Lagrange interpolation

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Constructs a polynomial of degree [math]n[/math] through [math]n+1[/math] given points. Points can be added by clicking on "Add point". The dotted line is the graph of the first derivative, the dashed line is the graph of the second derivative.

References

The underlying JavaScript code

<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>
        board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25});
        // Axes
        b1axisx = board.create('axis', [[0,0], [1,0]], {});
        b1axisy = board.create'axis', [[0,0], [0,1]], {});

        var p = [];
        p[0] = board.create('point', [-1,2], {style:6});
        p[1] = board.create('point', [3,-1], {style:6});
        
        var f = board.lagrangePolynomial(p);
        graph = board.create('functiongraph',  [f, -10, 10], {strokeWidth:3});
        d1 = board.create('functiongraph', [board.D(f), -10, 10], {dash:1});
        d2 = board.create('functiongraph', [board.D(board.D(f)), -10, 10], {dash:2});

        function addPoint() {
          p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
          board.update();
        }