-project-collaboration-mathematics.jpg?w=900&amp;ssl=1 900w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/bronna-butler-mathmalchemy-art-project-collaboration-mathematics.jpg?resize=300%2C300&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/bronna-butler-mathmalchemy-art-project-collaboration-mathematics.jpg?resize=150%2C150&amp;ssl=1 150w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/bronna-butler-mathmalchemy-art-project-collaboration-mathematics.jpg?resize=768%2C768&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/bronna-butler-mathmalchemy-art-project-collaboration-mathematics.jpg?resize=800%2C800&amp;ssl=1 800w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/bronna-butler-mathmalchemy-art-project-collaboration-mathematics.jpg?resize=400%2C400&amp;ssl=1 400w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2020\/09\/bronna-butler-mathmalchemy-art-project-collaboration-mathematics.jpg?resize=200%2C200&amp;ssl=1 200w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption class=\"wp-element-caption\">Bronna Butler &#8211; Headshot por Pat Paul Photography \u00a9 2019<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n<p>Desde 2015, mi musa son las matem\u00e1ticas. Mi <a href=\"https:\/\/www.bronnabutler.com\/home.html\" target=\"_blank\" rel=\"noreferrer noopener\">trabajo actual<\/a> se centra en las matem\u00e1ticas recreativas, los rompecabezas, los enigmas y las ilusiones \u00f3pticas, as\u00ed como en las matem\u00e1ticas y la ciencia en general. <\/p>\n\n<h3 class=\"wp-block-heading\">La aventura de MatemAlquimia comienza<\/h3>\n\n<p>A partir de febrero de 2020, he tenido la maravillosa oportunidad de colaborar con un <a href=\"https:\/\/mathemalchemy.org\/team-23-mathematicians-artists-of-mathemalchemy\/\">equipo de 23 artistas matem\u00e1ticos y matem\u00e1ticos art\u00edsticos<\/a> que est\u00e1n creando una gran instalaci\u00f3n art\u00edstica multimedia, llamada Mathemalchemy. Celebra la creatividad y la belleza de las matem\u00e1ticas. Es la visi\u00f3n de la matem\u00e1tica y f\u00edsica <g id=\"gid_1\">Ingrid Daubechies<\/g>. Con la ayuda de la artista <g id=\"gid_2\">Dominique Ehrmann<\/g>, Ingrid ha guiado la colaboraci\u00f3n en la gran instalaci\u00f3n durante los \u00faltimos diez meses, a trav\u00e9s de Zoom. Tras su finalizaci\u00f3n en 2021, se instalar\u00e1 en varios museos y otros lugares, y despu\u00e9s se instalar\u00e1 permanentemente en el nuevo edificio de Matem\u00e1ticas que proyecta <g id=\"gid_3\">la Universidad de Duke<\/g>. La instalaci\u00f3n incluye un faro de acero inoxidable de 7.5 pies de altura que se apoyar\u00e1 sobre una base de 2 pies. Yo fabriqu\u00e9 su baliza que es un dodecaedro de vitral.      <\/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<div class=\"wp-block-jetpack-tiled-gallery aligncenter is-style-rectangular\"><div class=\"tiled-gallery__gallery\"><div class=\"tiled-gallery__row\"><div class=\"tiled-gallery__col\" style=\"flex-basis:9.925966893905269%\"><figure class=\"tiled-gallery__item\"><img decoding=\"async\" role=\"button\" tabindex=\"0\" aria-label=\"Abrir la imagen 1 de 4 en pantalla completa\"srcset=\"https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/lighthouse-sabetta-matsumoto-mathemalchemy-art-project-1.jpg?strip=info&#038;w=600&#038;ssl=1 600w,https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/lighthouse-sabetta-matsumoto-mathemalchemy-art-project-1.jpg?strip=info&#038;w=752&#038;ssl=1 752w\" alt=\"\" data-height=\"1574\" data-id=\"1691\" data-link=\"https:\/\/mathemalchemy.org\/?attachment_id=1691\" data-url=\"https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/lighthouse-sabetta-matsumoto-mathemalchemy-art-project-1.jpg\" data-width=\"752\" src=\"https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/lighthouse-sabetta-matsumoto-mathemalchemy-art-project-1.jpg?ssl=1\" layout=\"responsive\"><\/figure><\/div><div class=\"tiled-gallery__col\" style=\"flex-basis:90.07403310609472%\"><figure class=\"tiled-gallery__item\"><img decoding=\"async\" role=\"button\" tabindex=\"0\" aria-label=\"Abrir la imagen 2 de 4 en pantalla