{"id":13062,"date":"2017-11-26T22:57:02","date_gmt":"2017-11-26T22:57:02","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13062"},"modified":"2022-01-17T21:14:26","modified_gmt":"2022-01-17T21:14:26","slug":"as-medianas-de-um-triangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13062","title":{"rendered":"As medianas de um tri\u00e2ngulo"},"content":{"rendered":"<ol>\n<li>Desenha, em cartolina, tr\u00eas tri\u00e2ngulos: um equil\u00e1tero, um is\u00f3sceles e um escaleno. Recorta-os.<\/li>\n<li>Em cada um deles, une cada v\u00e9rtice ao ponto m\u00e9dio do lado oposto.<br \/>\nQuantos segmentos de reta tra\u00e7aste em cada tri\u00e2ngulo?<\/li>\n<li>Os segmentos de reta tra\u00e7ados em cada um dos tri\u00e2ngulos t\u00eam algum ponto comum?<\/li>\n<li>Faz um pequeno orif\u00edcio no ponto referido em 3. em cada um dos tri\u00e2ngulos e, atrav\u00e9s dele, suspende o tri\u00e2ngulo por um fio.\u00a0O tri\u00e2ngulo fica em equil\u00edbrio numa posi\u00e7\u00e3o horizontal?<\/li>\n<li>Explora a anima\u00e7\u00e3o de geometria din\u00e2mica.<\/li>\n<\/ol>\n<p><!--more--><\/p>\n<p><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\":840,\r\n\"height\":520,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 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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': 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,iVBORw0KGgoAAAANSUhEUgAAA0sAAAH9CAYAAADLSOc3AAAACXBIWXMAAAsTAAALEwEAmpwYAABGIElEQVR42u3dC4zV5b03epOmabp7+na3u2lMT9P0NOnp2\/bt2zQ9aZpWEPGCqI0at61bfY1VHBgEQVtLVaxKZWu13orFeinFG1tlWwoDw2Vw5CIgCIIXijpeENhYyxZLiyIVfQ6\/Z1jjYjHMrIG5rvX5JN8owzCz1ppZ6\/\/8\/pfvOiQBAACwj0M8BAAAAIYlAAAAwxIAAIBhCQAAwLAEAABgWAIAADAsAQAAGJYAAAAMSwAAAIYlAAAAwxIAAIBhCQAAwLAEAABgWAIAAMCwBAAAYFgCAADoncPSsmXL0t13390leeyxx9KuXbv8NKGHeZ4DAIalDho3blwaMmRIuuuuuzp9AfX73\/8+DR06NH8PCynoOZ7nAIBhqYNiT3MsoHbs2NFl3yMWT8OHD897noHu53kOABiWDkDsFY49zV0t9jzH9wK6n+c5AGBYOsBFVHcsbrrr+wCe5wCAYckiCvA8BwAMSxZRgOc5AIBhCfA8BwCo7mHp29\/+dpo2bVqb\/zb+\/jvf+U6n3p7rr7++cn9pDjmk1f\/HsOR53j3Pu770tavxNRIAw1KfWUTFIuCwww5L27Zta\/Xfbd26NX3hC1\/o9MVCJQ8RBiQ8z7v\/uVBpzzuvIwAYlnrJIur222\/f717M+PiVV15pWHLf8Dw3LHkdAYDqG5Z27tyZvva1r7X67774xS+mzZs377Phrqury\/\/mwx\/+cP5v\/LnYrFmz8t\/Fv\/voRz+aBg4cmJ555pmW71mcwscaGxvTpz\/96fTNb36z5evcdNNN6Stf+Ur+WvF1Tj755Hx7im9\/a\/+u9D5Onz695et8+ctfTg0NDemhhx5KX\/rSl9KHPvSh\/PHZs2fv9e\/iz1\/\/+tfz38W\/jftUasGCBfnUpY985CN5z\/xtt93W7ml45dynOCUqHvv93bb2vkZbjz\/VOSxVw\/N8woQJ6fOf\/3x+Pn7rW9\/Kz\/MDef6Vfq\/WnsfxvT73uc\/lrzNgwIDU1NTUodePtp7nHXns2vsZAYBh6SAXUaG2tnafjWz8+ZRTTtlnsRAb9M9+9rPp8ccfz3+O\/37mM59JS5cubfmc4g3\/e++9l+677768YNjfEBF\/Puecc\/LnFhZbN9xwQxo0aFBav359\/vPf\/\/73dOmll+aPtfXvWruPcc3G888\/nz\/v6quvzguO\/v37pw0bNrTcp7jNBatXr873MRYnYeXKlfnPK1asaPmcp556Ki\/M4u9CfG48Dm0NS+Xep7ZuWzlfo73Hn+oblqrheR63r\/Ccjdsbw0w8lzv6\/Cv9XqX3I4acuJ8vvfRS\/rzJkyenb3zjGx16\/WjveV7OY1fOzwgADEudsIiKjXnsFS4WG\/I4clK64Y6Px6Ko2JQpU9Lxxx+\/19d97LHH9v\/AtrIQWLdu3V4fiz2usRgpFguF2Bvc1r9r7XsVL1LefffdVv9d8W2KxWMsgErvY2FRGU4\/\/fT8sWLxb9oalsq9T2vXrt3vbSv3a7T1+FOdw1KlP88nTZrU5nP2QL9X6f0YPHjwPkd7i5Xz+tHe87ycx66cnxEAGJY6YREVYs9oYWMc\/y0+Zaf482LvZ5zSUyz+\/PGPf7zlz6NGjUonnnhiXrwsWrQoL0jaW0S1ZseOHXlREnu\/f\/7zn+fbGKestPfvSr92e9+\/9GNxX+J7t3UfP\/GJT+zzOLz11lvtnoZ3IPep9GPtfY32Hn+qc1iq9Od5e8\/Zznr+xdds6zlVzutHe9+nnMeunJ8RABiWOmkR9Zvf\/CYvfkKcrhPn5JezES\/ecBcvSOLIS5wiEp8fg0WcBteRhUCcSvLJT34yX3tw1lln5dsXi7uOVnOXs\/gp\/VgsnkqvG4gUL6qK72+5C54