{"id":48459,"date":"2015-10-09T19:06:19","date_gmt":"2015-10-09T22:06:19","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=48459"},"modified":"2024-11-27T21:17:57","modified_gmt":"2024-11-28T00:17:57","slug":"sala-de-atividades-pavimentacao-sala-2","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/sala-de-atividades-pavimentacao-sala-2\/","title":{"rendered":"Sala de Atividades: Pavimenta\u00e7\u00e3o &#8211; Sala 2"},"content":{"rendered":"<p style=\"margin:20px;\">\n<hr style=\"height:3px;background-color:#6d360f; margin-top: 8px; margin-bottom: 8px;  border: 0 none\"\/>\n<hr style=\"height:1px;background-color:#6d360f; margin-top: 8px; margin-bottom: 8px;  border: 0 none\"\/>\n<div  class=\"nome c1\" style=\"margin:20px;\"><strong>Pavimenta\u00e7\u00e3o, caleidosc\u00f3pios,<br \/>\ncaleidociclos, <em>Escher<\/em> e, at\u00e9,<\/strong> <\/div>\n<p> <marquee behavior=\"scroll\" direction=\"left\" scrollamount=\"8\" style=\"font-family: calibri, sans-serif; \"><br \/>\n<span style=\"color:#6d360f;font-size: 50px;\">. . . <strong>Matem\u00e1tica!!!<\/strong><\/span><br \/>\n<\/marquee><\/p>\n<hr style=\"height:1px;background-color:#6d360f; margin-top: 8px; margin-bottom: 8px;  border: 0 none\"\/>\n<hr style=\"height:3px;background-color:#6d360f; margin-top: 8px; margin-bottom: 80px;  border: 0 none\"\/>\n<div class=\"grea c1 cb14\" >\n<div class=\"gr1 cb11\">\n<p class=\"ti1 c1\" style=\"line-height:40px;margin:1px\" ><em> T\u00f3picos &#8211; Sala 2<\/em><\/p>\n<hr style=\"height:3px;background-color:#6d360f; border: 0 none\"\/>\n<p style=\"margin:20px;\">\n<div class=\"gr2 cb12 bg1\" style=\"width:80%; font-size: 20px; line-height: 50px;\">\n<a href=\"#O1\"><span style=\"color: #6d360f;\">VI &#8211; <span style=\"text-decoration: underline;\"> <em>Escher<\/em><\/span><\/span><\/a><br \/>\n<a href=\"#O2\"><span style=\"color: #6d360f;\">VII &#8211; <span style=\"text-decoration: underline;\"> Um pouco sobre as pavimenta\u00e7\u00f5es de Escher<\/span><\/span><\/a><br \/>\n<a href=\"#O3\"><span style=\"color: #6d360f;\">VIII &#8211; <span style=\"text-decoration: underline;\">  Treinando para ser um  <em>Escher<\/em><\/span><\/span><\/a><br \/>\n<a href=\"#O4\"><span style=\"color: #6d360f;\">IX &#8211; <span style=\"text-decoration: underline;\">  Um dia de <em>Escher<\/em><\/span><\/span><\/a>\n<\/div>\n<\/div>\n<p><a id=\"O1\"><\/p>\n<hr style=\"height:1px; width:30%;background-color:#6d360f; margin-top: 40px; margin-bottom: 8px;  border: 0 none\"\/>\n<hr style=\"height:1px; width:50%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:70%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:90%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:90%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:70%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:50%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:30%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 40px; border: 0 none\"\/>\n<\/a><\/p>\n<div class=\"gr1 cb11\">\n<p class=\"ti1 c1\" style=\"line-height:40px;margin:1px\" ><em> VI &#8211; Escher <\/em><\/p>\n<hr style=\"height:3px;background-color:#6d360f; border: 0 none\"\/>\n<p style=\"text-indent:40px; margin-top:20px;\"> Voc\u00eas j\u00e1 ouviram falar de um artista gr\u00e1fico chamado <em>Escher<\/em>? <\/p>\n<p style=\"text-indent:40px; margin-bottom:20px;\"> Bem, aqui nos Clubes de Matem\u00e1tica da OBMEP voc\u00eas j\u00e1 devem ter se deparado com alguns v\u00eddeos a respeito dele. Na Videoteca dos Clubes temos o v\u00eddeo <a href=\"http:\/\/clubes.obmep.org.br\/blog\/video-007\/\" target=\"_blank\" title=\"Uma horinha dessas, assista ao v\u00eddeo.\"><span style=\"color: #b85b19;\"><strong>Inspirations<\/strong><\/span><\/a>, do cineasta espanhol Crist\u00f3bal Vila que imagina como seria o local de trabalho do artista, e o v\u00eddeo <a href=\"http:\/\/clubes.obmep.org.br\/blog\/video-6\/\" target=\"_blank\" title=\"Uma horinha dessas, assista ao v\u00eddeo.