Nem tudo que parece uma elípse, é uma elípse
Autor: Matematica | Publicado: 2011-11-14T18:55:00-08:00

                                                1. Você pode construir uma elípse usando apenas lápis, papel e barbante.                                                                                                                  1)                            Fixe o barbante em dois pontos, que serão os                            focos. Você deve deixar uma folga no barbante.                                                     2) É essa folga que lhe permite traçar                            a elipse. Encoste o lápis no barbante como se                            ele fosse o ponto A1 da animação, e faça-o                            deslizar pelo barbante, mantendo o barbante esticado.                            Pronto.                                                      Realizando esses passos você desenhou uma&nbsp;                            elipse, onde&nbsp; a distância entre os&nbsp;                            focos&nbsp; foi&nbsp; escolhida ao&nbsp; fixá-lo&nbsp;                            no papel.&nbsp; E a&nbsp; distância&nbsp; do&nbsp;                            foco&nbsp; ao vértice é&nbsp; o&nbsp;                            pedaço&nbsp; do&nbsp; barbante&nbsp; que&nbsp;                            fica duplo ao esticá-lo na direção                            de um dos focos.&nbsp;                    2.                      Definição                      de elipse:                      Sejam                      F1 e F2 dois pontos, denominados                      focos, e K um número constante tal                      que K é maior do que a distância                      entre F1 e F2. Chamamos                      de elipse o conjunto de pontos P tais que                      a distância de P a F1 mais a distância                      de P a F2 é igual a K.                      Observe                      que na construção feita acima, o comprimento                      do barbante corresponde ao número K. De outra forma:                      d(PF1)+d(PF2)=comprimento do barbante=K.
3. Construa                  facilmente uma elipse utilizando-se do software Régua                  e Compasso.&nbsp;                                                                                                                                
1)                Clicando no botão ,                você pode mover o quadrado azul para alterar                a distância entre os focos e ainda mover o quadrado vermelho                para alterar o tamanho da constante K (tamanho do barbante).                          2) Para                                     começar a animação e                                     desenhar a elipse escolhida dê um click                                     neste botão ,                                     depois clique no ponto A1, em seguida no                                     segmento K e por último clique no                                     ponto A2.                                                       ATENÇÃO: a animação                só vai funcionar&nbsp; se&nbsp; o ponto A2&nbsp; estiver                entre os quadradinhos verdes no segmento K. Para posicioná-lo                corretamente clique no 1º botão.
<!--[if gte mso 9]>     Normal   0            21         false   false   false      PT-BR   X-NONE   X-NONE                                                                                                     <![endif]--><!--[if gte mso 9]>  <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
  DefSemiHidden="true" DefQFormat="false" DefPriority="99"
  LatentStyleCount="267">   <w:LsdException Locked="false" Priority="0" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Normal"/>   <w:LsdException Locked="false" Priority="9" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>                                                         <w:LsdException Locked="false" Priority="10" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Title"/>      <w:LsdException Locked="false" Priority="11" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>   <w:LsdException Locked="false" Priority="22" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Strong"/>   <w:LsdException Locked="false" Priority="20" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>   <w:LsdException Locked="false" Priority="59" SemiHidden="false"
   UnhideWhenUsed="false" Name="Table Grid"/>      <w:LsdException Locked="false" Priority="1" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="No Spacing"/>   <w:LsdException Locked="false" Priority="60" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Shading"/>   <w:LsdException Locked="false" Priority="61" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light List"/>   <w:LsdException Locked="false" Priority="62" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Grid"/>   <w:LsdException Locked="false" Priority="63" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 1"/>   <w:LsdException Locked="false" Priority="64" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 2"/>   <w:LsdException Locked="false" Priority="65" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 1"/>   <w:LsdException Locked="false" Priority="66" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 2"/>   <w:LsdException Locked="false" Priority="67" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 1"/>   <w:LsdException Locked="false" Priority="68" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 2"/>   <w:LsdException Locked="false" Priority="69" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 3"/>   <w:LsdException Locked="false" Priority="70" SemiHidden="false"