DvU\/FHyvna7T3+FO9w1I1Pc9Lb29nPP8Krw9tKef1ozOGpXLuMwAYljppERXn78diJ2qEY0ERf27t82KvZUf2Zm7atCmfkhJlCh1ZCMTF0aUXRcf36Y5hKa51iNP12hKPUWt7j9u6fQd6n4o\/Vs7XaO\/xp3qHpUp+nrd2e+M+dubzL8Rpe20dWSrn9aMzhqWO\/owAwLB0EIuoEBcQH3XUUWnkyJH7\/bzvf\/\/7+5wnH38uvki6vcVBuaeYlC5I4tSZ7hiWzj777H2uR4o90MUXccfnlF6XEBd+t3X7DvQ+lZ4e1d7XKPdxoPqGpUp+nkfrZbF4fsYRpM58\/oW47mvu3Ln7vS3lvH50xrB0oD8jADAsHeAiKi7Wbu\/C4\/icQw89tKWBKU5tiT8XLhIPsSi45557WhYmpU1PH\/vYx\/KF1n\/+85\/3uxCIi5fHjBmT99DG14lBJL5PdwxLcf\/j1KJC9XDc1qgIf+CBB1o+J043igvGC58Tj0fhdKT9fZ8DvU+lF9639zXae\/yp7mGpUp\/nxY1zMcxEnX\/xaYGd8fwL8bYDUd8dR9MKLYDFg1A5rx\/tfZ9yHrtyfkYAYFjqxEVUqKmpaffzYpFReG+POLWldI9ubORj72u830n82\/i84tNf4lqB+LvI\/m5HvPdJ7CEtfF7sCY\/FWHcMSyFqfwsXf8dpNfEeSqWiXeywww7LnxOLo7vuuqvN23eg96n4Y+V8jfYef6p7WKrU53kMblHnH8\/H7373uy21\/p35\/Cu45ZZb8mASXye+ZqECvNzXj\/a+TzmPXTk\/IwAwLPWi7wN4ngMAhiWLKMDzHAAwLFlEAZ7nAACGJcDzHACg54elKAXoar\/\/\/e8toqAHhyXPc4DOs3x51Oc3\/xeo4GFp2bJlaciQIfu8uWln2rVrVxo+fHiumQW6n+c5QOe66aaUfvWrlG64wWMBFT0shXHjxuWFVOx5LpxG01mJPc2xgIrvEYspoGd4ngN0jvffT+nf\/i2ld95J6Yc\/bP4zUMHDUog9z529gCok9jRbQEHP8zwHOHjx3tNXX938\/\/HfPe9FDVTysAQAQPtuvjne+Ln5\/x95pPnPgGEJAKCqFU7B+\/vfm\/\/81ltOxQPDEgAA6cknU7rssr0\/NnZsSqtWeWzAsAQAUMVuuaW5Mrw0EyZ4bMCwBABQpQqn4L355t4f\/+tfUzrjDKfigWEJAKBKxSl4v\/hF638XH1+zxmMEhiUAgCp0660pLV\/e+t8tW9b894BhCQCgqsQpduefv\/9T7eLjw4d7nMCwBAAAYFgCAAAwLAEAABiWAAAADEsAAACGJQAAAMMSAACAYQkAAADDEgAAgGEJAADAsAQAUGE2btyYamtHp0MP\/UI65JBD0qc+dWg6++xhqampyYMDhiUAgOrU0NCQPv3pz6WvfvWKNGDAM+n7309p4MCm3X++Jv3Lv3wu1dXVeZDAsAQAUF3iiFIMSt\/73uI8JJXm8MNX54HJESYwLAEAVJU49S6OKLU2KBUSR5hOPvk0DxYYlgAAqkdco1Q49W5\/iVPy4homwLAEAFA9i7VDDmlzUCokPg8wLAEAVA1HlsCwBABAifff25VOP+GE9JUvX+aaJTAsAQAQtr++MS2fMCbdO+TI9Il\/+ufUr98TrQ5KRxyxThseGJYAAKrDxmVzU8NPT0n1Iwal6UMOS788rX\/61Cc+k77yP3+eh6PCqXdf+9ovvc8SGJYAACrfO9u2picnjU9zLvx+mll7ZPrjOd\/NR5c2LZ+XVtVPTScPPj595tP\/dy5z+PhHP56+9\/\/+P2n57Ic9cGBYAgCoXK89uSjNv\/S0VH\/B4DTjvH6pfuSg9Hzd5LR51YJ98sqCaXmQqh95bHpuxiQPHhiWAAAqz7tvb09\/evi3ae6PT0qzhh+dpp\/7vbTw6iHp1SWzWh2UCpl70Yn56NOS60bkIgjAsAQAUDHeXP9cWjS+Js0edXyaUXP47kHpsLTm7l+m\/1rZ2OagFFl200Vpxnn98yl72za95MEEwxIAQN8XR4JenDOl+WjS+cfko0kLrjw7vTjvwXaHpEKefejWfCre7NEnpFca\/+BBBcMSAEDf9taWzenxm3+S5uwecuqGDkh1Nf3T6snXlnU0qTjx+XHa3qzzj06r7hzngQXDEgBA37V+4fTUMObUXMwQleDzLj45Nc2d0qEhqTiLx9fkgSuKIVy3BIYlAIA+JyrB10y+dk8l+MB8+tzSGy\/MleAHOihFnrr3+nwKX3zdN5qe9kCDYQkAoO\/YtGJ+ahx7xp5K8P751LlnH\/j1QQ1Jhbzc+HBzhfjur\/3sgxM82GBYAgDo\/Xbt3JGeuu+GljeYjSNAi64Zll5dVNcpg1Ih0aQXR6uiVQ8wLAEA9GrbNjTl9z8qVILX7R5mnvmPmzt1SCokTueLN7GNoWzHm1s8+GBYAgDofaJkoan+vlwJXj9iUH7fpIafnZpPl+uKQSny4uz791SIH59P+QMMSwAAvcrbW19PKyaOzUeT6moG5EFp5R1XdbgSvKOJrx9HrmI4e2bKzX4QYFgCAOg94k1hiyvB5150Yj7i05VD0v4qxHf9Y6cfCBiWAAB6VlSCr7z9ipYShzgd7vFbLj7oSvCOJt7UtlAh\/pe1K\/xgwLAEANBzNq98dK9K8PjvczMmdeuQtE+F+Mhj820ADEsAAN0uKsHjPY3y0aThR+UjOnEa3KtLZvXIoLR3hfiRuR0PMCwBAHSrN5qezu9nNHvUcS2V4E\/ff2OPDkmFrLzt8jRjSL\/cxLdz+zY\/LDAsAQB0jxfnPVBUCf699MjY07u0EryjidPvcoX4qOPT+oXT\/cDAsAQA0LXe2rI5LZ8wJr+PUd3QI3Il+IpbL+n2EodyK8RnjTgmrbpznB8cGJYAALpOlDjkSvALBrdUgr9Qf2+vGpKKs2DcOalu2BG5QjzeIBcwLAEAdKq45mfNPdel2aNP2D18DMynt0VxQm87mrTfCvHdt3vrS2v9IMGwBADQeV5b81g+MlM4mlQ\/clBaO3Virx6SWirE50\/NpwlGhXhcYwUYlgAADlqhEjxKHGbWNleCL7x6SHp1UV2fGJQKieKJXCH+q1F+qGBYAgA4OHHK2oKrfpSb5OqiErxmQK4Ej9KEvjQoRZ6YeFl+k9x4H6i3t77uhwuGJQCAjosShDhdreGnp7S8wewjl\/ywV1WCH0yF+KYV8\/2QwbAEANAx2zY05dKG5krwAflan9WTxvfJo0nF2bS8IdXV9E+zzj8mPTPlZj9oMCwBAJRvw5L6fDQpihBiSIpT1p6vm9ynh6S9KsSvPDu\/J1ScWqhCHAxLAADtemfb1vyGrVGtPbO2uRL88Vsu7vWV4B1NXG+VK8R3D4FvND3tBw+GJQCA\/XvtyUUtleAzhvRLs4YfnZ594NcVNSQV8sqCaXkQjPv64pwpfvhgWAIA2Ne7b2\/P1+7EUZZCicPia4f3uUrwjiYKHuLo2YrfXOqXAAxLAAB7i1PQHr3irDw4zCiqBK\/kIamQFbdekivE432jdry5xS8DGJYAAFLa9Y+dae3UiXlQiFa4OJoUpQfrF06vikFJhTgYlgAA9rH99Y1pyXUjWt5gNtruVt52eZ+vBFchDoYlAIAD9tL8qalhzKktleBzLzoxNc2dUlVD0r4V4gNUiINhCQCoVlEJvmLi2FwJXjfsiHz6WVyzU2mV4CrEwbAEAFC2uB6npRL8vH6pfuSg9Pz031X1kLRPhfjIY1WIg2EJAKgWe1WC1x6Zh4K4Vmnj0jkGpX0qxI9UIQ6GJQCgGnxQCX5ccyV47cCqqQQ\/sArxfirEwbAEAFSyKCmI08mKK8EbLz+z4t9gtlMqxEerEAfDEgBQkUorwaMWe+UdV1VdJfiBV4gfrUIcDEsAQKXZsKR+n0rwF+c9aBjqSIX4sCNUiINhCQCoFCrBO7lCfPfjqEIcDEsAQB\/32pOLcomDSvBOrBDf\/ViqEAfDEgDQR+36x06V4CrEwbAEAFDszfXP7SlxOC4fTVIJ3nlZeuOF+TFt+Okp+T2qAMMSANBHfFAJfrRK8K6sEB+lQhwMSwBAnxCV4MsnjNmrEnzN3b9UCa5CHAxLAED1iiMcUQk+a8QxuRJ83sUnqwTvwsTRurqhR6SF4871yweGJQCgN4pK8JW3X7FXJfjK2y53NKmLE0fsYiiN8oy4PgwwLAEAvUi8z0+uBB95bJoxpF8+\/U4luApxMCwBAFUrKsHXTp2YSxyKK8G9wWwPVIgPP0qFOBiWAIDe4G+b1+9VCR5vMPvsA782vPRUhXjN4SrEwbAEAPQ0leC9tEJ8tApxMCwBAD3irS2bVYL35grxEceoEAfDEgDQ3TYsqc+V4FHioBJchTgYlgCAqrdz+7a05p7rcjX1zGEDVYL35grxISrEwbAEAHSL19Y81lwJfsHgNOO8\/vm\/0X5nOOnFFeIjj1UhDoYlAKCr7Nq5I\/3p4d82H02qPSqXOCz91ai0cekcg4kKcTAsAQDVaduml\/J1L7HwjjpqleAqxMGwBABUvRdm3t1cCT7imHw0acGVZ6sE72MV4vFzmz36BBXiYFgCADrD9tc35tPs5uxeZNfVDMhZPWm8Eoe+WiF+vgpxMCwBAAdt88pHU+PYM1L9iEG5ErzhZ6emprlTDB99NHE0sG6YCnEwLAEAByxXgk++Nh9Nmll7ZG5Se2LiZfnohKGj7+bp+29UIQ6GJQDgQG1Zt6qoErxfXli\/UH+vYaOSKsR3\/2xViINhCQAoU1SCP\/vghFziUFwJvmn5PINGBWXuRSfmo4UqxMGwBACUYetLa9Oi8TVp9qjjWirB1027w3BRgVl52+UqxMGwBACU45XGPzRXgp9\/tEpwFeJgWAIAeGfb1vT4zT\/ZvWg+PtUNHZDb7lZPvlYluApxMCwBANVrw5L6NP\/S01L9yGNbKsFfnj\/VMFElWXTNMBXiYFgCAIrF0aRVd47LDXczhw3MzWjLJ4xRCa5CHDAsAUD1eqPp6VzikI8m7V4oR320SnAV4irEwbAEAFXr\/fd25Yv6o\/2sUAm+5LoRaePSOQaHKs4jl\/xQhTgYlgCgem3b9FIejAqV4HU1A9KzD91qWBAV4mBYAoDq9eK8B\/JCuFAJvvDqIWn9wukGBVEhDoYlAKhOb23ZnEsbZo86Ph9JikQluAFB9qkQrx2oQhwMSwBQHaISvGHMqal+xKAPKsEbHzYcSKuJUzRViINhCQAqWlSCPzlpfJoz+oRcCR6D0opbL1EJLmVXiG9\/faMnEoYlDwEAVJY3XliTHr3irFwDPWNIv3z6nUpwKSdxDVsM1lEAokIcDEsAUDGiEvyFmXfvqQQ\/Ml+sv\/TGC9Om5fMMAlJ2Gi8\/U4U4GJYAoHK8uf65DyrBz+ufZg0\/Oq2dOtHiXw6qQnzXP3Z6cmFYAgD6rjhdqrgSfMGVZ6dXF9VZ+MsBJU7ZjN+juN7ttScXeYJhWAIA+p4db25prgQf3VwJHteaRCX4f61stOiXg0pc5zZrhApxMCwBQB8UbxraOPaMVD\/y2HwUIFeCz59qoS8qxMGwBADVadfOHWnNPdflaue4CP+P53w3PTHxMkeTRIU4GJYAoHpFJXjs6S+UOMRCViW4dEU2Lp2T6mr6qxDHsOQhAIDeLRrJ1k27M8398UktJQ6P33KxSnBRIQ6GJQCoXts2vbTnaNLxqW7ogFQ\/clB69oFfW8yLCnEwLAFA9Vq\/cHpqGHNqqh8xKDfdLbx6iEpw6bZEYYgKcQxLAECvEpXgcepTLFKjkSyOKK2eNF6Jg6gQB8MSAFSvqATPR5MuGJxmDOmX5l18skpwUSEOhiUAqF7vbNuaK8GjxGFm7cA0ffegtOLWS5Q4SI\/mTw\/\/VoU4hiUAoOdEJfijV5zVXAlec3iae9GJ6cV5D1qsS48nhvVChfhzMyZ5smJYAgC6RzSMxZ77aBubNby5EnzZTRc5miS9Ko+MPT1XiC+98UJPWgxLAEDXi0rwx2\/+SZo9OirBj0h1tQPz4GRxLr0tqydf23zE88cnpXff3u7Ji2EJAOga77+3K70w8+7mN5gdcUyuBI89968smGZhLr0ycUqoCnEMSwBAl3p76+tp+YQxH1SC1wzIbzCrElx6e+I00RjuV905zhMZwxIA0LleafxDcyX4yGNzu1jDz05NLzc+bCEufSJxLV0M+PMvPS0fHQXDEgBw0KISPPbGR\/VyXCQfleArb7s8bVreYBEufSbPPnRrS4V4tDeCYQkAOChxfUdLJfh5\/XMleNQvW3xLX8urS2apEMewBAAcvKgEf2bKzc1Hk4YflS+O9waz0tfTePmZKsQxLAEAB+6NpqfTovE1afao41NdzeGpfuSg9Pz031lsS59PnD4aFeKxE+CtLZs92TEsAQDliYveX5wzpbkS\/Pxj8tGkBVeenV5dVGehLRVXIf7q4pme9BiWAID2bX99Y1py3Yg0u6USvH966t7rVYJLxaX+gsG5QnzNPdd54mNYAgDatmFJ\/QeV4N5gVio8i68d3lIhHtfmgWEJANhHVIKvmDg2n5JUqASPN5x1NEkqukL8gV+3VIhvWbfKCwGGJQBgb3tXgvfLC8fn6yZbTEvFZ+PSOfkIavzuN9Xf58UAwxIA0Ky1SvClvxrlDWalqtLws1Pz0dTF19R6UcCwBADsWwleVzswrZt2h8WzVF2emHhZS4V4lJuAYQkAqtT+KsHXL5xu4SxVmaa5U1oqxDcum+tFAsMSAFSj1irBV08ar8RBVIhfMDg3QK68\/QovFBiWAKDavDR\/6l6V4PMuPjm93PiwhbLI7sROhNiBEEdcd+3c4QUDwxIAVIO9KsGHDUx\/POe7KsFFSvL0\/Te2VIi\/8cIaLxwYlgCg0m1aMT+\/2ebsC5orwaPM4fnpv7M4FinJq4vq9lSIH5\/WTp3oxQPDEgBUqnff3v5BJXjtkfloUlSCx3vKWBiLtJ4oOokK\/XjPMTAsAUAFikrw5jeY3VMJXjMgn2JkMSzSdqLspFAhvuPNLV5MMCwBQKWIN5h9Yebde1WCN15+pkpwkTLz4rwHWyrEX10804sKhiUAqAQtleBxNGnoEfnaC5XgIh3PrOFH58bIFb+51AsLhiUA6OtKK8HnXnRi3kNu4SvS8Sy+dniuEI\/nVBytBcMSAPRBrVWCP37LxWnT8nkWvSIHmGjCK1SI\/2XtCi80GJYAoK8prQSvHzlIJbhIJyR2NtTV9M+ntEajJBiWAKCP2LVzR3r2wQl7VYLHaUMqwUU6L1GMEhXii6+p9aKDYQkA+oKtL63Ni7fmEocBuRL8mf+42eJWpJOz8rbLWyrE3976uhcfDEsA0Fu9\/96u9OK8B1LDT09Js84\/OlcbN\/zsVCUOIl2UF+rvzUdtZ48+Pm1YUu9FCMMSAPRGf9u8Pi298cK9KsFjr7dKcJGuTTzn4v3KVIhjWAKAXij2aEeJg0pwke5PvG9ZtEzGEV0V4hiWAKCX2PHmlrTy9iuaK8FrmyvB4+iSSnCR7svT99\/YUiH+RtPTXpgwLAFAT3vtyUXp0SvOSvUXDE4zzuuvElykhxINk1EhHs\/FeO8lMCwBQA959+3tac091+2pBD8qlzgsumZYenVRnYWrSA9WiM8afnRaOO5cL1IYlgCgJ7zxwpo9leDH5aNJsTc7TgGyWBXp+QrxOhXiGJYAoPvFRePrpt2Z5v74pJZK8NiT\/XLjwxaqIirEwbAEQHXatqHpg0rwmsNVgouoEAfDEgBsWjE\/1xGrBBdRIQ6GJQDY7Z1tW9OqO8c1lzgMUwkuokIcDEsAkP6ydkXzG8xGJfiQfirBRVSIg2EJgOoWleDPTLm5+WjScJXgIn21Qnxm7ZEqxDEsAUBneXP9c\/kNZuMC8VwJXjtQJbhIH60Qn6FCHMMSABy8uAi8qf6+PZXgx7RUgjuaJKJCHAxLAFSt7a9vzG8wO2f0Calu6IB8rcPKO65SCS6iQhwMSwBUp\/ff25XWL5zeXAk+YlBuz1IJLqJCHAxLAFS1qAR\/\/Oaf5KNJhUrwFbdeohJcpNIqxM9VIY5hCQDK9tqTi1SCi1RB4shxDEvxZtIvzLzbix+GJQDYn6gEf3LS+L0qweM0nXhPFgtLERXiYFgCoCptWbdKJbiICnEvhhiWAKAgLuqO029ioTTr\/KNVgotUWZ6bMam5QnzU8WnTivleFDEsAUAoVILH+6yoBBepzsTzPa5PjJ0lK2+\/wgsjhiUAqtteleAjj80XeKsEF1EhrkIcwxIAVS0qwWPvcS5x2FMJvuymi1SCi6gQVyGOYQmA6vWXtSv2qQRfN+0Oi0URFeIqxDEsAVCd4mjSmnuuaz6aVHtUPpq0+NrhShxEpKRC\/CgV4hiWAKgeb7ywJi0aX5NmjzquuRK8ZkB65j9utjgUkX0rxHe\/RqgQx7AEQMWLi7TXTbszzf3xSWnW8A8qwV9ufNjCUETaqBA\/ToU4hiUAKte2DU1p6Y0X5vdNqRt6RL4WQSW4iJRTIT5z+FEqxDEsAVCZNiypb64EHzEoD0mPXPLD9OLs+y0GRaSsCvG6msNViGNYAqCy7Ny+La26c1yaM\/qENLN2YJo+pF96\/JaL06blDRaBItKBCvHv5dcRFeIYlgCoCFEJ3jj2jDT7guNaKsFfqL\/X4k9EVIhjWAKgOu3auSP96eHf5hKHuM4g9gjHaTSvLpll4SciB1EhfqQKcQxLAPRdf9u8Pi2+pnZPJXi\/VFc7UCW4iHRKhfj0IYepEMewBEDf9NL8qalhzKlp1vl7KsF\/\/n8cTRKRTq4QP16FOIYlAPqOd7ZtTSsmjk2zR5+Q31y2rqa\/SnAR6ZIK8VnnH6NCHMMSAH3DK41\/SPMvPS1feB2nyDT89F\/Ty\/OnWtyJiApxDEseAoDqtOPNLS2V4PEGs3F6zLKbLlIJLiIqxMGwBFC9CpXgcUpMoRL8+brJFnMiokIcDEsA1WmvSvDaI\/Me3qU3Xpg2Lp1jISciKsTBsARQnbZteumDSvCaw3ORg0pwEVEhDoYlgKr24pwpe73BbFSCx+kwFm4iokIcDEsAVamlEnz3oqRuz9Gk1ZPGqwQXERXiYFgCqF6bVz7aXOIwYlC+oHruRSeqBBcRFeJgWAKoXu++vT09dd8NzZXgw5orweMagU3L51mkiYgKcTAsAVSnLetWpUevOKvlDWajEjyuD7A4ExEV4mBYAqhKUQm+durElkrwOJq0eHxNenVRnYWZiKgQB8MSQHV6c\/1z+fz\/XAl+Xv98NCneS8liTERUiINhCaAqvf\/erpZK8FnDj87n\/y+48myV4CKiQhwMSwDVa\/vrG9PSGy9sqQSPc\/+fvOsXKsFFpM9k0\/KGVFc7MFeIr7nnOi\/sGJYAOHgbltTnut1CJXjDT\/81Nc2dYvElIn2zQnzoESrEMSwBcHCiEjzeYLa4EnzFrZfkvbMWXSKiQhwMSwBVKSrBF1z1o\/yu94ULop+vm2yxJSJ9Oq8smJZ3\/ESFeFyDCYYlAMoWp6U8++CEfSrBNy6dY6ElIhWRRy75YX59W3xNrRd9DEsAlCcqwRftHowKleDRePfsA7+2uBKRiqsQnzGknwpxDEsAtC8qwZvq79urEjz2vKoEFxEV4mBYAqhaf9u8fq9K8KjVXXP3L1WCi4gKcTAsAVSvVxfPTA1jTt2rEjwufraYEhEV4mBYAqhKO97csk8l+BMTL1MJLiIqxMGwBFC94vz8fDRpTyV4\/chBad20OyyeRESFOBiWAKrTzu3b8rn5sRe1UAm+fMIYleAiokJchTiGJYDqFW8w++gVZ+1VCb526kSLJRFRIa5CHMMSQPV6cd4De1WCL7jy7PTqojoLJRFRIV5UIR6FN2BYAqgSsZd0xW8u\/aASvKZ\/Wj1pvEpwEREV4hiWAKpXS4lDoRL8Z6eml+dPtTgSEdlfhfju10wV4hiWACrYO9u2ppW3X5FmF1WCR4mDSnARkfYrxN9c\/5wNCYYlgEpUKHGIGtw4mhSn3z1fN9liSESkzArxpvr7bEwwLAFUkjht5JkpN+c2p0IleJxWsmn5PAshEREV4hiWAKpTnDISg1FzJXg\/bzArIqJCHMMSAPGO87kS\/HyV4CIinVUhvn7hdBsYDEsAfdX21zfm0obiSvC4QNmCR0Tk4CvEV905zoYGwxJAX1SoBJ814phc4hDn2b8470GLHRGRTqoQn3\/paSrEMSwB9CWFSvA5RZXgcY69N5gVEen8CvFoFwXDEkAf0FIJfsHgXOIw96ITVYKLiKgQx7AEUL1UgouI9EyFeLzWgmEJoJfaqxK85nCV4CIi3VwhvnP7NhsjDEsAvcn77+0qqgQ\/RiW4iEgPVYhvXDbXRgnDEkBvEZXgzUeTVIKLiPR0hXicBg2GJYBeYMOS+lwJHhcWqwQXEen5CvHGsWfko\/1gWALoIVEJvmLi2FxVO3PYwDR9SD+V4CIivaRC\/I0X1thQYVgC6AmvPbkoV4LPvuC4lkpwR5NERHpPhfgLM++2scKwBNCdWqsEX3rjhSrBRUR6SWLnVbw+L76m1kYLwxJAd3mj6em0aHxNS4lDVII\/P\/13FiciIr2tQvy8\/nmnVpwuDYYlgC7UWiX4omuGqQQXEVEhDoYloHq1VIKPPiHVDTtCJbiISF+oEN\/9Wh07t9ZMvtaGDMMSQFcorQRvvPzM9HLjwxYjIiK9PHH0P3ZwRRGPCnEMSwCdaOf2bR9UgtceqRJcRKQPV4hv29Bkw4ZhCaAzvLbmsbRw3Llp9iiV4CIilVAhvm7anTZuGJYADsaunTvS2qkTc3vSrPOPznskVYKLiPT9CvF4LQfDEsABilM0comDSnARkYqrEI8m0x1vbrGxw7AE0FHrF07PJQ6zRhzTXOLw8\/+jElxEpMIqxF9dPNMGD8MSQLne3vp6S4lD3dAj8gZ15R1XKXEQEanECvF7rrPhw7AEUI7NKx9tqQSfMaRfavjZqenF2fdbXIiIVGiF+IKrfqRCHMMSQFve2bY1712M89fjot84mtRc4tBgUSEiUuEV4m80PW1DiGEJoDWxkYw9i\/UXDM4X\/M4afnR69qFbLSZERCo4cQ1qXI8aZxK8OGeKjSGGJYBicdrFnx7+bT6aFANS7GFU4iAiUj2JU63jbILHb\/6JjSKGJYCCv21en5b+alRuQoqjSbF3cc3dv1TiICJSRVk+YUzeBsT76EW5DxiWgKrXVH9f89Gk84\/JR5MeGXt6fkd3CwcRkerKy\/OntlSIb1ox3wYSwxJQvQqV4LP3VILH0aQn7\/qFEgcRkSpOXK8aO8+emXKzDSWGJaA6xR7DQiV4HE1q+Om\/phfq77VQEBGp8iy+dniuEJ9\/6Wlp1z922mBiWAKqR6ESPKphC5XgcY76puXzLBJERCQ9de\/1KsQxLAHV5y9rV6TGsWc0V4IP6ZfPSV837Q6LAxER2atCvK6mvwpxDEtAddi1c8fuoejOPSUOzZXgC648O21cOsfCQERE9kkU\/agQx7AEVLxtG5rSkutGNFeC1xye9xaunnytSnAREdlvVt52uQpxDEtABR9N+sfOfPpElDgUjiY9cskPU9PcKRYCIiLSZp6bMUmFOIYloDLFXsA4dWJOUSX4ilsvUQkuIiJlJbYXdbUDVYhjWAIqy4Yl9R9Ugg85LM296MT0fN1kG38REelQ4hRuFeIYloCKsHP7trTqznF7KsEH5tMnYkOnElxERA4kzz7waxXiGJaAvi\/OJ19w1Y\/S7FHH5UrwWcOPVgkuIiIHXSEep3GrEMewBPRJUQn+1H035LaiqHiNPYCLx9eoBBcRkU7JvItPViGOYQnoe\/atBB+Qnn3oVpXgIiLSeRXid1ylQhzDEtB3vP\/ertRUf19+g9n6EYPyKRLxBrOvLJhmwy4iIp2aF2ffr0IcwxLQN8RevRUTx+aNVhxJikEp9vo5miQiIl2R2L6oEMewBPR6rzT+YZ9K8NjjZ2MuIiJdmbgWNirEo0gozm4AwxLQa7yzbWtaefsVLSUOcTrE47dcrBJcRES6JasnX5t30sV2SIU4hiWg19i88tHUOPaMVH\/B4HyBbfz3uRmTbLxFRKT7KsSXzFIhjmEJ6D2iEvzZByc0H00aflRLJXhssGy4RUSku9Pws1Pz2Q0rfnOpjTSGJaDnxCkOi3YPRvkNZqMSvHZgevr+G22sRUSkx7J8wpi8TYom1h1vbrGxxrAEdL8X5z1QVAn+vfTI2NPTy40P21CLiEiP5vnpv1MhjmEJ6Blvbdmc99rNHn18qht6RD43fMWtlyhxEBGRXpFNyxtS\/chBKsQxLAHdK0occiX4BYNbKsFfqL\/XxllERHpXhfi1w1WIY1gCusfO7dvSmnuuS7NHn7B74zMwn96w9MYLHU0SEZFemafuvV6FOIYloOu9tuaxNP\/S01qOJsWpDWunTrQxFhGRXpu4hjZ27KkQx7AEdIlCJXiUOMysba4EX3j1kPTqojobYhER6fWJU8VViGNYAjrd1pfW5vO8o0moLirBawbkSvD\/WtloAywiIn0iK2+7XIU4hiWg88RFsFEJ3vDTU1reYPaRS36oElxERPpcnpsxSYU4hiWgc2zb0JRLG5orwQfkSvDVk8Y7miQiIn22Qryupr8KcQxLwMHZsKQ+H02KC2FjSIr2oOfrJtvYiohIn86CK8\/O7wmoQhzDEtBh72zbmlbdOS7NGX1CmlnbXAn++C0XqwQXEZGKSFxvG6eUqxDHsAR0yGtPLmqpBJ8xpF+aNfzo9OwDv7ZxFRGRiskrC6Y1V4jv3tapEMewBLTr3be353O3Yy9bocQh3ulcJbiIiFRiouAhzp5QIY5hCWhTnILw6BVn5Q3HjKJKcBtTERGp1Ky49ZI047z+KsQxLAGt2\/WPnWnt1Il5QxGtQHE0KS56Xb9wug2piIioEAfDElSn7a9vTEuuG9HyBrPRdhdv1KcSXEREVIiDYQmq1kvzp6aGMae2VILPvejE1DR3io2niIhUYYX4ABXiGJaA5krwFRPH5krwumFH5NMP4pxtleAiIqJCXIU4hiWoWnE+dksl+Hn9Uv3IQen56b+zsRQRERXiI49VIY5hCarRXpXgtUfmjUJcq7Rx6RwbShERUSGeK8SPVCGOYQmqzQeV4Mc1V4LXDlQJLiIisk+FeD8V4hiWoFrERapxOkFxJXjj5Wd6g1kREZH9VYiPViGOYQkqXmkleNSirrzjKpXgIiIibVaIH61CHMMSVLINS+r3qQR\/cd6DNoYiIiLtVYgPO0KFOIYlqEQqwUVERDqhQnz3dlSFOIYlqCCvPbkolzioBBcRETnICvHd21IV4hiWoALs+sdOleAiIiIqxDEsAcXeXP\/cnhKH4\/LRJJXgIiIiB5elN16Yt6kNPz0lv0chGJagD\/qgEvxoleAiIiKdXSE+SoU4hiXoc6ISfPmEMXtVgq+5+5cqwUVERFSIY1iC6hV7uKISfNaIY3Il+LyLT1YJLiIi0smJszXqhh6RFo471+IDwxL0dlEJvvL2K\/aqBF952+WOJomIiHRB4oyN2CkZ5UlxfTAYlqCXivd5yJXgI49NM4b0y6ffqQQXERFRIY5hCapWVIKvnToxlzgUV4J7g1kREZFuqhAffpQKcQxL0Nv8bfP6vSrB4w1mn33g1zZeIiIi3VkhXnO4CnEMS9CbqAQXERHpRRXio1WIY1iCHvfWls0qwUVERHpbhfiIY1SIY1iCnrRhSX2uBI8SB5XgIiIiKsQxLEHV27l9W1pzz3W5mnTmsIEqwUVERHpbhfgQFeIYlqDbvbbmseZK8AsGpxnn9c\/\/jfY7GycREZFeViE+8lgV4hiWoDvs2rkj\/enh3zYfTao9Kpc4LP3VqLRx6RwbJhERERXiGJagOm3b9FI+7zleeKOOVCW4iIiICnEMS1D1Xph5d3Ml+Ihj8tGkBVeerRJcRESkD1SIx3Z79ugTVIhjWILOtv31jfk0uzm7X2TragbkrJ40XomDiIhIX6oQP1+FOIYl6FSbVz6aGseekepHDMqV4A0\/OzU1zZ1i4yMiItKHEmeD1A1TIY5hCTpFrgSffG0+mjSz9sjcpPPExMvy3ikbHRERkb6Vp++\/UYU4hiXoDFvWrSqqBO+XX1hfqL\/XxkZERKSvV4jv3rarEMewBAcgKsGffXBCLnEorgTftHyeDY2IiEgfz9yLTsxni6gQx7AEHbT1pbVp0fiaNHvUcS2V4Oum3WHjIiIiUiFZedvlKsQxLEFHvdL4h+ZK8POPVgkuIiKiQhzDEvDOtq3p8Zt\/svtF8\/hUN3RAbrtbPflaleAiIiIqxDEsQfXasKQ+zb\/0tFQ\/8tiWSvCX50+1MREREangLLpmmApxDEvQ1tGkVXeOyw13M4cNzM04yyeMUQkuIiKiQhzDElSvN5qeziUO+WjS7hfKqA9VCS4iIqJCHAxLVK3339uVL+qM9ptCJfiS60akjUvn2HCIiIhUWR655IcqxDEsQdi26aU8GBUqwetqBqRnH7rVxkJERESFuApxDEtUrxfnPZBfCAuV4AuvHpLWL5xuQyEiIqJCXIU4hiWq01tbNufShtmjjs9HkiJRCW4DISIiIrlCvHagCnEMS1SfqARvGHNqqh8x6INK8MaHbRxERESkJXGKvgpxDEtUjagEf3LS+DRn9Am5EjwGpRW3XqISXERERNqsEN\/++kYLKQxLVK43XliTHr3irFwDOmNIv3z6nUpwERER2V\/iGubYsRoFUCrEMSxRkaIS\/IWZd++pBD8yX6y59MYL06bl82wIREREpM00Xn6mCnEMS1SmeNftlkrw8\/qnWcOPTmunTvTiLyIiIh2uEN\/1j50WV4YlqAxxuLy4EnzBlWenVxfVeeEXERGRshOn7Mc6Iq53fu3JRRZYhiXo23a8uaW5Enx0cyV4nGscleD\/tbLRi76IiIh0OHGd86wRKsQxLNHHxZvGNY49I9WPPDbvBcqV4POneqEXERERFeIYlqhOu3buSGvuuS5Xe8ZFmH8857vpiYmXOZokIiIiKsQxLFG9ohI89vQUShzihUwluIiIiHRWNi6dk+pq+qsQx7BEHzqa9I+dad20O9PcH5\/UUuLw+C0XqwQXERERFeIYlqhe2za9tOdo0vGpbuiAVD9yUHr2gV97MRcREREV4hiWqF7xbtoNY05N9SMG5aa7hVcPUQkuIiIiXZoojFIhjmGJXisqwePQd7xIRSNNHFFaPWm8EgcRERFRIY5hieoVleD5aNIFg9OMIf3SvItPVgkuIiIiKsQxLFG93tm2NVeCR4nDzNqBafruQWnFrZcocRAREZFuz58e\/q0KccMS9A5RCf7oFWc1V4LXHJ7mXnRienHeg16sRUREpEcSO2tzhfgFx6XnZkyyWDMsQfeLhpnYcxNtM7OGN1eCL7vpIkeTREREpMfzyNjT08zhR6WlN15o0WZYgu4VleCP3\/yTNHt0VIIfkepqB+bByYuziIiI9IasnnxtmnFe\/3yJwLtvb7d4MyxB13v\/vV3phZl3N7\/B7IhjciV47Ll5ZcE0L8wiIiLSaxKXBPzxnO\/mHbsqxA1L0OXe3vp6Wj5hzAeV4DUD8hvMqgQXERGR3pi4TCDe73HVneMs5AxL0HVeafxDcyX4yGNzu0zDz05NLzc+7IVYREREem3iWuq6YQPT\/EtPy2fHYFiCThWV4LE3Jqo3Z9YemSvBV952edq0vMGLsIiIiPTqPPvQrfmSgTgr5o2mpy3sDEvQeeINZmNPTK4EjwskLzox12968RUREZG+kFeXzMoV4nFmzEvzp1rcGZbg4O3auSM9M+Xm5qNJw4\/KleDeYFZERET6YhovPzOfHbP0V6M6vCZavz6lG25I6Qc\/SOmkk1I688yUJk5M6c03rRcNS1SlbRua0uJratPsUcenuprDU\/3IQen56b\/zYisiIiJ9MnH5wIzda5rYCbxz+7ay10SPPprSueem1NiY0rvvNn8s\/ht\/PueclLZssW40LFE14qLHpvr7ciV4LnE493tpwZVnp1cX1XmhFRERkT5dIR7rmtmjT0gbl80ta120cWPzQLS\/I0j\/+Z8pXXWV9aNhiarwt83r87tbf1AJfnh66t7rVYKLiIhIRaT+gsH5\/SHLrRC\/9daUZszY\/9+\/805KDQ3WkIYlKt6ri2fmEoc4mjRjSD9vMCsiIiIVl8XXDk91QwfkNc+uf+xsd30UR5Vee8060bBE1drx5pb05KTx+WhSoRI83nDW0SQRERGpuArxB36dT8WL65b+snZFu+ukE0+0VjQsUbVef3pZahx7Rpp9wXH5aFK8cDxfN9mLqYiIiFRkNi6dk99vKU7He2Hm3e2ulaL5DsMSVSZKHNZMvnavSvCo0fQGsyIiIlLpafjZqWlm7VG59bc9w4en9Prr1o6GJarGm+ufy4NRrgQfOiDV1Q5M66bd4cVTREREqiJPTLyspUL8nW1b21w33XFHSjNntr22igpxDEtUwNGkeMfqhp+ekupHDGqpBF+\/cLoXThEREamaxPtG\/vGc7+YdxxuW1Le5forq8HiPpb\/+tfW\/X7Yspfvvt840LNGn7VUJHkeTavqn1ZPGK3EQERGRqkusf3KF+PnlVYhPn57S0KHNb067a1fzx+KNaKdOTWnMmOb6cAxL9FHxpmstR5OGHJbmXXxyernxYS+WIiIiUrVZct2I\/J6S5VaIr1iR0mWXpXTKKc0NeTE8xRElg5JhiT4qzsFdefsVeyrBB+bDzSrBRURERBakZx+6Ne9EjuuWtqxbZeFoWKKavPbkovToFWel2aOOSzPO65\/PyY3zc704