{"id":10005,"date":"2012-10-04T11:18:38","date_gmt":"2012-10-04T10:18:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10005"},"modified":"2026-06-05T00:29:59","modified_gmt":"2026-06-04T23:29:59","slug":"o-caracol-e-a-alface","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10005","title":{"rendered":"O caracol e a alface"},"content":{"rendered":"<p><ul id='GTTabs_ul_10005' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10005' class='GTTabs_curr'><a  id=\"10005_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10005' ><a  id=\"10005_1\" onMouseOver=\"GTTabsShowLinks('Investigue&#8230;'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Investigue&#8230;<\/a><\/li>\n<li id='GTTabs_li_2_10005' ><a  id=\"10005_2\" onMouseOver=\"GTTabsShowLinks('Problema da Formiga'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Problema da Formiga<\/a><\/li>\n<li id='GTTabs_li_3_10005' ><a  id=\"10005_3\" onMouseOver=\"GTTabsShowLinks('Num cubo&#8230;'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Num cubo&#8230;<\/a><\/li>\n<li id='GTTabs_li_4_10005' ><a  id=\"10005_4\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_10005'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<div id=\"attachment_10007\" style=\"width: 436px\" class=\"wp-caption alignright\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-10007\" data-attachment-id=\"10007\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10007\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface.jpg\" data-orig-size=\"710,290\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349346968&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Caracol e alface\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;O caracol e a alface&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface.jpg\" class=\" wp-image-10007 \" title=\"Caracol e alface\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface.jpg\" alt=\"\" width=\"426\" height=\"174\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface.jpg 710w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-300x122.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-150x61.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-400x163.jpg 400w\" sizes=\"auto, (max-width: 426px) 100vw, 426px\" \/><\/a><p id=\"caption-attachment-10007\" class=\"wp-caption-text\">O caracol e a alface<\/p><\/div>\n<p>Um caracol colocado em $C$ quer atingir uma alface em $A$.<\/p>\n<p>Para isso, tem de escalar uma placa de vidro [de espessura desprez\u00e1vel], com $0,75$ m de altura.<\/p>\n<p>A dist\u00e2ncia do caracol \u00e0 placa \u00e9 $1,5$ m e da placa \u00e0 alface \u00e9 de $1$ m.<\/p>\n<p>Na figura est\u00e1 representado, a vermelho, um exemplo de trajeto que o caracol pode seguir.<\/p>\n<p>Se a sua velocidade \u00e9 de $5$ km\/h, quanto tempo, no m\u00ednimo, ter\u00e1 de esperar at\u00e9 alcan\u00e7ar a sua refei\u00e7\u00e3o?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10005' onClick='GTTabs_show(1,10005)'>Investigue&#8230; &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10005'>\n<span class='GTTabs_titles'><b>Investigue&#8230;<\/b><\/span><!--more--><\/p>\n<p>Utilize a aplica\u00e7\u00e3o apresentada abaixo para investigar o caminho mais curto.<\/p>\n<\/p>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":782,\r\n\"height\":442,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 59 || 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 || 16 51 64 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214px\" class=\"wp-caption alignright\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/problformiga.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-10013\" data-attachment-id=\"10013\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10013\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/problformiga.jpg\" data-orig-size=\"566,711\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349374069&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Problema da formiga\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Problema da Formiga&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/problformiga.jpg\" class=\" wp-image-10013   \" title=\"Problema da formiga\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/problformiga.jpg\" alt=\"\" width=\"204\" height=\"256\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/problformiga.jpg 