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Hyperbolic spiral
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<iframe 
    src="http://jsxgraph.uni-bayreuth.de/share/iframe/hyperbolic-spiral" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Hyperbolic 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';

    const board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-10, 10, 10, -10]
    });
    var a = board.create('slider', [[0, 5], [8, 5], [0, 4, 30]], {name: 'a'});
    
    var c = board.create('curve', [(phi) => a.Value() / 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!

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-10, 10, 10, -10]
});
var a = board.create('slider', [[0, 5], [8, 5], [0, 4, 30]], {name: 'a'});

var c = board.create('curve', [(phi) => a.Value() / phi,
    [0, 0], 0, 8 * Math.PI
], {curveType: 'polar', strokewidth: 4});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Hyperbolic 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.
   */
   
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-10, 10, 10, -10]
   });
   var a = board.create('slider', [[0, 5], [8, 5], [0, 4, 30]], {name: 'a'});
   
   var c = board.create('curve', [(phi) => a.Value() / phi,
       [0, 0], 0, 8 * Math.PI
   ], {curveType: 'polar', strokewidth: 4});
</jsxgraph>

Hyperbolic spiral

Curves
The hyperbolic spiral can be described in polar coordinates $(r, \theta)$ by the equation $$ r = \frac{a}{\theta}$$
// Define the id of your board in BOARDID

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-10, 10, 10, -10]
});
var a = board.create('slider', [[0, 5], [8, 5], [0, 4, 30]], {name: 'a'});

var c = board.create('curve', [(phi) => a.Value() / 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.