ioiIiCxIry6qa6kQb6q\/z+LRsEQ12LVzR3pmys37VILHewp4YRQREREpqhD\/6b+mmbVHpoXjzs1FWBiWqGDbNjTl9wuIo0l1NYfvzoD09P03ejEUERERaSVxecKM8\/rlncxRhoVhiT5q48aNqbZ2dDr00C+kQw45JH3qU4ems88elpqamvKekDh8PPfHJ6VZI47JR5MaLz9TJbiIiIhIG1k46Vdp8Fe\/mD71f31qn\/UVhiX6iIaGhvTpT38uffWrV6QBA55J3\/9+SgMHNu3+8zXpXz712XT9kBPT7KgErxmQz71VCS4iIiLSdh6ceEP61D8fmv7nly\/bd331L59LdXV1FqGGJfrCEaUYlL73vcX5SVyaww9fnT7xT59Mv\/3B\/5fmXnRienHeg14ARURERNrIqvqp6VOfPLTN9VUMTI4wGZbo5eLUuzii1NoTuZCvfmV8GvCN\/502LZ\/nBVBERESknZx16g93r59+3vb66qvXpJNPPs1i1LBEbxbXKBUODe8vccj4f\/zT\/8jXKYmIiIhI2\/nUx\/+lrPVVXMOEYYne\/MM95JA2n8iFxOdF9aWIiIiItJ2OrK8wLFEBR5Y+8bF\/Tit+c6mIiIiItJN\/+cRnHFkyLFE11yw5pxYAwPoKw1K1KbTh9ev3RKtP5COOWKetBQDA+grDUnUqvM\/SV75yRX7yFg4N\/6\/\/db33AQAAsL7CsFTdYg\/I6aefna9hKrzDdBwatscDAMD6CsMSAACAYanStXZ+7CmnpDRiREr\/+Z8eHwAAMCxV8bBU6v33U9qwIaUrr0ypsdFjBAAAhiXD0l7+9reUhg\/3GAEAgGHJsLSXt95K6dxzPUYAAGBYMixlhdPwfvGLlJYv9xgBAIBhqUqHpf3ld79L6a9\/9RgBAIBhqU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\/>\n\u00ad<\/p>\n<p><ul id='GTTabs_ul_13062' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13062' class='GTTabs_curr'><a  id=\"13062_0\" onMouseOver=\"GTTabsShowLinks(' Centroid balance'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'> Centroid balance<\/a><\/li>\n<li id='GTTabs_li_1_13062' ><a  id=\"13062_1\" onMouseOver=\"GTTabsShowLinks('Balancing a triangle with a centroid'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Balancing a triangle with a centroid<\/a><\/li>\n<li id='GTTabs_li_2_13062' ><a  id=\"13062_2\" onMouseOver=\"GTTabsShowLinks('Finding the center of mass'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Finding the center of mass<\/a><\/li>\n<li id='GTTabs_li_3_13062' ><a  id=\"13062_3\" onMouseOver=\"GTTabsShowLinks('The Idea of the Center of Gravity'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>The Idea of the Center of Gravity<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_13062'>\n<span class='GTTabs_titles'><b> Centroid balance<\/b><\/span><\/p>\n<p>Balancing a triangle on my pencil for extra credit&#8230;<\/p>\n<p><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\/l6pqzkm1EpQ\" frameborder=\"0\" allowfullscreen=\"\"><\/iframe><\/div><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13062' onClick='GTTabs_show(1,13062)'>Balancing a triangle with a centroid &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13062'>\n<span class='GTTabs_titles'><b>Balancing a triangle with a centroid<\/b><\/span><\/p>\n<p>This was a class project to learn how to use video in the classroom.<\/p>\n<p><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\/x94v4V2nVJM\" frameborder=\"0\" allowfullscreen=\"\"><\/iframe><\/div><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13062' onClick='GTTabs_show(0,13062)'>&lt;&lt;  Centroid balance<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13062' onClick='GTTabs_show(2,13062)'>Finding the center of mass &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_2_13062'>\n<span class='GTTabs_titles'><b>Finding the center of mass<\/b><\/span><\/p>\n<p>This is a quick explanation for finding the center of an object&#8217;s mass when the object has a consistent thickness throughout one dimension. The push-stick can be thought of as two-dimensional in a sense, because the plywood is 3\/8&#8243; no matter where we measure it. Because of this uniformity, z values will always be the