JSXGraph
JSXGraph share

Share

Approximate length of curve
QR code 
<iframe 
    src="https://www.jsxgraph.org/share/iframe/approximate-length-of-curve" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Approximate length of curve" 
    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: 2 / 1; width: 100%;" data-ar="2 / 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';

    const board = JXG.JSXGraph.initBoard(BOARDID, {
        axis: true,
        boundingbox: [-8, 6, 8, -2]
    });
    var n = board.create('slider', [
        [1, 3],
        [6, 3],
        [1, 10, 70]
    ], {
        name: 'n',
        snapWidth: 1
    });
    
    // Fixed function term
    var f = function(x) {
        return 0.2 * x * x + 2.0 * Math.sin(x);
    }
    var plot = board.create('functiongraph', [f], {
        strokeWidth: 1,
        strokeOpacity: 0.3
    });
    
    // Plot dashed horizontal and vertical lines 
    var start = -3.0;
    var end = 5.0;
    var sc = board.create('curve', [
        [0],
        [0]
    ], {
        dash: 1,
        strokeWidth: 1,
        strokeColor: 'red'
    });
    board.updateDataArray = function() {
        var i;
        var m = n.Value();
        var d = (end - start) / m;
        this.dataX = [];
        this.dataY = [];
        this.dataX[0] = start;
        this.dataY[0] = f(start);
        for (i = 1; i <= m; i++) {
            this.dataX.push(start + i * d);
            this.dataY.push(f(start + (i - 1) * d));
            this.dataX.push(start + i * d);
            this.dataY.push(f(start + i * d));
        }
    }
    // Plot secants
    var approx = board.create('curve', [
        [0],
        [0]
    ], {
        strokeColor: 'red'
    });
    approx.updateDataArray = function() {
        var i;
        var m = n.Value();
        var d = (end - start) / m;
        this.dataX = [];
        this.dataY = [];
        this.dataX[0] = start;
        this.dataY[0] = f(start);
        for (i = 1; i <= m; i++) {
            this.dataX.push(start + i * d);
            this.dataY.push(f(start + i * d));
        }
    }
    
    board.create('text', [-7, 1, function() {
        var i, s, f0, f1;
        var m = n.Value();
        var d = (end - start) / m;
        s = 0.0;
        f0 = f(start);
        for (i = 1; i <= m; i++) {
            f1 = f(start + i * d);
            s += Math.sqrt(d * d + (f1 - f0) * (f1 - f0));
            f0 = f1;
        }
        return 'Length = ' + s.toFixed(4);
    }], {
        fontSize: 24
    });
    board.update();
 </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!

const board = JXG.JSXGraph.initBoard(BOARDID, {
    axis: true,
    boundingbox: [-8, 6, 8, -2]
});
var n = board.create('slider', [
    [1, 3],
    [6, 3],
    [1, 10, 70]
], {
    name: 'n',
    snapWidth: 1
});

// Fixed function term
var f = function(x) {
    return 0.2 * x * x + 2.0 * Math.sin(x);
}
var plot = board.create('functiongraph', [f], {
    strokeWidth: 1,
    strokeOpacity: 0.3
});

// Plot dashed horizontal and vertical lines 
var start = -3.0;
var end = 5.0;
var sc = board.create('curve', [
    [0],
    [0]
], {
    dash: 1,
    strokeWidth: 1,
    strokeColor: 'red'
});
board.updateDataArray = function() {
    var i;
    var m = n.Value();
    var d = (end - start) / m;
    this.dataX = [];
    this.dataY = [];
    this.dataX[0] = start;
    this.dataY[0] = f(start);
    for (i = 1; i <= m; i++) {
        this.dataX.push(start + i * d);
        this.dataY.push(f(start + (i - 1) * d));
        this.dataX.push(start + i * d);
        this.dataY.push(f(start + i * d));
    }
}
// Plot secants
var approx = board.create('curve', [
    [0],
    [0]
], {
    strokeColor: 'red'
});
approx.updateDataArray = function() {
    var i;
    var m = n.Value();
    var d = (end - start) / m;
    this.dataX = [];
    this.dataY = [];
    this.dataX[0] = start;
    this.dataY[0] = f(start);
    for (i = 1; i <= m; i++) {
        this.dataX.push(start + i * d);
        this.dataY.push(f(start + i * d));
    }
}

board.create('text', [-7, 1, function() {
    var i, s, f0, f1;
    var m = n.Value();
    var d = (end - start) / m;
    s = 0.0;
    f0 = f(start);
    for (i = 1; i <= m; i++) {
        f1 = f(start + i * d);
        s += Math.sqrt(d * d + (f1 - f0) * (f1 - f0));
        f0 = f1;
    }
    return 'Length = ' + s.toFixed(4);
}], {
    fontSize: 24
});
board.update();
<jsxgraph width="100%" aspect-ratio="2 / 1" title="Approximate length of curve" 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.
   */
   