\"><span style=\"color: #b85b19;\"><strong>Escher e a Geometria<\/strong><\/span><\/a> &#8211; um passeio pela exposi\u00e7\u00e3o \u201cO mundo m\u00e1gico de Escher\u201d, que ficou em cartaz em S\u00e3o Paulo em julho de 2011. <\/p>\n<p class=\"ti2 c1\">Caso ainda n\u00e3o conhe\u00e7am Escher, vale a pena assistir aos v\u00eddeos!!<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/Escher.jpg\" style=\"border:5px solid #6d360f;\" alt=\"Escher\" width=\"320\" height=\"280\" class=\"aligncenter size-full wp-image-48479\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/Escher.jpg 320w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/Escher-300x263.jpg 300w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/p>\n<p style=\"text-indent:40px; margin-top:20px;margin-bottom:20px;\"><em><strong>Maurits Cornelis Escher<\/strong><\/em> (1898-1972) \u00e9 um dos mais famosos artistas gr\u00e1ficos do mundo e seus trabalhos s\u00e3o encontrados em muitos <em>sites <\/em>da <em>Internet<\/em>. Ele ficou conhecido, principalmente, pelas constru\u00e7\u00f5es imposs\u00edveis presentes em suas obras, como as duas apresentadas a seguir.<\/p>\n<table style=\"border: 2px dotted #6d360f; width:80%; height:auto; text-align:justify; margin-left: auto; margin-right: auto;\">\n<tr style=\"vertical-align: middle\">\n<td   style=\"border: 1px solid #FFFFFF; text-align:center;\">\n<p style=\"margin:10px\">\n<p><a href=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/m-c-escher-ascending-and-descending-1.jpg\" onclick=\"window.open(this.href, '_blank', 'width=850, height=1000, left=0,top=0'); return false\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/m-c-escher-ascending-and-descending-1.jpg\" style=\"border: 0px;\" alt=\"m-c-escher-ascending-and-descending (1)\" width=\"200\" height=\"260\" class=\"aligncenter size-full wp-image-47720\" \/><\/a> <\/td>\n<td  style=\"border: 1px solid #FFFFFF; text-align: left; width:60%;\">Cliquem na imagem para ampli\u00e1-la, observem-na atentamente e respondam:<br \/>\n<strong>as pessoas na escada est\u00e3o subindo ou descendo?<\/strong><br \/>\nEssa obra \u00e9 chamada <strong><em>Ascending and Descending<\/em><\/strong>, que podemos traduzir por Sobe e Desce, e \u00e9 um trabalho realizado em 1960.<br \/>\nDepois de analisar a situa\u00e7\u00e3o, n\u00e3o se esque\u00e7am de fechar a janela que se abriu.\n<\/td>\n<\/tr>\n<tr style=\"vertical-align: middle\">\n<td   style=\"border: 1px solid #FFFFFF; text-align:center;\">\n<p style=\"margin:10px\">\n<p><a href=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/mc-escher-waterfall.jpg\" onclick=\"window.open(this.href, '_blank', 'width=850, height=1000, left=0,top=0'); return false\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/mc-escher-waterfall.jpg\" alt=\"mc-escher-waterfall\" width=\"200\" height=\"260\" class=\"aligncenter size-full wp-image-47730\" \/><\/a> <\/td>\n<td  style=\"border: 1px solid #FFFFFF; text-align: left; width:60%;\">Cliquem na imagem para ampli\u00e1-la, observem-na atentamente e respondam:<br \/>\n<strong>a \u00e1gua est\u00e1 caindo ou subindo?<\/strong><br \/>\nEssa outra obra \u00e9 chamada <strong><em>Waterfall <\/em><\/strong>(Queda d\u00b4\u00e1gua) e \u00e9 de 1961.<br \/>\nDepois de analisar a situa\u00e7\u00e3o, n\u00e3o se esque\u00e7am de fechar a janela que se abriu.\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"text-indent:40px; margin-top:20px;\"> Mas n\u00e3o \u00e9 por suas constru\u00e7\u00f5es imposs\u00edveis que <em>Escher<\/em> est\u00e1 nesta Sala. Nos dias de hoje, n\u00e3o podemos falar de pavimenta\u00e7\u00e3o do plano sem cit\u00e1-lo. <\/p>\n<p style=\"text-indent:40px; margin-bottom:30px;\">Desde a sua primeira visita a um castelo Mouro em Granada, Espanha, no ano de 1922, <em>Escher<\/em> se inspirou nos azulejos espanh\u00f3is e se interessou pela divis\u00e3o regular do plano, criando v\u00e1rias pavimenta\u00e7\u00f5es. Para conhecer um pouco mais sobre o envolvimento de <em>Escher<\/em> com a pavimenta\u00e7\u00e3o, assistam ao v\u00eddeo <strong>O estranho mundo de Escher<\/strong>, da s\u00e9rie <strong><strong>Isto \u00e9 Matem\u00e1tica<\/strong><\/strong>.