same; thus, the center of mass is the average of all x and y values that the object occupies. The mass isn&#8217;t really &#8220;evenly spread all around the point,&#8221; so much as the point is the average location of the mass. Technically, the point is really inside of the wood, half-way through its thickness, but let&#8217;s try not to get too lost in the details ;)&#8230;<\/p>\n<p><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\/34AhmNi-uEw\" frameborder=\"0\" allowfullscreen=\"\"><\/iframe><\/div><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13062' onClick='GTTabs_show(1,13062)'>&lt;&lt; Balancing a triangle with a centroid<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13062' onClick='GTTabs_show(3,13062)'>The Idea of the Center of Gravity &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_3_13062'>\n<span class='GTTabs_titles'><b>The Idea of the Center of Gravity<\/b><\/span><\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Demonstrations_in_Physics\" target=\"_blank\" rel=\"noopener\">Demonstrations in Physics<\/a> was an educational science series produced in Australia by ABC Television in 1969. The series was hosted by American scientist <a href=\"https:\/\/en.wikipedia.org\/wiki\/Julius_Sumner_Miller\" target=\"_blank\" rel=\"noopener\">Julius Sumner Miller<\/a>, who demonstrated experiments involving various disciplines in the world of physics. The series was also released in the United States under the title Science Demonstrations. This program was a series of 45 15 (or so) minute shows on various topics in physics, organized into 3 units: Mechanics, Heat and Temperature\/Toys, and Waves and Sound\/Electricity and Magnetism.<\/p>\n<p><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\/YN2oALaRfL4\" frameborder=\"0\" allowfullscreen=\"\"><\/iframe><\/div><\/p>\n<ul style=\"list-style-type: square;\">\n<li><a href=\"https:\/\/cosmolearning.org\/courses\/julius-sumner-miller-dramatic-physics-demonstrations\/\" target=\"_blank\" rel=\"noopener\">Julius Sumner Miller&#8217;s Dramatic Demonstrations in Physics<\/a><\/li>\n<\/ul>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13062' onClick='GTTabs_show(2,13062)'>&lt;&lt; Finding the center of mass<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Desenha, em cartolina, tr\u00eas tri\u00e2ngulos: um equil\u00e1tero, um is\u00f3sceles e um escaleno. Recorta-os. Em cada um deles, une cada v\u00e9rtice ao ponto m\u00e9dio do lado oposto. Quantos segmentos de reta tra\u00e7aste em cada tri\u00e2ngulo?&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20536,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[100,97,187],"tags":[426,114,115],"series":[],"class_list":["post-13062","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-lugares-geometricos","tag-9-o-ano","tag-baricentro","tag-mediana"],"views":1507,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/9V1Pag097-T10_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13062","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=13062"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13062\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20536"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13062"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13062"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13062"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}