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Logarithmic spiral
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<iframe 
    src="https://jsxgraph.org/share/iframe/logarithmic-spiral" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Logarithmic 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 ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/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], axis: true, keepaspectratio: true });
    var a = board.create('slider', [[1, -2], [5, -2], [0, 0.3, 1]], { name: 'a' });
    var b = board.create('slider', [[1, -3], [5, -3], [-1, 0.15, 1]], { name: 'b' });
    var c = board.create('curve', [function(phi) { return a.Value() * Math.exp(b.Value() * phi); }, [0, 0], 0, 8 * Math.PI],
                 { curveType: 'polar', strokewidth: 4 });
    var g = board.create('glider', [c]);
    var t = board.create('tangent', [g], { dash: 2, strokeColor: '#a612a9' });
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/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], axis: true, keepaspectratio: true });
var a = board.create('slider', [[1, -2], [5, -2], [0, 0.3, 1]], { name: 'a' });
var b = board.create('slider', [[1, -3], [5, -3], [-1, 0.15, 1]], { name: 'b' });
var c = board.create('curve', [function(phi) { return a.Value() * Math.exp(b.Value() * phi); }, [0, 0], 0, 8 * Math.PI],
             { curveType: 'polar', strokewidth: 4 });
var g = board.create('glider', [c]);
var t = board.create('tangent', [g], { dash: 2, strokeColor: '#a612a9' });
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Logarithmic 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 ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/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], axis: true, keepaspectratio: true });
   var a = board.create('slider', [[1, -2], [5, -2], [0, 0.3, 1]], { name: 'a' });
   var b = board.create('slider', [[1, -3], [5, -3], [-1, 0.15, 1]], { name: 'b' });
   var c = board.create('curve', [function(phi) { return a.Value() * Math.exp(b.Value() * phi); }, [0, 0], 0, 8 * Math.PI],
                { curveType: 'polar', strokewidth: 4 });
   var g = board.create('glider', [c]);
   var t = board.create('tangent', [g], { dash: 2, strokeColor: '#a612a9' });
</jsxgraph>
It can be described in polar coordinates $(r, \theta)$ by the equation $$r = ae^{b\theta}\,$$ with real numbers $a$ and $b$.
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-10, 10, 10, -10], axis: true, keepaspectratio: true });
var a = board.create('slider', [[1, -2], [5, -2], [0, 0.3, 1]], { name: 'a' });
var b = board.create('slider', [[1, -3], [5, -3], [-1, 0.15, 1]], { name: 'b' });
var c = board.create('curve', [function(phi) { return a.Value() * Math.exp(b.Value() * phi); }, [0, 0], 0, 8 * Math.PI],
             { curveType: 'polar', strokewidth: 4 });
var g = board.create('glider', [c]);
var t = board.create('tangent', [g], { dash: 2, strokeColor: '#a612a9' });

license

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