566w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/problformiga-238x300.jpg 238w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/problformiga-119x150.jpg 119w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/problformiga-400x502.jpg 400w\" sizes=\"auto, (max-width: 204px) 100vw, 204px\" \/><\/a><p id=\"caption-attachment-10013\" class=\"wp-caption-text\">Problema da Formiga<br \/>Matem\u00e1tica Viva &#8211; Pavilh\u00e3o do Conhecimento, 2000<\/p><\/div>\n<p>A superf\u00edcie do bloco de madeira mostrado na fotografia \u00e9 \u201co mundo\u201d onde vive uma formiga imagin\u00e1ria, que, quando se desloca entre dois pontos quaisquer, escolhe sempre, de entre todos os caminhos poss\u00edveis, um mais curto. Uma ponta do fio est\u00e1 presa junto de um dos v\u00e9rtices &#8211; A &#8211; da base do paralelep\u00edpedo.<\/p>\n<p>Tente, com a ajuda do fio e para v\u00e1rios pares de pontos, encontrar os caminhos mais curtos unindo os dois pontos de cada par. Descubra, em particular, um caminho mais curto unindo o v\u00e9rtice A ao v\u00e9rtice que lhe \u00e9 diametralmente oposto, na face de cima e note que esse caminho n\u00e3o atravessa a face superior.<\/p>\n<p>Tente imaginar qual \u00e9, para a formiga, o ponto P mais afastado de A e verifique, com a ajuda do fio, se a sua resposta est\u00e1 correta. Para isso, comece por apertar com os dedos o fio (esticado) junto ao ponto P; se a sua resposta estiver correta, deve poder chegar com esse bocado de fio a todos os outros pontos da superf\u00edcie (porque est\u00e3o mais perto de A).<\/p>\n<\/p>\n<p>Para saber mais:<\/p>\n<ul>\n<li><a href=\"https:\/\/www.atractor.pt\/matviva\/index2.html\" target=\"_blank\" rel=\"noopener\">Atractor &#8211; Matem\u00e1tica Viva<\/a><\/li>\n<li><a href=\"https:\/\/www.atractor.pt\/matviva\/geral\/PF\/PF.html\" target=\"_blank\" rel=\"noopener\">Atractor &#8211; Ploblema da Formiga<\/a><\/li>\n<li><a href=\"https:\/\/www.atractor.pt\/matviva\/geral\/formiga\/formi1\/oproblem.htm\" target=\"_blank\" rel=\"noopener\">Interpretandao e tentando resolver o problema<\/a><\/li>\n<\/ul>\n<p style=\"text-align: center;\">\u00a0<iframe loading=\"lazy\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/9hb9ct-XotU\" frameborder=\"0\" allowfullscreen><\/iframe><\/p>\n<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10005' onClick='GTTabs_show(1,10005)'>&lt;&lt; Investigue&#8230;<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10005' onClick='GTTabs_show(3,10005)'>Num cubo&#8230; &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_3_10005'>\n<span class='GTTabs_titles'><b>Num cubo&#8230;<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/cubo.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10042\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10042\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/cubo.jpg\" data-orig-size=\"561,558\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349392385&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Cubo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/cubo.jpg\" class=\"alignright  wp-image-10042\" title=\"Cubo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/cubo.jpg\" alt=\"\" width=\"202\" height=\"201\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/cubo.jpg 561w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/cubo-150x150.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/cubo-300x298.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/cubo-400x397.jpg 400w\" sizes=\"auto, (max-width: 202px) 100vw, 202px\" \/><\/a>Na figura est\u00e1 representado o cubo $\\left[ {ABCDEFGH} \\right]$.<\/p>\n<p>Cada um dos pontos $I$, $J$, $K$, $L$, $M$ e $N$ \u00e9 ponto m\u00e9dio de uma aresta.<\/p>\n<p>O volume do cubo \u00e9 igual a $8$.<\/p>\n<p>Considere o trajeto mais curto de $I$ a $J$ que passa pela aresta $\\left[ {EF} \\right]$. Determine o comprimento desse trajeto.<\/p>\n<\/p>\n<p><strong>Sugest\u00e3o<\/strong>: comece por desenhar uma planifica\u00e7\u00e3o do cubo, na qual <em>esse trajeto possa ser representado por um segmento de reta<\/em>.<\/p>\n<\/p>\n<p><strong>Resolu\u00e7\u00e3o<\/strong>:<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/planif2facescubo.