   UnhideWhenUsed="false" Name="Dark List"/>   <w:LsdException Locked="false" Priority="71" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Shading"/>   <w:LsdException Locked="false" Priority="72" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful List"/>   <w:LsdException Locked="false" Priority="73" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Grid"/>   <w:LsdException Locked="false" Priority="60" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Shading Accent 1"/>   <w:LsdException Locked="false" Priority="61" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light List Accent 1"/>   <w:LsdException Locked="false" Priority="62" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Grid Accent 1"/>   <w:LsdException Locked="false" Priority="63" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>   <w:LsdException Locked="false" Priority="64" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>   <w:LsdException Locked="false" Priority="65" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>      <w:LsdException Locked="false" Priority="34" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>   <w:LsdException Locked="false" Priority="29" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Quote"/>   <w:LsdException Locked="false" Priority="30" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>   <w:LsdException Locked="false" Priority="66" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>   <w:LsdException Locked="false" Priority="67" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>   <w:LsdException Locked="false" Priority="68" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>   <w:LsdException Locked="false" Priority="69" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>   <w:LsdException Locked="false" Priority="70" SemiHidden="false"
   UnhideWhenUsed="false" Name="Dark List Accent 1"/>   <w:LsdException Locked="false" Priority="71" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>   <w:LsdException Locked="false" Priority="72" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful List Accent 1"/>   <w:LsdException Locked="false" Priority="73" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>   <w:LsdException Locked="false" Priority="60" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Shading Accent 2"/>   <w:LsdException Locked="false" Priority="61" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light List Accent 2"/>   <w:LsdException Locked="false" Priority="62" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Grid Accent 2"/>   <w:LsdException Locked="false" Priority="63" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>   <w:LsdException Locked="false" Priority="64" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>   <w:LsdException Locked="false" Priority="65" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>   <w:LsdException Locked="false" Priority="66" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>   <w:LsdException Locked="false" Priority="67" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>   <w:LsdException Locked="false" Priority="68" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>   <w:LsdException Locked="false" Priority="69" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>   <w:LsdException Locked="false" Priority="70" SemiHidden="false"
   UnhideWhenUsed="false" Name="Dark List Accent 2"/>   <w:LsdException Locked="false" Priority="71" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>   <w:LsdException Locked="false" Priority="72" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful List Accent 2"/>   <w:LsdException Locked="false" Priority="73" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>   <w:LsdException Locked="false" Priority="60" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Shading Accent 3"/>   <w:LsdException Locked="false" Priority="61" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light List Accent 3"/>   <w:LsdException Locked="false" Priority="62" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Grid Accent 3"/>   <w:LsdException Locked="false" Priority="63" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>   <w:LsdException Locked="false" Priority="64" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>   <w:LsdException Locked="false" Priority="65" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>   <w:LsdException Locked="false" Priority="66" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>   <w:LsdException Locked="false" Priority="67" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>   <w:LsdException Locked="false" Priority="68" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>   <w:LsdException Locked="false" Priority="69" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>   <w:LsdException Locked="false" Priority="70" SemiHidden="false"
   UnhideWhenUsed="false" Name="Dark List Accent 3"/>   <w:LsdException Locked="false" Priority="71" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>   <w:LsdException Locked="false" Priority="72" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful List Accent 3"/>   <w:LsdException Locked="false" Priority="73" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>   <w:LsdException Locked="false" Priority="60" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Shading Accent 4"/>   <w:LsdException Locked="false" Priority="61" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light List Accent 4"/>   <w:LsdException Locked="false" Priority="62" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Grid Accent 4"/>   <w:LsdException Locked="false" Priority="63" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>   <w:LsdException Locked="false" Priority="64" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>   <w:LsdException Locked="false" Priority="65" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>   <w:LsdException Locked="false" Priority="66" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>   <w:LsdException Locked="false" Priority="67" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>   <w:LsdException Locked="false" Priority="68" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>   <w:LsdException Locked="false" Priority="69" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>   <w:LsdException Locked="false" Priority="70" SemiHidden="false"