<\/p>\n<hr style=\"height:6px; background-color:#6d360f;  margin-top: 30px; margin-bottom: 8px;border:  0 none\"\/>\n<hr style=\"height:1px; background-color:#6d360f; margin-top: 3px; margin-bottom: 30px; border: 0 none\"\/>\n<p style=\"text-align:center;\">\n<iframe loading=\"lazy\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/7ac0WC3tzwU?rel=0&amp;\" allowfullscreen style=\"border:0;\"><\/iframe><\/p>\n<hr style=\"height:1px; background-color:#6d360f;  margin-top: 30px; margin-bottom: 8px;border:  0 none\"\/>\n<hr style=\"height:6px; background-color:#6d360f;   margin-top: 8px; margin-bottom: 30px;border: 0 none\"\/>\n<p class=\"ti2 c1\" style=\"margin-top:30px;\">Vamos, ent\u00e3o, conhecer um pouquinho sobre<br \/>\no imenso e maravilhoso &#8220;estranho mundo das pavimenta\u00e7\u00f5es de Escher&#8221;.<\/p>\n<\/div>\n<p><a id=\"O2\"><\/p>\n<hr style=\"height:1px; width:30%;background-color:#6d360f; margin-top: 40px; margin-bottom: 8px;  border: 0 none\"\/>\n<hr style=\"height:1px; width:50%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:70%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:90%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:90%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:70%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:50%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:30%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 40px; border: 0 none\"\/>\n<\/a><\/p>\n<div class=\"gr1 cb11\">\n<p class=\"ti1 c1\" style=\"line-height:40px;margin:1px\" ><em> VII &#8211; Um pouco sobre as pavimenta\u00e7\u00f5es de Escher <\/em><\/p>\n<hr style=\"height:3px;background-color:#6d360f; border: 0 none\"\/>\n<p style=\"text-indent:40px; margin-top:30px;\"> <em>Escher <\/em> explorou de forma brilhante a geometria plana e a geometria espacial em suas obras, mesmo n\u00e3o tendo qualquer forma\u00e7\u00e3o ou conhecimento de ci\u00eancias exatas. O seu encanto por figuras geom\u00e9tricas e padr\u00f5es levou-o a descobrir a Teoria da Divis\u00e3o do Plano Regular: uma superf\u00edcie pode ser dividida regularmente em figuras iguais e totalmente preenchida com elas sem a exist\u00eancia de espa\u00e7os vazios.<\/p>\n<p style=\"text-indent:40px; margin-bottom:20px;\">Essa t\u00e9cnica j\u00e1 era dominada por povos antigos, que a utilizavam na confec\u00e7\u00e3o de seus mosaicos, conforme vimos na Sala 1; mas <em>Escher <\/em> foi al\u00e9m dos tri\u00e2ngulos equil\u00e1teros, quadrados e hex\u00e1gonos regulares capazes de cobrir o plano sem deixar buracos ou se sobreporem. Ele substituiu os pol\u00edgonos regulares por figuras que representam coisas existentes na natureza &#8211;  pessoas, p\u00e1ssaros, peixes, r\u00e9pteis, etc. &#8211; e criou imagens envolventes, como as que vemos abaixo.<\/p>\n<hr style=\"height:6px; background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<table style=\"border:0px; width:99%; height:auto; margin-left: auto; margin-right: auto;\">\n<tr>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/escher5.jpg\" alt=\"escher5\" width=\"250\" height=\"272\" style=\"border:5px solid #6d360f;\" class=\"aligncenter size-full wp-image-48488\" \/><\/td>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/E8-MC-Escher-No-8-Horse-1937-1938.jpg\" style=\"border:5px solid #6d360f;\" alt=\"E8-MC-Escher-No-8-Horse-1937-1938\" width=\"250\" height=\"340\" class=\"aligncenter size-full wp-image-48490\" \/><\/td>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/E34-MC-Escher-No-34-BirdFish-1941.jpg\" style=\"border:5px solid #6d360f;\" alt=\"E34-MC-Escher-No-34-BirdFish-1941\" width=\"250\" height=\"340\" class=\"aligncenter size-large wp-image-48492\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF; text-align:center;\"> MC Escher: <em>Plane Filing II<\/em>, 1957 <\/td>\n<td style=\"border: 1px solid #FFFFFF; text-align:center;\"> MC Escher: <em>Horse<\/em>, 1937-1938<\/td>\n<td style=\"border: 1px solid #FFFFFF; text-align:center;\"> MC Escher: <em>BirdFish<\/em>, 1941<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/E55-MC-Escher-No-55-Fish-1942.jpg\" style=\"border:5px