{"id":5946,"date":"2010-11-23T20:54:50","date_gmt":"2010-11-23T20:54:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=5946"},"modified":"2022-11-18T16:09:14","modified_gmt":"2022-11-18T16:09:14","slug":"teorema-de-pitagoras","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=5946","title":{"rendered":"Teorema de Pit\u00e1goras"},"content":{"rendered":"<p style=\"text-align: left;\"><ul id='GTTabs_ul_5946' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_5946' class='GTTabs_curr'><a  id=\"5946_0\" onMouseOver=\"GTTabsShowLinks('Teorema'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Teorema<\/a><\/li>\n<li id='GTTabs_li_1_5946' ><a  id=\"5946_1\" onMouseOver=\"GTTabsShowLinks('Pit\u00e1goras de Samos'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Pit\u00e1goras de Samos<\/a><\/li>\n<li id='GTTabs_li_2_5946' ><a  id=\"5946_2\" onMouseOver=\"GTTabsShowLinks('Demonstra\u00e7\u00f5es'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Demonstra\u00e7\u00f5es<\/a><\/li>\n<li id='GTTabs_li_3_5946' ><a  id=\"5946_3\" onMouseOver=\"GTTabsShowLinks('Um document\u00e1rio'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Um document\u00e1rio<\/a><\/li>\n<li id='GTTabs_li_4_5946' ><a  id=\"5946_4\" onMouseOver=\"GTTabsShowLinks('Uma banda desenhada'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Uma banda desenhada<\/a><\/li>\n<li id='GTTabs_li_5_5946' ><a  id=\"5946_5\" onMouseOver=\"GTTabsShowLinks('Um problema'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Um problema<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_5946'>\n<span class='GTTabs_titles'><b>Teorema<\/b><\/span><\/p>\n<p style=\"text-align: center;\"><script 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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, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/p>\n<\/p>\n<p>Considera o tri\u00e2ngulo ret\u00e2ngulo e os quadrados constru\u00eddos sobre os seus lados.<\/p>\n<\/p>\n<ol>\n<li>Ativa a caixa &#8220;Mostrar \u00c1reas&#8221; e tenta perceber qual a rela\u00e7\u00e3o entre as \u00e1reas dos tr\u00eas quadrados.<\/li>\n<li>Seguidamente, ativa a caixa &#8220;Dividir Quadrado M\u00e9dio&#8221; e <strong>mant\u00e9m a &gt; b<\/strong>.<br \/>\nO quadrado m\u00e9dio foi dividido em quatro pe\u00e7as.<br \/>\nUtilizando essas quatro pe\u00e7as verdes e ainda o quadrado\u00a0azul, tenta construir um quadrado.<br \/>\nQue verificas?<\/li>\n<li>Completa a afirma\u00e7\u00e3o seguinte:<\/li>\n<\/ol>\n<blockquote>\n<p style=\"text-align: center;\"><strong>A \u00e1rea do quadrado constru\u00eddo sobre a ________________ de um tri\u00e2ngulo ret\u00e2ngulo \u00e9 igual \u00e0 soma as \u00e1reas dos quadrados constru\u00eddos sobre os ___________<\/strong>.<\/p>\n<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000080;\"><strong><span style=\"font-size: large;\">\\[{{a}^{2}}+{{b}^{2}}={{c}^{2}}\\]<\/span><\/strong><\/span><\/p>\n<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000080;\"><strong><span style=\"font-size: large;\"><div id=\"ggbApplet2\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet2\",\r\n\"width\":630,\r\n\"height\":314,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ 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VI a.C.)<\/strong><\/p>\n<div style=\"width: 171px\" class=\"wp-caption alignright\"><a href=\"http:\/\/upload.wikimedia.org\/wikipedia\/commons\/1\/1a\/Kapitolinischer_Pythagoras_adjusted.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"  \" src=\"http:\/\/upload.wikimedia.org\/wikipedia\/commons\/1\/1a\/Kapitolinischer_Pythagoras_adjusted.jpg\" alt=\"\" width=\"161\" height=\"215\" \/><\/a><p class=\"wp-caption-text\">Busto de Pit\u00e1goras de Samos (Capitoline Museums &#8211; Roma)<\/p><\/div>\n<p>Diz-se que viajou pelo Egipto, talvez pela Babil\u00f3nia, e que, regressado \u00e0 sua ilha natal, a encontrou sob o dom\u00ednio de um tirano; decidiu, ent\u00e3o fixar-se no Sul da It\u00e1lia mais precisamente em Crotona (nessa \u00e9poca pertencente \u00e0 Grande Gr\u00e9cia) e a\u00ed, ao que parece, fundou uma seita grega de car\u00e1cter m\u00edstico-pol\u00edtico e cient\u00edfico-religioso que se chamou \u201cescola pitag\u00f3rica\u201d.