{"id":23707,"date":"2022-12-11T10:25:58","date_gmt":"2022-12-11T10:25:58","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23707"},"modified":"2022-12-28T00:03:28","modified_gmt":"2022-12-28T00:03:28","slug":"numero-de-ouro-no-retangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23707","title":{"rendered":"N\u00famero de ouro no ret\u00e2ngulo"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23707' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23707' class='GTTabs_curr'><a  id=\"23707_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23707' ><a  id=\"23707_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<li id='GTTabs_li_2_23707' ><a  id=\"23707_2\" onMouseOver=\"GTTabsShowLinks('V\u00eddeo 1'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>V\u00eddeo 1<\/a><\/li>\n<li id='GTTabs_li_3_23707' ><a  id=\"23707_3\" onMouseOver=\"GTTabsShowLinks('V\u00eddeo 2'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>V\u00eddeo 2<\/a><\/li>\n<li id='GTTabs_li_4_23707' ><a  id=\"23707_4\" onMouseOver=\"GTTabsShowLinks('V\u00eddeo 3'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>V\u00eddeo 3<\/a><\/li>\n<li id='GTTabs_li_5_23707' ><a  id=\"23707_5\" onMouseOver=\"GTTabsShowLinks('V\u00eddeo 4'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>V\u00eddeo 4<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_23707'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O Diogo ouviu falar no n\u00famero de ouro, \\(\\Phi = \\frac{{1 + \\sqrt 5 }}{2}\\), na aula de Matem\u00e1tica.<\/p>\n<p>Curioso, decidiu investigar na Internet. Encontrou uma refer\u00eancia ao n\u00famero de ouro na seguinte constru\u00e7\u00e3o geom\u00e9trica:<\/p>\n<p>&#8220;Dois quadrados, unidos por um dos seus lados, formam o ret\u00e2ngulo [ABCD], com os lados que medem, respetivamente, 1 e 2 unidades de medida. A diagonal [AC] interseta o lado comum aos dois quadrados. Centrada nesse ponto de interse\u00e7\u00e3o, desenha-se uma circunfer\u00eancia de di\u00e2metro 1, que interseta [AC} nos pontos M e N.<\/p>\n<p>Ent\u00e3o, \\(\\overline {AN} = \\Phi \\).&#8221;<\/p>\n<p>\u00a0<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag073-T11.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23711\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23711\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag073-T11.png\" data-orig-size=\"763,402\" 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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag073-T11\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag073-T11.png\" class=\"aligncenter wp-image-23711\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag073-T11-300x158.png\" alt=\"\" width=\"480\" height=\"253\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag073-T11-300x158.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag073-T11.png 763w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a><\/p>\n<ol>\n<li>Reproduz, na tua folha, a constru\u00e7\u00e3o geom\u00e9trica descrita, utilizando instrumentos de desenho.<\/li>\n<li>Verifica que a medida de [AN] \u00e9 o n\u00famero de ouro, sem recorrer a medi\u00e7\u00f5es.<br \/>Apresenta os c\u00e1lculos que realizaste.<\/li>\n<\/ol>\n<p><span style=\"font-size: revert; color: initial;\"><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23707' onClick='GTTabs_show(1,23707)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23707'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><\/span><!--more--><\/p>\n<ol>\n<li>Apresenta-se seguidamente a constru\u00e7\u00e3o geom\u00e9trica descrita.<br \/><br \/><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 = 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator DA=Data Analysis, FI=Function Inspector, macro=Macros\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\napplet.setPreviewImage('data:image\/png;base64,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');\r\n<\/script><br \/><br \/><\/li>\n<li>Determinemos agora a medida de [AN]:<br \/>\\[\\begin{array}{*{20}{l}}{\\overline {AN} }&amp; = &amp;{\\overline {AC} &#8211; \\overline {NC} }\\\\{}&amp; = &amp;{\\overline {AC} &#8211; \\frac{{\\overline {AC} &#8211; \\overline {MN} }}{2}}\\\\{}&amp; = &amp;{\\sqrt {{{\\overline {AB} }^2} + {{\\overline {BC} }^2}} &#8211; \\frac{{\\sqrt {{{\\overline {AB} }^2} + {{\\overline {BC} }^2}} &#8211; \\overline {MN} }}{2}}\\\\{}&amp; = &amp;{\\sqrt {{2^2} + {1^2}} &#8211; \\frac{{\\sqrt {{2^2} + {1^2}} &#8211; 1}}{2}}\\\\{}&amp; = &amp;{\\sqrt 5 &#8211; \\frac{{\\sqrt 5 &#8211; 1}}{2}}\\\\{}&amp; = &amp;{\\frac{{2\\sqrt 5 &#8211; \\sqrt 5 + 1}}{2}}\\\\{}&amp; = &amp;{\\frac{{\\sqrt 5 + 1}}{2}}\\end{array}\\]<br \/>Portanto, \\(\\Phi = \\frac{{\\sqrt 5 + 1}}{2}\\).