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       axis: true,
       boundingbox: [-8, 6, 8, -2]
   });
   var n = board.create('slider', [
       [1, 3],
       [6, 3],
       [1, 10, 70]
   ], {
       name: 'n',
       snapWidth: 1
   });
   
   // Fixed function term
   var f = function(x) {
       return 0.2 * x * x + 2.0 * Math.sin(x);
   }
   var plot = board.create('functiongraph', [f], {
       strokeWidth: 1,
       strokeOpacity: 0.3
   });
   
   // Plot dashed horizontal and vertical lines 
   var start = -3.0;
   var end = 5.0;
   var sc = board.create('curve', [
       [0],
       [0]
   ], {
       dash: 1,
       strokeWidth: 1,
       strokeColor: 'red'
   });
   board.updateDataArray = function() {
       var i;
       var m = n.Value();
       var d = (end - start) / m;
       this.dataX = [];
       this.dataY = [];
       this.dataX[0] = start;
       this.dataY[0] = f(start);
       for (i = 1; i <= m; i++) {
           this.dataX.push(start + i * d);
           this.dataY.push(f(start + (i - 1) * d));
           this.dataX.push(start + i * d);
           this.dataY.push(f(start + i * d));
       }
   }
   // Plot secants
   var approx = board.create('curve', [
       [0],
       [0]
   ], {
       strokeColor: 'red'
   });
   approx.updateDataArray = function() {
       var i;
       var m = n.Value();
       var d = (end - start) / m;
       this.dataX = [];
       this.dataY = [];
       this.dataX[0] = start;
       this.dataY[0] = f(start);
       for (i = 1; i <= m; i++) {
           this.dataX.push(start + i * d);
           this.dataY.push(f(start + i * d));
       }
   }
   
   board.create('text', [-7, 1, function() {
       var i, s, f0, f1;
       var m = n.Value();
       var d = (end - start) / m;
       s = 0.0;
       f0 = f(start);
       for (i = 1; i <= m; i++) {
           f1 = f(start + i * d);
           s += Math.sqrt(d * d + (f1 - f0) * (f1 - f0));
           f0 = f1;
       }
       return 'Length = ' + s.toFixed(4);
   }], {
       fontSize: 24
   });
   board.update();
</jsxgraph>
Approximate the length of curve by summing up the length of secants.
// Define the id of your board in BOARDID

const board = JXG.JSXGraph.initBoard(BOARDID, {
    axis: true,
    boundingbox: [-8, 6, 8, -2]
});
var n = board.create('slider', [
    [1, 3],
    [6, 3],
    [1, 10, 70]
], {
    name: 'n',
    snapWidth: 1
});

// Fixed function term
var f = function(x) {
    return 0.2 * x * x + 2.0 * Math.sin(x);
}
var plot = board.create('functiongraph', [f], {
    strokeWidth: 1,
    strokeOpacity: 0.3
});

// Plot dashed horizontal and vertical lines 
var start = -3.0;
var end = 5.0;
var sc = board.create('curve', [
    [0],
    [0]
], {
    dash: 1,
    strokeWidth: 1,
    strokeColor: 'red'
});
board.updateDataArray = function() {
    var i;
    var m = n.Value();
    var d = (end - start) / m;
    this.dataX = [];
    this.dataY = [];
    this.dataX[0] = start;
    this.dataY[0] = f(start);
    for (i = 1; i <= m; i++) {
        this.dataX.push(start + i * d);
        this.dataY.push(f(start + (i - 1) * d));
        this.dataX.push(start + i * d);
        this.dataY.push(f(start + i * d));
    }
}
// Plot secants
var approx = board.create('curve', [
    [0],
    [0]
], {
    strokeColor: 'red'
});
approx.updateDataArray = function() {
    var i;
    var m = n.Value();
    var d = (end - start) / m;
    this.dataX = [];
    this.dataY = [];
    this.dataX[0] = start;
    this.dataY[0] = f(start);
    for (i = 1; i <= m; i++) {
        this.dataX.push(start + i * d);
        this.dataY.push(f(start + i * d));
    }
}

board.create('text', [-7, 1, function() {
    var i, s, f0, f1;
    var m = n.Value();
    var d = (end - start) / m;
    s = 0.0;
    f0 = f(start);
    for (i = 1; i <= m; i++) {
        f1 = f(start + i * d);
        s += Math.sqrt(d * d + (f1 - f0) * (f1 - f0));
        f0 = f1;
    }
    return 'Length = ' + s.toFixed(4);
}], {
    fontSize: 24
});
board.update();

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.