{"id":20771,"date":"2021-03-23T21:00:16","date_gmt":"2021-03-23T20:00:16","guid":{"rendered":"http:\/\/agora.xtec.cat\/insbitacola\/?p=20771"},"modified":"2021-03-23T19:33:51","modified_gmt":"2021-03-23T18:33:51","slug":"geometria-impossible-als-quaderns-de-3r","status":"publish","type":"post","link":"https:\/\/agora.xtec.cat\/insbitacola\/general\/geometria-impossible-als-quaderns-de-3r\/","title":{"rendered":"Geometria impossible als quaderns de 3r"},"content":{"rendered":"<p><span class=\"hiddenSpellError\">Maurits<\/span>\u00a0Cornelis\u00a0<span class=\"hiddenSpellError\">Escher<\/span>\u00a0(Ljouwert, 17 de juny de 1898 &#8211;\u00a0<span class=\"hiddenSpellError\">Laren<\/span>, 27 de mar\u00e7 de 1972) fou un artista neerland\u00e8s fam\u00f3s pels seus gravats, litografies i il\u00b7lustracions a tinta, que representen construccions impossibles, exploracions de l&#8217;infinit i tessel\u00b7les.<\/p>\n<p><span class=\"hiddenGrammarError\" style=\"padding-bottom: 2px; background-image: url('..\/..\/..\/..\/..\/images\/squiggle.png'); cursor: default; color: #666666; font-family: 'Open Sans', Helvetica, Arial, sans-serif; font-size: 16px; font-style: normal; font-weight: 300; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none;\">Oscar<\/span>\u00a0<span class=\"hiddenSpellError\">Reutersv\u00e4rd<\/span>\u00a0(1915,\u00a0<span class=\"hiddenSpellError\">Estocolm<\/span>,\u00a0<span class=\"hiddenSpellError\">Su\u00e8cia<\/span>\u00a0\u2013 2 de\u00a0<span class=\"hiddenSpellError\">febrer<\/span>\u00a0de 2002), pare de les figures impossibles, va ser un\u00a0artista\u00a0pioner en el m\u00f3n de l&#8217;impossible. Un dels seus objectes m\u00e9s famosos, el triangle de Penrose, ens ha servit com a\u00a0inspiraci\u00f3\u00a0per a omplir les nostres l\u00e0mines d&#8217;il\u00b7lusions\u00a0\u00f2ptiques.<\/p>\n<p>En aquest segon projecte matem\u00e0tic del trimestre ens hem fixat en les propietats de la geometria per a poder crear figures impossibles. Amb esfor\u00e7 i a c\u00f2pia de tornar a comen\u00e7ar des de zero molts cops, hem plasmat en dues dimensions, cossos geom\u00e8trics en 3D. I hem aprofitat les propietats de la perspectiva isom\u00e8trica per a crear els efectes que enganyen els nostres ulls.<\/p>\n<p>Amb l&#8217;ajuda dels estris de dibuix, no solament hem aconseguit impressionants il\u00b7lustracions com les que veureu a continuaci\u00f3, sin\u00f3 que de mica en mica hem anat entenent les propietats geom\u00e8triques de figures tan b\u00e0siques com els hex\u00e0gons i els triangles.<\/p>\n<p>Demostrant que les matem\u00e0tiques poden ser unes\u00a0fant\u00e0stiques\u00a0aliades de la creativitat, aqu\u00ed us deixem una galeria d&#8217;algunes de les\u00a0il\u00b7lustracions\u00a0m\u00e9s impressionants que han sortit a les aules.<\/p>\n\n\t\t<style type=\"text\/css\">\n\t\t\t#gallery-1 {\n\t\t\t\tmargin: auto;\n\t\t\t}\n\t\t\t#gallery-1 .gallery-item {\n\t\t\t\tfloat: left;\n\t\t\t\tmargin-top: 10px;\n\t\t\t\ttext-align: center;\n\t\t\t\twidth: 33%;\n\t\t\t}\n\t\t\t#gallery-1 img {\n\t\t\t\tborder: 2px solid #cfcfcf;\n\t\t\t}\n\t\t\t#gallery-1 .gallery-caption {\n\t\t\t\tmargin-left: 0;\n\t\t\t}\n\t\t\t\/* see gallery_shortcode() in wp-includes\/media.php *\/\n\t\t<\/style>\n\t\t<div id='gallery-1' class='gallery galleryid-20771 gallery-columns-3 gallery-size-thumbnail'><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/agora.xtec.cat\/insbitacola\/general\/geometria-impossible-als-quaderns-de-3r\/attachment\/whatsapp-image-2021-03-19-at-18-20-45\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/agora.xtec.cat\/insbitacola\/wp-content\/uploads\/usu1329\/2021\/03\/WhatsApp-Image-2021-03-19-at-18.20.45-150x150.jpeg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-21149\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-21149'>\n\t\t\t\tMandala floral a partir de la partici\u00f3 de l&#8217;hex\u00e0gon\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/agora.xtec.cat\/insbitacola\/general\/geometria-impossible-als-quaderns-de-3r\/attachment\/img-2538\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/agora.xtec.cat\/insbitacola\/wp-content\/uploads\/usu1329\/2021\/03\/IMG-2538-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-21147\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-21147'>\n\t\t\t\tTriangle de Penrose\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/agora.xtec.cat\/insbitacola\/general\/geometria-impossible-als-quaderns-de-3r\/attachment\/113-2\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/agora.xtec.cat\/insbitacola\/wp-content\/uploads\/usu1329\/2021\/03\/113-1-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-21143\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-21143'>\n\t\t\t\tTriangle