solid #6d360f;\" alt=\"E55-MC-Escher-No-55-Fish-1942\" width=\"250\" height=\"340\" class=\"aligncenter size-large wp-image-48493\" \/><\/td>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/E57-MC-Escher-No-57-Two-Fish-1942.jpg\" style=\"border:5px solid #6d360f;\" alt=\"E57-MC-Escher-No-57-Two-Fish-1942\" width=\"250\" height=\"340\" class=\"aligncenter size-large wp-image-48494\" \/><\/td>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/E17-MC-Escher-No-17-Eagle-1938-138x180.jpg\" style=\"border:5px solid #6d360f;\" alt=\"E17-MC-Escher-No-17-Eagle-1938-138x180\" width=\"250\" height=\"340\" class=\"aligncenter size-large wp-image-48491\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF; text-align:center;\"> MC Escher: <em>Fish<\/em>, 1942 <\/td>\n<td style=\"border: 1px solid #FFFFFF; text-align:center;\"> MC Escher: <em>Two-Fish<\/em>, 1942<\/td>\n<td style=\"border: 1px solid #FFFFFF; text-align:center;\">MC Escher: <em>Eagle<\/em>, 1938<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/E21-MC-Escher-No-21-IMP-1938.jpg\" style=\"border:5px solid #6d360f;\" alt=\"E21-MC-Escher-No-21-IMP-1938\" width=\"250\" height=\"340\" class=\"aligncenter size-full wp-image-48503\" \/><\/td>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/E25-MC-Escher-No-25-Lizard-1939.jpg\" style=\"border:5px solid #6d360f;\" alt=\"E25-MC-Escher-No-25-Lizard-1939\" width=\"250\" height=\"340\" class=\"aligncenter size-large wp-image-48504\" \/><\/td>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/E28-MC-Escher-No-28-Three-Birds-1938.jpg\" style=\"border:5px solid #6d360f;\" alt=\"E28-MC-Escher-No-28-Three-Birds-1938\" width=\"250\" height=\"340\" class=\"aligncenter size-large wp-image-48505\" \/><\/td>\n<tr>\n<td style=\"border: 1px solid #FFFFFF; text-align:center;\"> MC Escher: <em>IMP<\/em>, 1938 <\/td>\n<td style=\"border: 1px solid #FFFFFF; text-align:center;\"> MC Escher: <em>Lizard<\/em>, 1939<\/td>\n<td style=\"border: 1px solid #FFFFFF; text-align:center;\">MC Escher: <em>Three-Birds<\/em>, 1938<\/td>\n<\/tr>\n<\/table>\n<hr style=\"height:1px; background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:6px; background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<p style=\"text-align:right; font-size:12px;\">Imagens extra\u00eddas de:  <a href=\"http:\/\/www.mcescher.com\/\" target=\"_blank\" title=\"Visitem o site, \u00e9 muito bacana!\"><span style=\"color: #d66a1d;\"><strong>M.C.Escher<\/strong><\/span><\/a><\/p>\n<p style=\"text-indent:40px; margin-top:20px;\">Muito embora  os \u00fanicos pol\u00edgonos regulares que s\u00e3o poss\u00edveis de serem utilizados para pavimentar o plano sejam  o tri\u00e2ngulo, o quadrado e o hex\u00e1gono, <em>Escher<\/em> combinou, <strong>deslocou<\/strong>, <strong>girou<\/strong>, <strong>refletiu <\/strong>e distorceu essas tr\u00eas figuras matem\u00e1ticas, obtendo  uma maior variedade de padr\u00f5es e criando pavimenta\u00e7\u00f5es mais elaboradas. As tr\u00eas palavras em negrito <strong>deslocou<\/strong>, <strong>girou<\/strong> e <strong>refletiu <\/strong> representam o resultado de tr\u00eas a\u00e7\u00f5es poss\u00edveis de se fazer em um plano de modo que uma figura sobre a qual elas foram aplicadas muda de posi\u00e7\u00e3o, mas n\u00e3o de forma. Na matem\u00e1tica, essas a\u00e7\u00f5es s\u00e3o estudadas e recebem, respectivamente, os seguintes nomes: <strong>transla\u00e7\u00e3o;  rota\u00e7\u00e3o; reflex\u00e3o<\/strong>.<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/simetriatodos2.png\"  style=\"border: 0px;\"alt=\"simetriatodos2\" width=\"520\" height=\"186\" class=\"aligncenter size-full wp-image-49438\" \/><\/p>\n<p style=\"text-indent:40px;\">Para relembrar um pouco sobre elas, cliquem <a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=47954\" target=\"_blank\"   title=\"Se precisar relembrar, visite a Sala.\"><span style=\"color: #d66a1d;\"><strong>AQUI<\/strong><\/span><\/a>.