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10044\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10044\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/planif2facescubo.jpg\" data-orig-size=\"251,403\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349393033&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Planifica\u00e7\u00e3o parcial\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/planif2facescubo.jpg\" class=\"alignright  wp-image-10044\" title=\"Planifica\u00e7\u00e3o parcial\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/planif2facescubo.jpg\" alt=\"\" width=\"151\" height=\"242\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/planif2facescubo.jpg 251w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/planif2facescubo-93x150.jpg 93w\" sizes=\"auto, (max-width: 151px) 100vw, 151px\" \/><\/a>Como o trajeto pedido passa pela aresta $\\left[ {EF} \\right]$, \u00e9 suficiente considerar uma planifica\u00e7\u00e3o parcial do cubo que inclua as faces superior e de frente.<\/p>\n<p>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo $\\left[ {AIJ} \\right]$, temos: $\\overline {IJ}\u00a0 = \\sqrt {{{\\overline {AI} }^2} + {{\\overline {AJ} }^2}}\u00a0 = \\sqrt {{1^2} + {3^2}}\u00a0 = \\sqrt {10} $.<\/p>\n<p>Portanto, o trajeto mais curto, de acordo com as condi\u00e7\u00f5es estabelecidas, tem $\\sqrt {10} $ unidades de comprimento.<\/p>\n<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10005' onClick='GTTabs_show(2,10005)'>&lt;&lt; Problema da Formiga<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10005' onClick='GTTabs_show(4,10005)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_4_10005'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><\/p>\n<p>Como \u00e9 considerado que o caracol se desloca a velocidade constante, o tempo de espera at\u00e9 alcan\u00e7ar a alface ser\u00e1 m\u00ednimo para o menor trajeto poss\u00edvel.<\/p>\n<p>Planificada a superf\u00edcie sobre a qual o caracol se desloca para atingir a alface, conclui-se que o menor trajeto corresponde ao segmento de reta $\\left[ {{C_2}{A_2}} \\right]$:<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-2a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10034\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10034\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-2a.png\" data-orig-size=\"664,268\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Esquema\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-2a.png\" class=\"aligncenter  wp-image-10034\" title=\"Esquema\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-2a.png\" alt=\"\" width=\"664\" height=\"268\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-2a.png 664w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-2a-300x121.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-2a-150x60.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/caracol-alface-2a-400x161.png 400w\" sizes=\"auto, (max-width: 664px) 100vw, 664px\" \/><\/a><\/p>\n<p>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo assinalado da figura, temos: $$\\overline {{C_2}{A_2}}\u00a0 = \\sqrt {{{\\left( {1,5 + 0,75 + 0,75 + 1} \\right)}^2} + {3^2}}\u00a0 = \\sqrt {{4^2} + {3^2}}\u00a0 = 5$$<\/p>\n<p>Portanto, para alcan\u00e7ar a sua refei\u00e7\u00e3o, o caracol ter\u00e1 de esperar $1$ hora, no m\u00ednimo.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10005' onClick='GTTabs_show(3,10005)'>&lt;&lt; Num cubo&#8230;<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Investigue&#8230; Enunciado Um caracol colocado em $C$ quer atingir uma alface em $A$. Para isso, tem de escalar uma placa de vidro [de espessura desprez\u00e1vel], com $0,75$ m de altura. A dist\u00e2ncia do&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20778,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,322],"tags":[429,67,430],"series":[],"class_list":["post-10005","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-modulo-inicial","tag-10-o-ano","tag-geometria","tag-modulo-inicial"],"views":3551,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/10V1Pag036-16_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10005","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10005"}],"version-history":[{"count":3,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10005\/revisions"}],"predecessor-version":[{"id":27919,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10005\/revisions\/27919"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20778"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10005"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}