de Penrose inscrit en hex\u00e0gon regular\n\t\t\t\t<\/dd><\/dl><br style=\"clear: both\" \/><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/agora.xtec.cat\/insbitacola\/general\/geometria-impossible-als-quaderns-de-3r\/attachment\/111111-2\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/agora.xtec.cat\/insbitacola\/wp-content\/uploads\/usu1329\/2021\/03\/111111-1-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-21145\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-21145'>\n\t\t\t\tTriangle de Penrose amb detall de teranyina el\u00b7l\u00edptica\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/agora.xtec.cat\/insbitacola\/general\/geometria-impossible-als-quaderns-de-3r\/attachment\/114-2\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/agora.xtec.cat\/insbitacola\/wp-content\/uploads\/usu1329\/2021\/03\/114-1-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-21144\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-21144'>\n\t\t\t\tDoble triangle de Penrose\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/agora.xtec.cat\/insbitacola\/general\/geometria-impossible-als-quaderns-de-3r\/attachment\/112-2\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/agora.xtec.cat\/insbitacola\/wp-content\/uploads\/usu1329\/2021\/03\/112-1-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-21142\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-21142'>\n\t\t\t\tDoble triangle de Penrose ambmarc doble\n\t\t\t\t<\/dd><\/dl><br style=\"clear: both\" \/><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/agora.xtec.cat\/insbitacola\/general\/geometria-impossible-als-quaderns-de-3r\/attachment\/1616496569550\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/agora.xtec.cat\/insbitacola\/wp-content\/uploads\/usu1329\/2021\/03\/1616496569550-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-21146\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-21146'>\n\t\t\t\tTriangle de Penrose engabiat en cub impossible\n\t\t\t\t<\/dd><\/dl><dl class='gallery-item'>\n\t\t\t<dt class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/agora.xtec.cat\/insbitacola\/general\/geometria-impossible-als-quaderns-de-3r\/attachment\/dav-46\/'><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/agora.xtec.cat\/insbitacola\/wp-content\/uploads\/usu1329\/2021\/03\/Tringle-de-penrose-engabiat-150x150.jpg\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" aria-describedby=\"gallery-1-21148\" \/><\/a>\n\t\t\t<\/dt>\n\t\t\t\t<dd class='wp-caption-text gallery-caption' id='gallery-1-21148'>\n\t\t\t\tTriangle de Penrose engabiat en cub impossible\n\t\t\t\t<\/dd><\/dl>\n\t\t\t<br style='clear: both' \/>\n\t\t<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Maurits\u00a0Cornelis\u00a0Escher\u00a0(Ljouwert, 17 de juny de 1898 &#8211;\u00a0Laren, 27 de mar\u00e7 de 1972) fou un artista neerland\u00e8s fam\u00f3s pels seus gravats, litografies i il\u00b7lustracions a tinta, que representen construccions impossibles, exploracions de l&#8217;infinit i tessel\u00b7les.<br \/>\nOscar\u00a0Reutersv\u00e4rd\u00a0(1915,\u00a0Estocolm,\u00a0Su\u00e8cia\u00a0\u2013 2 de\u00a0febrer\u00a0de 2002), pare de les figures impossibles, va ser un\u00a0artista\u00a0pioner&hellip;  <a href=\"https:\/\/agora.xtec.cat\/insbitacola\/general\/geometria-impossible-als-quaderns-de-3r\/\" title=\"Read Geometria impossible als quaderns de 3r\">Llegeix m\u00e9s\u00bb<\/a><\/p>\n","protected":false},"author":1,"featured_media":21146,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[107,109,1,29],"tags":[],"class_list":["post-20771","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-eso-3","category-ambit-matematic","category-general","category-portada"],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/posts\/20771","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/comments?post=20771"}],"version-history":[{"count":3,"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/posts\/20771\/revisions"}],"predecessor-version":[{"id":21153,"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/posts\/20771\/revisions\/21153"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/media\/21146"}],"wp:attachment":[{"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/media?parent=20771"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/categories?post=20771"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/agora.xtec.cat\/insbitacola\/wp-json\/wp\/v2\/tags?post=20771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}