   UnhideWhenUsed="false" Name="Dark List Accent 4"/>   <w:LsdException Locked="false" Priority="71" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>   <w:LsdException Locked="false" Priority="72" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful List Accent 4"/>   <w:LsdException Locked="false" Priority="73" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>   <w:LsdException Locked="false" Priority="60" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Shading Accent 5"/>   <w:LsdException Locked="false" Priority="61" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light List Accent 5"/>   <w:LsdException Locked="false" Priority="62" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Grid Accent 5"/>   <w:LsdException Locked="false" Priority="63" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>   <w:LsdException Locked="false" Priority="64" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>   <w:LsdException Locked="false" Priority="65" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>   <w:LsdException Locked="false" Priority="66" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>   <w:LsdException Locked="false" Priority="67" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>   <w:LsdException Locked="false" Priority="68" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>   <w:LsdException Locked="false" Priority="69" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>   <w:LsdException Locked="false" Priority="70" SemiHidden="false"
   UnhideWhenUsed="false" Name="Dark List Accent 5"/>   <w:LsdException Locked="false" Priority="71" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>   <w:LsdException Locked="false" Priority="72" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful List Accent 5"/>   <w:LsdException Locked="false" Priority="73" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>   <w:LsdException Locked="false" Priority="60" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Shading Accent 6"/>   <w:LsdException Locked="false" Priority="61" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light List Accent 6"/>   <w:LsdException Locked="false" Priority="62" SemiHidden="false"
   UnhideWhenUsed="false" Name="Light Grid Accent 6"/>   <w:LsdException Locked="false" Priority="63" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>   <w:LsdException Locked="false" Priority="64" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>   <w:LsdException Locked="false" Priority="65" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>   <w:LsdException Locked="false" Priority="66" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>   <w:LsdException Locked="false" Priority="67" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>   <w:LsdException Locked="false" Priority="68" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>   <w:LsdException Locked="false" Priority="69" SemiHidden="false"
   UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>   <w:LsdException Locked="false" Priority="70" SemiHidden="false"
   UnhideWhenUsed="false" Name="Dark List Accent 6"/>   <w:LsdException Locked="false" Priority="71" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>   <w:LsdException Locked="false" Priority="72" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful List Accent 6"/>   <w:LsdException Locked="false" Priority="73" SemiHidden="false"
   UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>   <w:LsdException Locked="false" Priority="19" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>   <w:LsdException Locked="false" Priority="21" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>   <w:LsdException Locked="false" Priority="31" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>   <w:LsdException Locked="false" Priority="32" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>   <w:LsdException Locked="false" Priority="33" SemiHidden="false"
   UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>         <![endif]--><!--[if gte mso 10]> 
 /* Style Definitions */
 table.MsoNormalTable
 {mso-style-name:"Tabela normal";
 mso-tstyle-rowband-size:0;
 mso-tstyle-colband-size:0;
 mso-style-noshow:yes;
 mso-style-priority:99;
 mso-style-qformat:yes;
 mso-style-parent:"";
 mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
 mso-para-margin-top:0cm;
 mso-para-margin-right:0cm;
 mso-para-margin-bottom:10.0pt;
 mso-para-margin-left:0cm;
 line-height:115%;
 mso-pagination:widow-orphan;
 font-size:11.0pt;
 font-family:"Calibri","sans-serif";
 mso-ascii-font-family:Calibri;
 mso-ascii-theme-font:minor-latin;
 mso-fareast-font-family:"Times New Roman";
 mso-fareast-theme-font:minor-fareast;
 mso-hansi-font-family:Calibri;
 mso-hansi-theme-font:minor-latin;
 mso-bidi-font-family:"Times New Roman";
 mso-bidi-theme-font:minor-bidi;}
 <![endif]-->Atividade disponível em:&nbsp;http://www.edumatec.mat.ufrgs.br/atividades_diversas/Elipse/index.html 
&nbsp;