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<svg width="1200px" height="700px" viewBox="-550 -400 1200 700" xmlns="http://www.w3.org/2000/svg" version="1.1">
 <title>Lemniscate of Bernoulli NURBS</title>
  <!-- Created by Zorgit (zorgit@gmail.com) on 13 August 2008 Anno Domini -->
  <!-- Cubic Bezier (a=274) by Georg-Johann on 18 September 2010 Anno Domini -->
  <!-- Cubic Bezier upgraded, NURBS polygon added by Eastnman (eastnman@yandex.ru) on 29 April 2016 -->
  <!--   Center of the lemniscate is placed to the point (0, 0) -->
  <!--   Lemniscate Bezier curve is resized (c=338) and simplified (composed of 8 patches) -->
  <!--   Value c=338 is chosen because of 338/239=1.41422 is very close to sqrt(2)=1.41421 -->
  <!--   This allows to build high accuracy Bezier approximation of lemniscate with all Bezier control point coordinates represented by whole numbers -->


  <!-- "Background (Optional). Set "r" to 700 or higher to turn background on" -->
  <circle cx="0"  cy="0"  r="0"  fill="yellow" stroke="none"/>

  <!-- "Label c" -->
  <g transform="translate(360, -15)">
    <g transform="scale(30, -30)">
      <path fill="black" stroke="none" d="M -0.46,0.50 L -0.42,0.50 C -0.39,0.80   -0.83,0.80   -0.92,0.37 C -1.02,-0.10   -0.50,-0.10   -0.43,0.25 L -0.47,0.25 C -0.57,-0.02   -0.88,0.02   -0.80,0.37 C -0.72,0.71   -0.47,0.72   -0.46,0.50 Z " />
    </g>
  </g>

  <!-- "Label c*sqrt(2)" -->
  <g transform="translate(515, -15)">
    <g transform="scale(30, -30)">
      <path fill="black" stroke="none" d="M -0.36,0.50 L -0.32,0.50 C -0.29,0.8   -0.73,0.8   -0.82,0.37 C -0.92,-0.1   -0.4,-0.1   -0.33,0.25 L -0.37,0.25 C -0.47,-0.02   -0.78,0.02   -0.7,0.37 C -0.62,0.71   -0.37,0.72   -0.36,0.50 Z " />
      <path fill="black" stroke="none" d="M 0.0,0.0 L -0.1650,0.33 Q -0.1950,0.39   -0.29,0.4 L -0.11,0.46 L 0.04,0.16 L 0.49,1.0 L 1.02,1.0 L 1.01,0.94 L 0.5,0.94 L 0.0,0.0 Z " />
      <path fill="black" stroke="none" d="M 0.80,0.0 L 0.84,0.19 Q 0.78,0.12   0.72,0.12 L 0.49,0.12 C 0.67,0.28   0.88,0.41   0.92,0.57 C 1.02,0.95   0.51,0.95   0.44,0.63 L 0.48,0.63 C 0.57,0.86   0.87,0.84   0.81,0.60 C 0.77,0.44   0.67,0.33   0.30,0.02 L 0.30,0.0 L 0.80,0.0 Z " />
    </g>
  </g>

  <!-- "Label c/sqrt(2)" -->
  <g transform="translate(20, -250)">
    <g transform="scale(30, -30)">
      <path fill="black" stroke="none" d="M 0.64,1.70 L 0.68,1.70 C 0.71,2.0   0.27,2.0   0.18,1.57 C 0.08,1.10   0.60,1.10   0.67,1.45 L 0.63,1.45 C 0.53,1.18   0.22,1.22   0.30,1.57 C 0.38,1.91   0.63,1.92   0.64,1.70 Z " />
      <path fill="black" stroke="none" d="M -0.3,1.07 L 1.09,1.07 L 1.1,1.13 L -0.29,1.13 L -0.3,1.07 Z " />
      <path fill="black" stroke="none" d="M 0.0,0.0 L -0.1650,0.33 Q -0.1950,0.39   -0.29,0.4 L -0.11,0.46 L 0.04,0.16 L 0.49,1.0 L 1.02,1.0 L 1.01,0.94 L 0.5,0.94 L 0.0,0.0 Z " />
      <path fill="black" stroke="none" d="M 0.80,0.0 L 0.84,0.19 Q 0.78,0.12   0.72,0.12 L 0.49,0.12 C 0.67,0.28   0.88,0.41   0.92,0.57 C 1.02,0.95   0.51,0.95   0.44,0.63 L 0.48,0.63 C 0.57,0.86   0.87,0.84   0.81,0.60 C 0.77,0.44   0.67,0.33   0.30,0.02 L 0.30,0.0 L 0.80,0.0 Z " />
    </g>
  </g>