<\/li>\n<\/ol>\n\n\n\n<div style=\"height:35px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"style-scope ytd-watch-metadata\"><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23707' onClick='GTTabs_show(0,23707)'>&lt;&lt; Enunciado<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23707' onClick='GTTabs_show(2,23707)'>V\u00eddeo 1 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_2_23707'>\n<span class='GTTabs_titles'><b>V\u00eddeo 1<\/b><\/span><\/p>\n<h5>Arte &amp; Matem\u00e1tica &#8211; O N\u00famero de Ouro<\/h5>\n\n\n\n<style>.embed-container { position: relative; padding-bottom: 56.25%; height: 0; overflow: hidden; max-width: 100%; } .embed-container iframe, .embed-container object, .embed-container embed { position: absolute; top: 0; left: 0; width: 100%; height: 100%; }<\/style><div class=\"embed-container\"><iframe src=\"https:\/\/www.youtube.com\/embed\/Eo0gxSx34VI\" frameborder=\"0\" allowfullscreen=\"\"><\/iframe><\/div>\n\n\n\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23707' onClick='GTTabs_show(1,23707)'>&lt;&lt; Resolu\u00e7\u00e3o<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23707' onClick='GTTabs_show(3,23707)'>V\u00eddeo 2 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_3_23707'>\n<span class='GTTabs_titles'><b>V\u00eddeo 2<\/b><\/span><\/p>\n<h5>Mas por menos &#8211; El n\u00famero \u00e1ureo<\/h5>\n\n\n\n<style>.embed-container { position: relative; padding-bottom: 56.25%; height: 0; overflow: hidden; max-width: 100%; } .embed-container iframe, .embed-container object, .embed-container embed { position: absolute; top: 0; left: 0; width: 100%; height: 100%; }<\/style><div class=\"embed-container\"><iframe src=\"https:\/\/www.youtube.com\/embed\/cBCxWKr-dlc\" frameborder=\"0\" allowfullscreen=\"\"><\/iframe><\/div>\n\n\n\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23707' onClick='GTTabs_show(2,23707)'>&lt;&lt; V\u00eddeo 1<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23707' onClick='GTTabs_show(4,23707)'>V\u00eddeo 3 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_4_23707'>\n<span class='GTTabs_titles'><b>V\u00eddeo 3<\/b><\/span><\/p>\n<h5>Fibonacci and the golden mean<\/h5>\n\n\n\n<style>.embed-container { position: relative; padding-bottom: 56.25%; height: 0; overflow: hidden; max-width: 100%; } .embed-container iframe, .embed-container object, .embed-container embed { position: absolute; top: 0; left: 0; width: 100%; height: 100%; }<\/style><div class=\"embed-container\"><iframe src=\"https:\/\/www.youtube.com\/embed\/hbauYiy-uB8\" frameborder=\"0\" allowfullscreen=\"\"><\/iframe><\/div>\n\n\n\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23707' onClick='GTTabs_show(3,23707)'>&lt;&lt; V\u00eddeo 2<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23707' onClick='GTTabs_show(5,23707)'>V\u00eddeo 4 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_5_23707'>\n<span class='GTTabs_titles'><b>V\u00eddeo 4<\/b><\/span><\/p>\n<h5>Isto \u00e9 Matem\u00e1tica &#8211; A Propor\u00e7\u00e3o Divina<\/h5>\n\n\n\n<style>.embed-container { position: relative; padding-bottom: 56.25%; height: 0; overflow: hidden; max-width: 100%; } .embed-container iframe, .embed-container object, .embed-container embed { position: absolute; top: 0; left: 0; width: 100%; height: 100%; }<\/style><div class=\"embed-container\"><iframe src=\"https:\/\/www.youtube.com\/embed\/mfL6-g5mQw4\" frameborder=\"0\" allowfullscreen=\"\"><\/iframe><\/div>\n\n\n\n<div style=\"height:60px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<style>.embed-container { position: relative; padding-bottom: 56.25%; height: 0; overflow: hidden; max-width: 100%; } .embed-container iframe, .embed-container object, .embed-container embed { position: absolute; top: 0; left: 0; width: 100%; height: 100%; }<\/style><div class=\"embed-container\"><iframe src=\"https:\/\/www.youtube.com\/embed\/xtsTXAwWF20\" frameborder=\"0\" allowfullscreen=\"\"><\/iframe><\/div>\n\n\n\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23707' onClick='GTTabs_show(4,23707)'>&lt;&lt; V\u00eddeo 3<\/a><\/span><\/div><\/div>\n\n<\/p>\n<p><strong>Hiperliga\u00e7\u00f5es relacionadas<\/strong>:<\/p>\n<ul>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/?p=6814\" target=\"_blank\" rel=\"noopener\">Nature by Numbers<\/a><\/li>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/?p=1837\" target=\"_blank\" rel=\"noopener\">Donald no Pa\u00eds da Matem\u00e1gica<\/a><\/li>\n<li><a href=\"https:\/\/pt.wikipedia.org\/wiki\/Propor%C3%A7%C3%A3o_%C3%A1urea\" target=\"_blank\" rel=\"noopener\">Propor\u00e7\u00e3o \u00e1urea<\/a><\/li>\n<li><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Golden_ratio\/\" target=\"_blank\" rel=\"noopener\">The Golden ratio<\/a><\/li>\n<li><a href=\"https:\/\/www.goldennumber.net\/\" target=\"_blank\" rel=\"noopener\">The Golden Ratio: Phi, 1.618<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Golden_ratio\" target=\"_blank\" rel=\"noopener\">Golden ratio<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Diogo ouviu falar no n\u00famero de ouro, \\(\\Phi = \\frac{{1 + \\sqrt 5 }}{2}\\), na aula de Matem\u00e1tica. Curioso, decidiu investigar na Internet. Encontrou uma refer\u00eancia ao n\u00famero de ouro&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23712,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,67,118],"series":[],"class_list":["post-23707","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-teorema-de-pitagoras","tag-8-o-ano","tag-geometria","tag-teorema-de-pitagoras"],"views":361,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag073-T11_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23707","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=23707"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23707\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23712"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23707"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23707"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23707"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23707"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}