<\/p>\n<p style=\"text-indent:40px; margin-bottom:20px;\">Mesmo desenhando p\u00e1ssaros, peixes e outros animais para dar vida \u00e0s suas pavimenta\u00e7\u00f5es, Escher n\u00e3o abandonou os pol\u00edgonos; pelo contr\u00e1rio, utilizou-os como base para gerar as figuras que compuseram suas pavimenta\u00e7\u00f5es. Assim, desenhando dentro de  pol\u00edgonos e utilizando  <em>degradees <\/em> de cores e sombras, criou padr\u00f5es que ficaram conhecidos como metamorfoses (gradativamente, uma figura vai se transformando em outra). Um exemplo dessa t\u00e9cnica voc\u00eas podem ver nas pr\u00f3ximas figuras. Clicando sobre a primeira figura, voc\u00eas poder\u00e3o assistir a uma anima\u00e7\u00e3o que brinca com a obra! Clicando sobre a segunda, voc\u00eas poder\u00e3o assistir a um v\u00eddeo mostrando detalhes da obra, que mede 19,2 cm x 680 cm. Isso mesmo, 6,8 metros de comprimento.<\/p>\n<hr style=\"height: 3px; background-color: #6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none;\" \/>\n<hr style=\"height: 1px; background-color: #6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none;\" \/>\n<p style=\"text-align: center; font-size: 12px; margin-top: 10px ;margin-bottom: 10px; line-height: 15px; color: #6d360f;\"><strong>Cliquem em uma figura e na janela que ir\u00e1 abrir, \u00e9 s\u00f3 clicar na setinha. Depois de assistir ao v\u00eddeo, \u00e9 s\u00f3 fechar a janela que se abriu.<\/strong><\/p>\n<table style=\"border: 1px solid #6d360f; width: 95%; height: auto; text-align: justify; margin-left: auto; margin-right: auto;\">\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<a href=\"https:\/\/www.youtube.com\/embed\/D32XQLIUcgI?rel=0&amp;showinfo=0\" onclick=\"window.open(this.href, '_blank', 'width=720, height=480,'); return false\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/LW306-MC-Escher-Sky-and-Water-I-1938-1.jpg\" alt=\"LW306-MC-Escher-Sky-and-Water-I-1938 (1)\" width=\"330\" height=\"330\" style=\"border:5px solid #6d360f;\" class=\"aligncenter size-full wp-image-48529\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/LW306-MC-Escher-Sky-and-Water-I-1938-1.jpg 425w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/LW306-MC-Escher-Sky-and-Water-I-1938-1-150x150.jpg 150w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/LW306-MC-Escher-Sky-and-Water-I-1938-1-300x300.jpg 300w\" sizes=\"auto, (max-width: 330px) 100vw, 330px\" \/><\/a><\/td>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<a href=\"https:\/\/www.youtube.com\/embed\/ZFwoinhJj-c?rel=0&amp;showinfo=0\" onclick=\"window.open(this.href, '_blank', 'width=720, height=480,'); return false\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/300px-Escher_Metamorphosis_II.jpg\" alt=\"300px-Escher,_Metamorphosis_II\" width=\"380\" height=\"310\" style=\"border:5px solid #6d360f;\"  class=\"aligncenter size-full wp-image-48549\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF; text-align: center;\">MC Escher: <em>Sky and Water<\/em>, 1938 <\/td>\n<td style=\"border: 1px solid #FFFFFF; text-align: center;\">MC Escher: <em>Metamorfoses II<\/em>, 1967-1968  <\/td>\n<\/tr>\n<\/table>\n<\/div>\n<p><a id=\"O3\"><\/p>\n<hr style=\"height:1px; width:30%;background-color:#6d360f; margin-top: 40px; margin-bottom: 8px;  border: 0 none\"\/>\n<hr style=\"height:1px; width:50%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:70%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:90%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:90%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:70%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:50%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:30%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 40px; border: 0 none\"\/>\n<\/a><\/p>\n<div class=\"gr1 cb11\">\n<p class=\"ti1 c1\" style=\"line-height:40px;margin:1px\" ><em> VIII &#8211; Treinando para ser um Escher <\/em><\/p>\n<hr style=\"height:3px;background-color:#6d360f; border: 0 none\"\/>\n<p style=\"margin:40px;\">\n<div class=\"gr2 cb15\" style=\"width:80%\">\n<p style=\"margin: 20px 40px 20px 40px;\"> Para identificar os padr\u00f5es e simetrias nas pavimenta\u00e7\u00f5es de <em>Escher<\/em>, \u00e9 preciso algum, digamos, &#8220;treino visual&#8221;.