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Fermat's spiral
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<iframe 
    src="http://jsxgraph.org/share/iframe/fermats-spiral" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Fermat's spiral" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution 4.0 International License.
    https://creativecommons.org/licenses/by/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    var board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-10, 10, 10, -10]
    });
    
    var a = board.create('slider', [[1, 9], [5, 9], [0, 1, 4]], {name: 'a'});
    
    var c1 = board.create('curve', [
        (phi) => a.Value() * Math.sqrt(phi),
        [0, 0], 0, 8 * Math.PI
    ], {curveType: 'polar', strokewidth: 4});
    
    var c2 = board.create('curve', [
        (phi) => -a.Value() * Math.sqrt(phi),
        [0, 0], 0, 8 * Math.PI
    ], {curveType: 'polar', strokewidth: 4});
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

var board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-10, 10, 10, -10]
});

var a = board.create('slider', [[1, 9], [5, 9], [0, 1, 4]], {name: 'a'});

var c1 = board.create('curve', [
    (phi) => a.Value() * Math.sqrt(phi),
    [0, 0], 0, 8 * Math.PI
], {curveType: 'polar', strokewidth: 4});

var c2 = board.create('curve', [
    (phi) => -a.Value() * Math.sqrt(phi),
    [0, 0], 0, 8 * Math.PI
], {curveType: 'polar', strokewidth: 4});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Fermat's spiral" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution 4.0 International License.
   https://creativecommons.org/licenses/by/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   var board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-10, 10, 10, -10]
   });
   
   var a = board.create('slider', [[1, 9], [5, 9], [0, 1, 4]], {name: 'a'});
   
   var c1 = board.create('curve', [
       (phi) => a.Value() * Math.sqrt(phi),
       [0, 0], 0, 8 * Math.PI
   ], {curveType: 'polar', strokewidth: 4});
   
   var c2 = board.create('curve', [
       (phi) => -a.Value() * Math.sqrt(phi),
       [0, 0], 0, 8 * Math.PI
   ], {curveType: 'polar', strokewidth: 4});
</jsxgraph>

Fermat's spiral

Curves
Fermat's spiral can be described in polar coordinates $(r, \theta)$ by the equation $$r = \pm a\theta^{1/2}\,$$ with $a$ being a real number.
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-10, 10, 10, -10]
});

var a = board.create('slider', [[1, 9], [5, 9], [0, 1, 4]], {name: 'a'});

var c1 = board.create('curve', [
    (phi) => a.Value() * Math.sqrt(phi),
    [0, 0], 0, 8 * Math.PI
], {curveType: 'polar', strokewidth: 4});

var c2 = board.create('curve', [
    (phi) => -a.Value() * Math.sqrt(phi),
    [0, 0], 0, 8 * Math.PI
], {curveType: 'polar', strokewidth: 4});

license

This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.