  <!-- "Lemniscate focuses" -->
  <circle cx="-338" cy="0" r="10" fill="black" stroke="none" />
  <circle cx="+338" cy="0" r="10" fill="black" stroke="none" />


  <!-- "Lemniscate curve" -->
  <path fill="none" stroke="red" stroke-width="8" d="M 478,0 C 478,92   400,169   292,169 C 169,169   73,73   0,0 C -73,-73   -169,-169   -292,-169 C -400,-169   -478,-92   -478,0 C -478,92   -400,169   -292,169 C -169,169   -73,73   0,0 C 73,-73   169,-169   292,-169 C 400,-169   478,-92   478,0 Z " />


  <!-- "Axes lines" -->
  <path fill="none" stroke="black" stroke-width="2" d="M -530 0 590 0"/>
  <path fill="none" stroke="black" stroke-width="2" d="M 0 280 0 -350"/>

  <!-- "Axes arrows" -->
  <path d="M 580,0 570,10 630,0 570,-10" style="fill:#000000;stroke:none" />
  <path d="M 0,-340 10,-330 0,-380 -10,-330" style="fill:#000000;stroke:none" />

  <!-- "Axes labels" -->
  <text style="font-size:45px;font-style:italic;font-weight:normal;text-anchor:middle;fill:#000000;font-family:Times New Roman">
    <tspan x="25" y="-35">O</tspan>
    <tspan x="605" y="-15">x</tspan>
    <tspan x="30"  y="-350">y</tspan>
  </text>


  <!-- "Lemniscate control polygon" -->
  <path fill="none" stroke="blue" stroke-width="4" d="M 478 0 L 478 239 0 239 0 -239 -478 -239 -478 0 -478 239 0 239 0 -239 478 -239 478 0"/>

  <!-- "Lemniscate control points" -->
  <circle cx="+478"  cy="0"     r="12" fill="lime" stroke="green" stroke-width="4"/>
  <circle cx="+478"  cy="+239"  r="9"  fill="lime" stroke="green" stroke-width="4"/>
  <circle cx="0"     cy="+239"  r="9"  fill="lime" stroke="green" stroke-width="4"/>
  <circle cx="0"     cy="-239"  r="9"  fill="lime" stroke="green" stroke-width="4"/>
  <circle cx="-478"  cy="-239"  r="9"  fill="lime" stroke="green" stroke-width="4"/>
  <circle cx="-478"  cy="0"     r="12" fill="lime" stroke="green" stroke-width="4"/>
  <circle cx="-478"  cy="+239"  r="9"  fill="lime" stroke="green" stroke-width="4"/>
  <circle cx="0"     cy="+239"  r="9"  fill="lime" stroke="green" stroke-width="4"/>
  <circle cx="0"     cy="-239"  r="9"  fill="lime" stroke="green" stroke-width="4"/>
  <circle cx="+478"  cy="-239"  r="9"  fill="lime" stroke="green" stroke-width="4"/>


  <!-- "Lemniscate control point numbers" -->
  <text style="font-size:35px;font-style:;font-weight:normal;text-anchor:middle;fill:#007F00;font-family:Times New Roman">
    <tspan x="+460"  y="-10">1</tspan>
    <tspan x="+460"  y="-205">2</tspan>
    <tspan x="+25"   y="-205">3</tspan>
    <tspan x="-15"   y="+230">4</tspan>
    <tspan x="-455"  y="+230">5</tspan>
    <tspan x="-450"  y="-10">6</tspan>
    <tspan x="-455"  y="-205">7</tspan>
    <tspan x="-15"   y="-205">8</tspan>
    <tspan x="+25"   y="+230">9</tspan>
    <tspan x="+455"  y="+230">10</tspan>
    <tspan x="+450"  y="+35">11</tspan>
  </text>

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