<br \/>\nNesta atividade disponibilizaremos material com essa finalidade.<\/p>\n<div style=\"margin-top:30px;text-align:center;\">\n<input class=\"bo1 bbg1\" type=\"button\"  value=\"Atividade 10\" onclick=\"window.open('http:\/\/clubes.obmep.org.br\/blog\/?p=49131');\" title=\"Clique aqui\"\/><\/div>\n<p style=\"margin:10px;\">\n<\/div>\n<p style=\"margin:40px;\">\n<div class=\"gr2 cb15\" style=\"width:80%\">\n<p style=\"margin: 20px 40px 20px 40px;\"> Voc\u00eas perceberam que algumas isometrias fixam pontos e outras n\u00e3o? Algumas isometrias mant\u00eam orienta\u00e7\u00f5es e outras n\u00e3o?<br \/>\nEsta atividade explora exatamente isso!<\/p>\n<div style=\"text-align:center;\">\n<input class=\"bo1 bbg1\" value=\"Atividade 11\" title=\"Clique aqui\" type=\"button\" onclick=    \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar a atividade';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Atividade 11';}\" \/>    <\/p>\n<div  style=\"display: none;\">\n<div class=\"gr3 cb14\">\n<div class=\"gr3 cb13 bg1\">\nEsta atividade envolve pontos fixos e orienta\u00e7\u00e3o. Se considerarmos tanto a orienta\u00e7\u00e3o como os poss\u00edveis pontos fixos, o comportamento de cada tipo de isometria tem caracter\u00edsticas \u00fanicas. Assim, observem as tr\u00eas isometrias principais &#8211; transla\u00e7\u00e3o;  rota\u00e7\u00e3o; reflex\u00e3o &#8211; sendo aplicadas em v\u00e1rias figuras e respondam \u00e0s seguintes perguntas:<br \/>\n<span style=\"color: #b85b19;\">&#9679;<\/span> A <strong>transla\u00e7\u00e3o <\/strong>deixa pontos fixos? Quais? Quantos?<br \/>\n<span style=\"color: #b85b19;\">&#9679;<\/span> A <strong>transla\u00e7\u00e3o <\/strong>preserva orienta\u00e7\u00e3o?<br \/>\n<span style=\"color: #b85b19;\">&#9679;<\/span> A <strong>rota\u00e7\u00e3o <\/strong>deixa pontos fixos? Quais? Quantos?<br \/>\n<span style=\"color: #b85b19;\">&#9679;<\/span> A <strong>rota\u00e7\u00e3o <\/strong>preserva orienta\u00e7\u00e3o?<br \/>\n<span style=\"color: #b85b19;\">&#9679;<\/span> A <strong>reflex\u00e3o por uma reta<\/strong> deixa pontos fixos? Quais? Quantos?<br \/>\n<span style=\"color: #b85b19;\">&#9679;<\/span> A <strong>reflex\u00e3o por uma reta<\/strong> preserva orienta\u00e7\u00e3o?\n<\/div>\n<p style=\"margin:40px;\">\n<hr style=\"height:2px;background-color:#6d360f; border: 0 none\"\/>\n<p style=\"margin:20px;\">\nSe for conveniente, voc\u00eas podem utilizar a tabela abaixo para registrar suas conclus\u00f5es.<\/p>\n<hr style=\"height:2px;background-color:#6d360f; border: 0 none\"\/>\n<p style=\"margin:40px;\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/atividade-11.png\" alt=\"atividade 11\" width=\"632\" height=\"313\" class=\"aligncenter size-full wp-image-49193\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/atividade-11.png 632w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/atividade-11-300x149.png 300w\" sizes=\"auto, (max-width: 632px) 100vw, 632px\" \/>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p style=\"margin:40px;\">\n<div class=\"gr2 cb15\"  style=\"width:80%\">\n<p style=\"margin: 20px 40px 20px 40px;\"> <em>Escher <\/em> criava padr\u00f5es e efeitos surpreendentes a partir de formas geom\u00e9tricas b\u00e1sicas.<br \/>\nCom esta atividade vamos procurar objetos matem\u00e1ticos disfar\u00e7ados de arte.<\/p>\n<div style=\"text-align:center;\">\n<input class=\"bo1 bbg1\" value=\"Atividade 12\" title=\"Clique aqui\" type=\"button\" onclick=    \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar a atividade';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Atividade 12';}\" \/>    <\/p>\n<div  style=\"display: none;\">\n<div class=\"gr3 cb14\">\n<table style=\"border:0px;  height:auto; margin-left: auto; margin-right: auto;\">\n<tr>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/pavi6.png\" style=\"border: 0px;\" alt=\"pavi6\" width=\"200\" height=\"295\" class=\"aligncenter size-full wp-image-49195\" \/><\/td>\n<td style=\"border: 1px solid #FFFFFF;  width:50%; vertical-align:middle;color:#000000;text-align: justify;font-size: 14px; font-family: verdana, Arial, Helvetica, sans-serif;line-height: 25px;\">Esta \u00e9 uma bela forma para se criar um padr\u00e3o de pavimenta\u00e7\u00e3o, n\u00e3o \u00e9?