completa\"srcset=\"https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/lighthouse-beacon-sabetta-matsumoto-bronna-butler-mathemalchemy-art-project.jpg?strip=info&#038;w=600&#038;ssl=1 600w,https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/lighthouse-beacon-sabetta-matsumoto-bronna-butler-mathemalchemy-art-project.jpg?strip=info&#038;w=900&#038;ssl=1 900w\" alt=\"\" data-height=\"751\" data-id=\"1693\" data-link=\"https:\/\/mathemalchemy.org\/?attachment_id=1693\" data-url=\"https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/lighthouse-beacon-sabetta-matsumoto-bronna-butler-mathemalchemy-art-project.jpg\" data-width=\"900\" src=\"https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/lighthouse-beacon-sabetta-matsumoto-bronna-butler-mathemalchemy-art-project.jpg?ssl=1\" layout=\"responsive\"><\/figure><figure class=\"tiled-gallery__item\"><img decoding=\"async\" role=\"button\" tabindex=\"0\" aria-label=\"Abrir la imagen 3 de 4 en pantalla completa\"srcset=\"https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecadron-over-led-light-beacon-bronna-butler-mathemalchemy-art-project.jpg?strip=info&#038;w=600&#038;ssl=1 600w,https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecadron-over-led-light-beacon-bronna-butler-mathemalchemy-art-project.jpg?strip=info&#038;w=900&#038;ssl=1 900w\" alt=\"\" data-height=\"731\" data-id=\"1695\" data-link=\"https:\/\/mathemalchemy.org\/?attachment_id=1695\" data-url=\"https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecadron-over-led-light-beacon-bronna-butler-mathemalchemy-art-project.jpg\" data-width=\"900\" src=\"https:\/\/i1.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecadron-over-led-light-beacon-bronna-butler-mathemalchemy-art-project.jpg?ssl=1\" layout=\"responsive\"><\/figure><figure class=\"tiled-gallery__item\"><img decoding=\"async\" role=\"button\" tabindex=\"0\" aria-label=\"Abrir la imagen 4 de 4 en pantalla completa\"srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/fresnel-lenses-dodecahedron-bronna-butler-mathemalchemy-art-project.jpg?strip=info&#038;w=600&#038;ssl=1 600w,https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/fresnel-lenses-dodecahedron-bronna-butler-mathemalchemy-art-project.jpg?strip=info&#038;w=900&#038;ssl=1 900w\" alt=\"\" data-height=\"588\" data-id=\"1697\" data-link=\"https:\/\/mathemalchemy.org\/?attachment_id=1697\" data-url=\"https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/fresnel-lenses-dodecahedron-bronna-butler-mathemalchemy-art-project.jpg\" data-width=\"900\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/fresnel-lenses-dodecahedron-bronna-butler-mathemalchemy-art-project.jpg?ssl=1\" layout=\"responsive\"><\/figure><\/div><\/div><\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>El faro de acero inoxidable fue dise\u00f1ado por la f\u00edsica <a href=\"https:\/\/mathemalchemy.org\/team-23-mathematicians-artists-of-mathemalchemy\/#Sabetta-Matsumoto\">Sabetta Matsumoto<\/a> y se situar\u00e1 en un extremo de la instalaci\u00f3n.<\/p>\n\n\n\n<p>Como har\u00eda un faro real en funcionamiento, la baliza dodeca\u00e9drica tendr\u00e1 lentes de Fresnel para enfocar la luz, en este caso procedente de un LED, que se muestra aqu\u00ed en nuestro banco de trabajo.<\/p>\n\n\n\n<p>El dodecaedro de cristal encajar\u00e1 encima de las lentes y el LED.<\/p>\n<\/div>\n<\/div>\n\n<p><\/p>\n\n<h3 class=\"wp-block-heading\">Un descubrimiento inspirador sobre el dodecaedro<\/h3>\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<p>En septiembre, Ingrid present\u00f3 al grupo <a href=\"https:\/\/www.quantamagazine.org\/mathematicians-report-new-discovery-about-the-dodecahedron-20200831\/\" target=\"_blank\" rel=\"noreferrer noopener\">un art\u00edculo de la revista \u00abQuanta<\/a> \u00bb sobre el descubrimiento de algo nuevo sobre el dodecaedro. \u00ab<a href=\"https:\/\/www.maa.org\/press\/periodicals\/american-mathematical-monthly\" target=\"_blank\" rel=\"noreferrer noopener\">American Mathematical Monthly<\/a>\u00bb hab\u00eda publicado la prueba de los matem\u00e1ticos Jayadev Athreya y David Aulicino de que existe una trayectoria geod\u00e9sica en el dodecaedro desde un v\u00e9rtice hasta s\u00ed mismo que no pasa por ning\u00fan otro v\u00e9rtice.  <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\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\/G9_l8QASobI?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\n\n<p style=\"font-size:11px\">Jayadev Athreya explica el nuevo descubrimiento sobre los dodecaedros en Numberphile.<\/p>\n<\/div>\n<\/div>\n\n<p>Esto puede demostrarse con la red\/patr\u00f3n desplegado de las caras pentagonales del dodecaedro. Nuestro subgrupo del faro fue un\u00e1nime: la baliza del dodecaedro de la instalaci\u00f3n deber\u00eda \u00abreflejar\u00bb este descubrimiento. <\/p>\n\n<div class=\"wp-block-jetpack-slideshow aligncenter\" data-autoplay=\"true\" data-delay=\"5\" data-effect=\"fade\"><div class=\"wp-block-jetpack-slideshow_container swiper-container\"><ul class=\"wp-block-jetpack-slideshow_swiper-wrapper swiper-wrapper\"><li class=\"wp-block-jetpack-slideshow_slide swiper-slide\"><figure><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"860\" height=\"490\" alt=\"\" class=\"wp-block-jetpack-slideshow_image wp-image-1713\" data-id=\"1713\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecahedron-net-bronna-butler-mathemalchemy-art-project-1.jpg?resize=860%2C490&#038;ssl=1\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecahedron-net-bronna-butler-mathemalchemy-art-project-1.jpg?w=860&amp;ssl=1 860w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecahedron-net-bronna-butler-mathemalchemy-art-project-1.jpg?resize=300%2C171&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecahedron-net-bronna-butler-mathemalchemy-art-project-1.jpg?resize=768%2C438&amp;ssl=1 768w\" sizes=\"(max-width: 860px) 100vw, 860px\" \/><figcaption class=\"wp-block-jetpack-slideshow_caption gallery-caption\">Fotos del video (arriba de la cr\u00f3nica): 1. el dise\u00f1o del art\u00edculo de Quanta se us\u00f3 como patr\u00f3n <\/figcaption><\/figure><\/li><li class=\"wp-block-jetpack-slideshow_slide swiper-slide\"><figure><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"860\" height=\"490\" alt=\"\" class=\"wp-block-jetpack-slideshow_image wp-image-1714\" data-id=\"1714\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecahedron-net-white-area-bronna-butler-mathemalchemy-art-project-1.jpg?resize=860%2C490&#038;ssl=1\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecahedron-net-white-area-bronna-butler-mathemalchemy-art-project-1.jpg?w=860&amp;ssl=1 860w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecahedron-net-white-area-bronna-butler-mathemalchemy-art-project-1.jpg?resize=300%2C171&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecahedron-net-white-area-bronna-butler-mathemalchemy-art-project-1.jpg?resize=768%2C438&amp;ssl=1 768w\" sizes=\"(max-width: 860px) 100vw, 860px\" \/><figcaption class=\"wp-block-jetpack-slideshow_caption gallery-caption\">Fotos del video (arriba de la cr\u00f3nica) 2. de un lado de la l\u00ednea las piezas penatgonales son m\u00e1s claras <\/figcaption><\/figure><\/li><li class=\"wp-block-jetpack-slideshow_slide swiper-slide\"><figure><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"509\" alt=\"\" class=\"wp-block-jetpack-slideshow_image wp-image-1705\" data-id=\"1705\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/stained-glass-dodecahedral-trajectory-bronna-butler-mathemalchemy-art-project.jpg?resize=900%2C509&#038;ssl=1\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/stained-glass-dodecahedral-trajectory-bronna-butler-mathemalchemy-art-project.jpg?w=1000&amp;ssl=1 1000w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/stained-glass-dodecahedral-trajectory-bronna-butler-mathemalchemy-art-project.jpg?resize=300%2C170&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/stained-glass-dodecahedral-trajectory-bronna-butler-mathemalchemy-art-project.jpg?resize=768%2C434&amp;ssl=1 768w\" sizes=\"(max-width: 900px) 100vw, 900px\" \/><figcaption class=\"wp-block-jetpack-slideshow_caption gallery-caption\">Fotos del video (arriba de la cr\u00f3nica): 3. patrones hechos del dibujo en vidrio y cortados; aqu\u00ed se muestran en la mesa de luz. <\/figcaption><\/figure><\/li><li