<\/p>\n<p>O segredo e o mist\u00e9rio com que se rodeavam os dogmas (por exemplo, o lema m\u00e1ximo \u201cTudo \u00e9 N\u00famero\u201d) e os ensinamentos desta \u201cescola\u201d, assim como o car\u00e1cter exclusivamente oral destes e a obriga\u00e7\u00e3o de atribuir todas as descobertas ao chefe da \u201cescola\u201d, torna dif\u00edcil averiguar em que consistem efetivamente as contribui\u00e7\u00f5es de PIT\u00c1GORAS ou melhor dos \u201cpitag\u00f3ricos\u201d, como j\u00e1 Arist\u00f3teles os designava ao referir-lhes.<\/p>\n<p>Os pitag\u00f3ricos rendiam verdadeiro culto m\u00edstico ao n\u00famero natural considerando-o como a ess\u00eancia de todas as coisas. Veremos mais adiante um das implica\u00e7\u00f5es desta posi\u00e7\u00e3o.<\/p>\n<p>\u00c9 ent\u00e3o que aparece pela primeira vez o termo \u201cmatem\u00e1tica\u201d \u2013 na palavra grega \u201c$\\mu \\alpha \\theta \\eta \\mu \\alpha \\tau \\iota \\kappa \\alpha $\u201d (miu, alfa, teta, eta, miu, alfa, tau, iota, capa, alfa), usada por uns como o significado \u201co que \u00e9 aprendido\u201d, por outros como sin\u00f3nimo de \u201cci\u00eancia por excel\u00eancia\u201d e ainda por outros por \u201cci\u00eancia racional\u201d.<\/p>\n<p>Da\u00ed certamente PIT\u00c1GORAS pode ser cognominado como \u201cO Pai da Matem\u00e1tica\u201d.<\/p>\n<p style=\"text-align: center;\"><div id=\"ggbApplet3\" style=\"float: right;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet3\",\r\n\"width\":239,\r\n\"height\":226,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 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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, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet3 = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet'); applet2.inject('ggbApplet2'); applet3.inject('ggbApplet3')};\r\n<\/script><\/p>\n<p>A \u201cescola pitag\u00f3rica\u201d usava um s\u00edmbolo de reconhecimento dos membros da seita: o Pentagrama ou a Estrela de Cinco Pontos ou ainda O Pent\u00e1gono Estrelado, formado unindo n\u00e3o consecutivamente e com um s\u00f3 tra\u00e7ado (isto \u00e9, sem levantar o l\u00e1pis, por exemplo) os cinco pontos obtidos na divis\u00e3o da circunfer\u00eancia em cinco partes iguais.<\/p>\n<p>Como referimos atr\u00e1s, os pitag\u00f3ricos pretendiam explicar tudo por meio dos n\u00fameros constitu\u00eddos \u00e0 custa dos n\u00fameros naturais.<\/p>\n<p>Admitiam que toda a figura geom\u00e9trica fosse formada por um n\u00famero finito de pontos, sendo estes pensados como \u00ednfimos corp\u00fasculos (\u201cm\u00f3nadas\u201d) todos iguais entre si; da\u00ed resultava que dois comprimentos seriam sempre \u201ccomensur\u00e1veis\u201d, pois, com efeito, sendo um segmento formado por n \u201cm\u00f3nadas\u201d e outro por m \u201cm\u00f3nadas\u201d, a raz\u00e3o entre o 1.\u00ba e o 2.\u00ba seria $\\frac{n}{m}$ (representativa de um n\u00famero racional).<\/p>\n<p>Todavia, por ironia do destino, foi o pr\u00f3prio teorema de Pit\u00e1goras que veio demolir tal doutrina permitindo demonstrar que a hipotenusa do tri\u00e2ngulo ret\u00e2ngulo de catetos iguais \u00e9 \u201cincomensur\u00e1vel\u201d com qualquer desses catetos tomado como comprimento unidade, ou seja que $\\sqrt{2}$ n\u00e3o \u00e9 um n\u00famero racional.<\/p>\n<div style=\"width: 171px\" class=\"wp-caption alignright\"><a href=\"http:\/\/jeff560.tripod.com\/images\/theorem.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"   \" src=\"http:\/\/jeff560.tripod.com\/images\/theorem.jpg\" alt=\"\" width=\"161\" height=\"222\" \/><\/a><p class=\"wp-caption-text\">Selo comemorativo do 2500.\u00ba anivers\u00e1rio da funda\u00e7\u00e3o da &#8220;Escola Pitag\u00f3rica&#8221;<\/p><\/div>\n<p>Esta descoberta \u2013 que constitui um dos acontecimentos capitais da hist\u00f3ria do pensamento \u2013 foi tida como um esc\u00e2ndalo pelos pr\u00f3prios autores que tentaram ocult\u00e1-la, convencidos que alguma calamidade cairia sobre eles se a divulgassem! Mas, desde ent\u00e3o, a teoria geom\u00e9trica das \u201cm\u00f3nadas\u201d ficou condenada ao fracasso. Em seu lugar, triunfou outra teoria que concebia o espa\u00e7o geom\u00e9trico como um todo cont\u00ednuo.