<br \/>\nMas vamos explor\u00e1-la matematicamente com uma \u00fanica pergunta:<br \/>\nSabendo que as curvas que definem a figura s\u00e3o semicircunfer\u00eancia de mesmo raio, voc\u00eas saberiam calcular a \u00e1rea dessa figura?<br \/>\nSe n\u00e3o sabem, acompanhem as sugest\u00f5es.<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/pavi7.png\" style=\"border: 0px;\"  alt=\"pavi7\" width=\"200\" height=\"205\" class=\"aligncenter size-full wp-image-49196\" \/><\/td>\n<td style=\"border: 1px solid #FFFFFF;  width:50%; vertical-align:middle;color:#000000;text-align: justify;font-size: 14px; font-family: verdana, Arial, Helvetica, sans-serif;line-height: 25px;\">Suponham que voc\u00eas conhe\u00e7am as dist\u00e2ncias entre os pontos A, B e C.<br \/>\nAjudou?\n<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/pavi7.png\" style=\"border: 0px;\"  alt=\"pavi7\" width=\"200\" height=\"205\" class=\"aligncenter size-full wp-image-49196\" \/><\/td>\n<td style=\"border: 1px solid #FFFFFF;  width:50%; vertical-align:middle;color:#000000;text-align: justify;font-size: 14px; font-family: verdana, Arial, Helvetica, sans-serif;line-height: 25px;\">Suponham que voc\u00eas saibam que as dist\u00e2ncias entre os pontos [tex]A[\/tex], [tex]B[\/tex] e [tex]C[\/tex] s\u00e3o iguais.<br \/>\nNada, ainda?<\/td>\n<\/tr>\n<tr>\n<td style=\"border: 1px solid #FFFFFF; vertical-align:middle;\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/pavi8.png\" alt=\"pavi8\" width=\"200\" height=\"205\" class=\"aligncenter size-full wp-image-49197\" \/><\/p>\n<td style=\"border: 1px solid #FFFFFF;  width:50%; vertical-align:middle;color:#000000;text-align: justify;font-size: 14px; font-family: verdana, Arial, Helvetica, sans-serif;line-height: 25px;\">\u00daltima dica, hem?<br \/>\nSuponha que<br \/>\n[tex]\\qquad d(A,B) = d(B,C) = d(C,A) = d[\/tex],<br \/>\nuna os pontos [tex]A[\/tex], [tex]B[\/tex] e [tex]C[\/tex] por segmentos de reta e calcule a \u00e1rea em fun\u00e7\u00e3o de [tex]d[\/tex].<br \/>\nAgora \u00e9 com voc\u00eas!<\/td>\n<\/tr>\n<\/table>\n<p>Esta era uma das t\u00e9cnicas utilizadas por <em>Escher <\/em> para desenhar seus padr\u00f5es de pavimenta\u00e7\u00e3o.<\/p>\n<p style=\"margin:30px;\">\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p style=\"margin:40px;\">\n<div class=\"gr2 cb15\" style=\"width:80%\">\n<p style=\"margin: 20px 40px 20px 40px;\"> Voc\u00ea conhece a &#8220;t\u00e9cnica da dentada&#8221;?<\/p>\n<div style=\"margin-top:30px;text-align:center;\">\n<input class=\"bo1 bbg1\" type=\"button\"  value=\"Atividade 13\" onclick=\"window.open('http:\/\/clubes.obmep.org.br\/blog\/?p=49273');\" title=\"Clique aqui\"\/><\/div>\n<p style=\"margin:10px;\">\n<\/div>\n<p style=\"margin:40px;\">\n<\/div>\n<p><a id=\"O4\"><\/p>\n<hr style=\"height:1px; width:30%;background-color:#6d360f; margin-top: 40px; margin-bottom: 8px;  border: 0 none\"\/>\n<hr style=\"height:1px; width:50%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:70%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:90%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:90%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:70%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:50%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:30%;background-color:#6d360f;  margin-top: 8px; margin-bottom: 40px; border: 0 none\"\/>\n<\/a><\/p>\n<div class=\"gr1 cb11\">\n<p class=\"ti1 c1\"><em> IX &#8211; Um dia de Escher <\/em><\/p>\n<hr style=\"height:3px;background-color:#6d360f; border: 0 none\"\/>\n<p style=\"margin:40px;\">\n<p class=\"ti2\">E a\u00ed, prontos para um dia de Escher?<\/p>\n<p class=\"ti2\">Vamos l\u00e1, cliquem neste \u00faltimo bot\u00e3o.<\/p>\n<p class=\"ti2\">Bom trabalho, pessoal!  <\/p>\n<p class=\"ti2\">Boa divers\u00e3o!!! <\/p>\n<p><a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=49325\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/botao.jpg\" alt=\"botao\" width=\"100\" height=\"100\" style=\"border:3px solid #6d360f;\" class=\"aligncenter size-full wp-image-49323\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/botao.jpg 600w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/botao-150x150.jpg 150w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/botao-300x297.jpg 300w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/><\/a><\/p>\n<p style=\"margin:30px;\">\n<\/div>\n<p style=\"margin:40px\">\n<div style=\" float:right;  width: 500px;  height:auto;\">\n<table style=\"border:0px;  height:auto; margin-left: auto; margin-right: auto;\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"75\" height=\"90\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala bg1\" style=\"width:350px;\" > Esperamos que voc\u00eas tenham gostado da divers\u00e3o!!<\/p>\n<p>&nbsp;<\/td>\n<\/tr>\n<\/table>\n<\/div>\n<div style=\"clear: both;\"><\/div>\n<hr style=\"height:1px;background-color:#6d360f;  margin-top: 10px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px;background-color:#6d360f;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<p style=\"text-align: right;\"><span style=\"color: #6d360f; font-size: 18px;\"><strong>Equipe COM &#8211; OBMEP<\/strong><\/span><\/p>\n<\/div>\n<p style=\"font-size: 16px;line-height: 30px;text-align: right; color: #6d360f;\">Outubro de 2015.<\/p>\n<p class=\"fim\"><a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=48005\" target=\"_blank\"><span style=\"color: #d66a1d;\"><strong>Ir para a Sala 1<\/strong><\/span><\/a><\/p>\n<p style=\"margin:30px;\">\n<div style=\"padding-left: 20px; padding-right:200px;\">\n<div class=\"ref\">\nFiguras, v\u00eddeos e material eventual adaptados ou extra\u00eddos de:<br \/>\n<a href=\"http:\/\/artperceptions.blogspot.com\/2010\/02\/m-c-escher.html\" target=\"_blank\"><span style=\"color: #b85b19;\">&#10152; Art Perceptions<\/span><\/a> &nbsp;&nbsp;&nbsp;(&Uacute;ltimo acesso em 18\/06\/20)<br \/>\n<a href=\"http:\/\/www.mcescher.com\/\" target=\"_blank\"><span style=\"color: #b85b19;\">&#10152;M.C.Escher<\/span><\/a> &nbsp;&nbsp;&nbsp;(&Uacute;ltimo acesso em 18\/06\/20)<br \/>\n<a href=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/10\/monografia1.pdf\" target=\"_blank\"><span style=\"color: #b85b19;\">&#10152;PAVIMENTA\u00c7\u00d5ES NO PLANO EUCLIDIANO<\/span><\/a> &nbsp;&nbsp;&nbsp;(&Uacute;ltimo acesso em 18\/06\/20)<br \/>\n<a href=\"http:\/\/totallyhistory.com\/art-history\/\" target=\"_blank\"><span style=\"color: #b85b19;\">&#10152;Totally History<\/span><\/a> &nbsp;&nbsp;&nbsp;(&Uacute;ltimo acesso em 18\/06\/20)<br \/>\n<a href=\"https:\/\/www.youtube.com\/\" target=\"_blank\"><span style=\"color: #b85b19;\">&#10152;YouTube<\/span><\/a> &nbsp;&nbsp;&nbsp;(&Uacute;ltimo acesso em 18\/06\/20)<br \/>\n<span style=\"color: #d66a1d;\">&#10152;<\/span> Licen\u00e7as sob Dom\u00ednio p\u00fablico via <a href=\"\/\/commons.wikimedia.org\/wiki\/\" target=\"_blank\" ><span style=\"color: #b85b19;\">Wikimedia Commons<\/span><\/a>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Pavimenta\u00e7\u00e3o, caleidosc\u00f3pios, caleidociclos, Escher e, at\u00e9, . . . Matem\u00e1tica!!! T\u00f3picos &#8211; Sala 2 VI &#8211; Escher VII &#8211; Um pouco sobre as pavimenta\u00e7\u00f5es de Escher VIII &#8211; Treinando para ser um Escher IX &#8211; Um dia de Escher VI &#8211; Escher Voc\u00eas j\u00e1 ouviram falar de um artista gr\u00e1fico chamado Escher? Bem, aqui nos &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/sala-de-atividades-pavimentacao-sala-2\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-48459","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/48459","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=48459"}],"version-history":[{"count":139,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/48459\/revisions"}],"predecessor-version":[{"id":223592,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/48459\/revisions\/223592"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=48459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}