class=\"wp-block-jetpack-slideshow_slide swiper-slide\"><figure><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"425\" alt=\"\" class=\"wp-block-jetpack-slideshow_image wp-image-1707\" data-id=\"1707\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/paper-dodecahedron-bronna-buthler-mathemalchemy-art-project.jpg?resize=900%2C425&#038;ssl=1\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/paper-dodecahedron-bronna-buthler-mathemalchemy-art-project.jpg?resize=1024%2C484&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/paper-dodecahedron-bronna-buthler-mathemalchemy-art-project.jpg?resize=300%2C142&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/paper-dodecahedron-bronna-buthler-mathemalchemy-art-project.jpg?resize=768%2C363&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/paper-dodecahedron-bronna-buthler-mathemalchemy-art-project.jpg?resize=1200%2C567&amp;ssl=1 1200w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/paper-dodecahedron-bronna-buthler-mathemalchemy-art-project.jpg?w=1270&amp;ssl=1 1270w\" sizes=\"(max-width: 900px) 100vw, 900px\" \/><figcaption class=\"wp-block-jetpack-slideshow_caption gallery-caption\">Fotos del video (arriba de la cr\u00f3nica):: 4. modelo de papel del dodecaedro bicolor. <\/figcaption><\/figure><\/li><li class=\"wp-block-jetpack-slideshow_slide swiper-slide\"><figure><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"509\" alt=\"\" class=\"wp-block-jetpack-slideshow_image wp-image-1717\" data-id=\"1717\" src=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/stained-glass-piece-dodecahedron-bronna-butler-mathemalchemy-art-project.jpg?resize=900%2C509&#038;ssl=1\" srcset=\"https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/stained-glass-piece-dodecahedron-bronna-butler-mathemalchemy-art-project.jpg?resize=1024%2C579&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/stained-glass-piece-dodecahedron-bronna-butler-mathemalchemy-art-project.jpg?resize=300%2C170&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/stained-glass-piece-dodecahedron-bronna-butler-mathemalchemy-art-project.jpg?resize=768%2C435&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/stained-glass-piece-dodecahedron-bronna-butler-mathemalchemy-art-project.jpg?w=1200&amp;ssl=1 1200w\" sizes=\"(max-width: 900px) 100vw, 900px\" \/><figcaption class=\"wp-block-jetpack-slideshow_caption gallery-caption\">Fotos del video (arriba de la cr\u00f3nica): 5. los asteriscos en estas piezas de vidrio indican d\u00f3nde un extremao de la l\u00ednea se va a unir con el otro. <\/figcaption><\/figure><\/li><\/ul><a class=\"wp-block-jetpack-slideshow_button-prev swiper-button-prev swiper-button-white\" role=\"button\"><\/a><a class=\"wp-block-jetpack-slideshow_button-next swiper-button-next swiper-button-white\" role=\"button\"><\/a><a aria-label=\"Pause Slideshow\" class=\"wp-block-jetpack-slideshow_button-pause\" role=\"button\"><\/a><div class=\"wp-block-jetpack-slideshow_pagination swiper-pagination swiper-pagination-white\"><\/div><\/div><\/div>\n\n<p><\/p>\n\n<p>Athreya y Aulicino, junto con el matem\u00e1tico Patrick Hooper, determinaron que existe un n\u00famero infinito de trayectorias de este tipo en el dodecaedro. <a href=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/10586458.2020.1712564\" target=\"_blank\" rel=\"noreferrer noopener\">Su art\u00edculo<\/a>, publicado en mayo de 2020 por \u00abExperimental Mathematics\u00bb, muestra que estos caminos pueden dividirse en 31 familias naturales.<\/p>\n\n<p>El faro estar\u00e1 9 \u00bd pies m\u00e1s alto que el espectador. Por tanto, quer\u00eda resaltar el camino. Para ello, puse cristal carmes\u00ed debajo de la trayectoria y cristal \u00e1mbar encima de la trayectoria. \u00c9ste es el v\u00e9rtice donde comienza nuestra trayectoria. Atraviesa las caras del dodecaedro. Mire, \u00e9sta es la trayectoria de la l\u00e1mina de cobre. Se salta este v\u00e9rtice, pasa por debajo. Da la vuelta, vuelve&#8230;. al v\u00e9rtice original sin pasar por ninguno de los otros v\u00e9rtices.