<\/p>\n<p><em>Extra\u00eddo de Galeria dos Matem\u00e1ticos do Jornal de Mathematica Elementar, Volume 1, 1991<\/em><\/p>\n<\/p>\n<p>Saber mais:<\/p>\n<ul>\n<li><a href=\"http:\/\/www.educ.fc.ul.pt\/icm\/icm2001\/icm32\/index.html\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/www.educ.fc.ul.pt\/icm\/icm2001\/icm32\/index.html<\/a><\/li>\n<li><a href=\"http:\/\/en.wikipedia.org\/wiki\/Pythagoras\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/en.wikipedia.org\/wiki\/Pythagoras<\/a><\/li>\n<\/ul>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5946' onClick='GTTabs_show(0,5946)'>&lt;&lt; Teorema<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_5946' onClick='GTTabs_show(2,5946)'>Demonstra\u00e7\u00f5es &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_2_5946'>\n<span class='GTTabs_titles'><b>Demonstra\u00e7\u00f5es<\/b><\/span><\/p>\n<p><a href=\"http:\/\/sunsite.ubc.ca\/DigitalMathArchive\/Euclid\/java\/html\/babylon.gif\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright\" src=\"http:\/\/sunsite.ubc.ca\/DigitalMathArchive\/Euclid\/java\/html\/babylon.gif\" alt=\"\" width=\"320\" height=\"220\" \/><\/a>H\u00e1 ind\u00edcios de que o Teorema de Pit\u00e1goras foi descoberto mais cedo pelos Chineses e Indianos, mas exatamente quando n\u00e3o \u00e9 sabido.<\/p>\n<p>O mais antigo registo do Teorema de Pit\u00e1goras consta em placas da Babil\u00f3nia datando cerca de 1000 a. C. Al\u00e9m das placas contendo exerc\u00edcios que dependem do conhecimento de pelo menos alguns casos espec\u00edficos, outras placas foram encontradas com imagens que s\u00e3o provas efetivas do Teorema em casos especiais em que os catetos s\u00e3o iguais.<\/p>\n<p>S\u00e3o conhecidas centenas de demonstra\u00e7\u00f5es do Teorema de Pit\u00e1goras.<\/p>\n<p>No site <a href=\"http:\/\/www.cut-the-knot.org\/pythagoras\/\" target=\"_blank\" rel=\"noopener noreferrer\">Cut-The-Knot<\/a> s\u00e3o apresentadas mais de 70 demonstra\u00e7\u00f5es.<\/p>\n<\/p>\n<p style=\"text-align: center;\"><span class=\"aligncenter\"><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/CAkMUdeB06o\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/span><\/p>\n<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5946' onClick='GTTabs_show(1,5946)'>&lt;&lt; Pit\u00e1goras de Samos<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_5946' onClick='GTTabs_show(3,5946)'>Um document\u00e1rio &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_3_5946'>\n<span class='GTTabs_titles'><b>Um document\u00e1rio<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/08\/GeniusPythagoras-.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"2853\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=2853\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/08\/GeniusPythagoras-.jpg\" data-orig-size=\"647,466\" 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=\"Genius: Pythagoras\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/08\/GeniusPythagoras-.jpg\" class=\"alignright size-medium wp-image-2853\" title=\"Genius: Pythagoras\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/08\/GeniusPythagoras--300x216.jpg\" alt=\"\" width=\"144\" height=\"104\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/08\/GeniusPythagoras--300x216.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/08\/GeniusPythagoras--150x108.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/08\/GeniusPythagoras--400x288.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/08\/GeniusPythagoras-.jpg 647w\" sizes=\"auto, (max-width: 144px) 100vw, 144px\" \/><\/a>This Documentary describes Pythagoras. It was produced by Cromwell Productions in 1996.<\/p>\n<p>Pythagoras (fl. 530 BCE) must have been one of the world&#8217;s greatest men, but he wrote nothing, and it is hard to say how much of the doctrine we know as Pythagorean is due to the founder of the society and how much is later development.<\/p>\n<p>It is also hard to say how much of what we are told about the life of Pythagoras is trustworthy; for a mass of legend gathered around his name at an early date.<\/p>\n<p>Sometimes he is represented as a man of science, and sometimes as a preacher of mystic doctrines, and we might be tempted to regard one or other of those characters as alone historical.