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>El faro de MatemAlquimia refleja un avance de 2020 de los matem\u00e1ticos Jayadev Athreya, David Aulicino y Patrick Hooper. <\/p>\n<p>Bronna Butler, artista profesional, amante de las matem\u00e1ticas y miembro del equipo de MatemAlquimia, demuestra c\u00f3mo su creaci\u00f3n en vitral ilustra una de las infinitas trayectorias dodeca\u00e9dricas.<\/p>\n","protected":false},"author":44503782,"featured_media":13900,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[7466],"tags":[7469,7471,7467,7472,7474,7468,7470,7473],"class_list":["post-13899","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-teoria-en-matemalquimia","tag-bronna-butler-es","tag-dodecahedro","tag-faro","tag-faro-es","tag-lentes-led","tag-sabetta-matsumoto-es","tag-trayectoria-dodecaedrica","tag-vitrales","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Trayectoria dodeca\u00e9drica - Mathemalchemy<\/title>\n<meta name=\"description\" content=\"El faro de MatemAlquimia refleja un avance de 2020 de los matem\u00e1ticos Jayadev Athreya, David Aulicino y Patrick Hooper. 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Bronna Butler, artista profesional, amante de las matem\u00e1ticas y miembro del equipo de MatemAlquimia muestra c\u00f3mo su creaci\u00f3n en forma de vitral ilustra una de las infinitas trayectorias dodeca\u00e9dricas.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/mathemalchemy.org\/wp-content\/uploads\/2021\/01\/dodecahedronal-trajectory-bronna-butler-mathemalchemy-art-project.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@https:\/\/twitter.com\/BronnaButler\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Bronna Butler\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/mathemalchemy.org\\\/es\\\/2021\\\/01\\\/19\\\/trayectoria-dodecaedrica\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/mathemalchemy.org\\\/es\\\/2021\\\/01\\\/19\\\/trayectoria-dodecaedrica\\\/\"},\"author\":{\"name\":\"Bronna Butler\",\"@id\":\"https:\\\/\\\/mathemalchemy.org\\\/#\\\/schema\\\/person\\\/4619da04ce80983557dce039046d2c0a\"},\"headline\":\"Trayectoria dodeca\u00e9drica\",\"datePublished\":\"2021-01-19T15:05:00+00:00\",\"dateModified\":\"2026-01-17T01:15:47+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/mathemalchemy.org\\\/es\\\/2021\\\/01\\\/19\\\/trayectoria-dodecaedrica\\\/\"},\"wordCount\":789,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/mathemalchemy.org\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/mathemalchemy.org\\\/es\\\/2021\\\/01\\\/19\\\/trayectoria-dodecaedrica\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/i0.wp.com\\\/mathemalchemy.org\\\/wp-content\\\/uploads\\\/2021\\\/01\\\/dodecahedronal-trajectory-bronna-butler-mathemalchemy-art-project.jpg?fit=1280%2C720&ssl=1\",\"keywords\":[\"Bronna Butler\",\"dodecahedro\",\"Faro\",\"faro\",\"lentes led\",\"Sabetta Matsumoto\",\"trayectoria dodeca\u00e9drica\",\"vitrales\"],\"articleSection\":[\"Teor\u00eda en MatemAlquimia\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/mathemalchemy.org\\\/es\\\/2021\\\/01\\\/19\\\/trayectoria-dodecaedrica\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/mathemalchemy.org\\\/es\\\/2021\\\/01\\\/19\\\/trayectoria-dodecaedrica\\\/\",\"url\":\"https:\\\/\\\/mathemalchemy.org\\\/es\\\/2021\\\/01\\\/19\\\/trayectoria-dodecaedrica\\\/\",\"name\":\"Trayectoria dodeca\u00e9drica - Mathemalchemy\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/mathemalchemy.org\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/mathemalchemy.org\\\/es\\\/2021\\\/01\\\/19\\\/trayectoria-dodecaedrica\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/mathemalchemy.org\\\/es\\\/2021\\\/01\\\/19\\\/trayectoria-dodecaedrica\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/i0.wp.com\\\/mathemalchemy.org\\\/wp-content\\\/uploads\\\/2021\\\/01\\\/dodecahedronal-trajectory-bronna-butler-mathemalchemy-art-project.jpg?fit=1280%2C720&ssl=1\",\"datePublished\":\"2021-01-19T15:05:00+00:00\",\"dateModified\":\"2026-01-17T01:15:47+00:00\",\"description\":\"El faro de MatemAlquimia refleja un avance de 2020 de los matem\u00e1ticos Jayadev Athreya, David Aulicino y Patrick Hooper. 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