<\/p>\n<p style=\"text-align: center;\"><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/3fos_pXOfe0\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5946' onClick='GTTabs_show(2,5946)'>&lt;&lt; Demonstra\u00e7\u00f5es<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_5946' onClick='GTTabs_show(4,5946)'>Uma banda desenhada &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_4_5946'>\n<span class='GTTabs_titles'><b>Uma banda desenhada<\/b><\/span><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/cm\/af18\/t5\/pitag_1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/cm\/af18\/t5\/pitag_1.jpg\" alt=\"\" width=\"359\" height=\"319\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/cm\/af18\/t5\/pitag_2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/cm\/af18\/t5\/pitag_2.jpg\" alt=\"\" width=\"359\" height=\"319\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/cm\/af18\/t5\/pitag_3.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/cm\/af18\/t5\/pitag_3.jpg\" alt=\"\" width=\"359\" height=\"319\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/cm\/af18\/t5\/pitag_4.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/cm\/af18\/t5\/pitag_4.jpg\" alt=\"\" width=\"359\" height=\"319\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/cm\/af18\/t5\/pitag_5.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/cm\/af18\/t5\/pitag_5.jpg\" alt=\"\" width=\"359\" height=\"319\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><em>Mais Matem\u00e1ticas Assassinas<\/em>, Kjartan Poskitt, Ilustrado por Philip Reeve, Publica\u00e7\u00f5es Europa-Am\u00e9rica<\/p>\n<p>A raz\u00e3o da hist\u00f3ria: <a href=\"http:\/\/www.educ.fc.ul.pt\/icm\/icm99\/icm17\/incomens.htm\" target=\"_blank\" rel=\"noopener noreferrer\">A QUEST\u00c3O DA INCOMENSURABILDADE<\/a><\/p>\n<p>Ficha de Trabalho: <a href=\"https:\/\/www.acasinhadamatematica.pt\/?page_id=5993\">Duplica\u00e7\u00e3o do Quadrado<\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5946' onClick='GTTabs_show(3,5946)'>&lt;&lt; Um document\u00e1rio<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_5946' onClick='GTTabs_show(5,5946)'>Um problema &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_5_5946'>\n<span class='GTTabs_titles'><b>Um problema<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/findx2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6905\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6905\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/findx2.jpg\" data-orig-size=\"480,480\" 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=\"Find x\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/findx2.jpg\" class=\"aligncenter size-full wp-image-6905\" title=\"Find x\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/findx2.jpg\" alt=\"\" width=\"480\" height=\"480\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/findx2.jpg 480w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/findx2-150x150.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/findx2-300x300.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/findx2-400x400.jpg 400w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a><\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5946' onClick='GTTabs_show(4,5946)'>&lt;&lt; Uma banda desenhada<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Explora\u00e7\u00e3o din\u00e2mica de puzzles geom\u00e9tricos conducentes \u00e0 perce\u00e7\u00e3o de que a \u00e1rea do quadrado constru\u00eddo sobre a hipotenusa de um tri\u00e2ngulo ret\u00e2ngulo \u00e9 igual \u00e0 soma as \u00e1reas dos quadrados constru\u00eddos sobre os catetos.<\/p>\n","protected":false},"author":1,"featured_media":19192,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,112,682],"tags":[424,67,118],"series":[],"class_list":["post-5946","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-decomposicao-de-figuras-teorema-de-pitagoras","category-teorema-de-pitagoras","tag-8-o-ano","tag-geometria","tag-teorema-de-pitagoras"],"views":7063,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/Teorema_de_Pitagoras.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5946","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=5946"}],"version-history":[{"count":1,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5946\/revisions"}],"predecessor-version":[{"id":24227,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5946\/revisions\/24227"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19192"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5946"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5946"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5946"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=5946"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}