Approximation of the circle area: Difference between revisions

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<jsxgraph width="800" height="500">
<jsxgraph width="809" height="500">
         board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1.5,2,8,-3], keepaspectratio:true, axis:true});
         board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1.5,2,8,-3], keepaspectratio:true, axis:true});
         var N = board.createElement('slider', [[0,1.5],[3,1.5],[1,3,40]], {name:'n',snapWidth:1});
         var N = board.create('slider', [[0,1.5],[3,1.5],[1,3,40]], {name:'n',snapWidth:1});
         var circ = board.createElement('circle',[[4,-1.5],1],{strokeWidth:1, strokecolor:'black', strokeWidth:2, fillColor:'#0055ff13'});
         var circ = board.create('circle',[[4,-1.5],1],{strokeWidth:1, strokecolor:'black', strokeWidth:2, fillColor:'#0055ff', fillOpacity:0.3});
          
          
         var c = board.createElement('curve', [[0],[0]],{strokecolor:'red', strokeWidth:2});  
         var c = board.create('curve', [[0],[0]],{strokecolor:'red', strokeWidth:2});  
         c.updateDataArray = function() {
         c.updateDataArray = function() {
                 var r = 1, n = Math.floor(N.Value()),  
                 var r = 1, n = Math.floor(N.Value()),  
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             }
             }


         var c2 = board.createElement('curve', [[0],[0]],{strokecolor:'red', strokeWidth:1});  
         var c2 = board.create('curve', [[0],[0]],{strokecolor:'red', strokeWidth:1});  
         c2.updateDataArray = function() {
         c2.updateDataArray = function() {
                 var r = 1, n = Math.floor(N.Value()),  
                 var r = 1, n = Math.floor(N.Value()),  
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===The underlying JavaScript code===
===The underlying JavaScript code===
<source lang="xml">
<source lang="javascript">
<jsxgraph width="700" height="500">
         board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1.5,2,8,-3], keepaspectratio:true, axis:true});
         board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1.5,2,8,-3], keepaspectratio:true, axis:true});
         var N = board.createElement('slider', [[0,1.5],[3,1.5],[1,3,40]], {name:'n',snapWidth:1});
         var N = board.create('slider', [[0,1.5],[3,1.5],[1,3,40]], {name:'n',snapWidth:1});
         var circ = board.createElement('circle',[[4,-1.5],1],{strokeWidth:1, strokecolor:'black', strokeWidth:2, fillColor:'#0055ff13'});
         var circ = board.create('circle',[[4,-1.5],1],{strokeWidth:1, strokecolor:'black', strokeWidth:2, fillColor:'#0055ff13'});
          
          
         var c = board.createElement('curve', [[0],[0]],{strokecolor:'red', strokeWidth:2});  
         var c = board.create('curve', [[0],[0]],{strokecolor:'red', strokeWidth:2});  
         c.updateDataArray = function() {
         c.updateDataArray = function() {
                 var r = 1, n = Math.floor(N.Value()),  
                 var r = 1, n = Math.floor(N.Value()),  
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             }
             }


         var c2 = board.createElement('curve', [[0],[0]],{strokecolor:'red', strokeWidth:1});  
         var c2 = board.create('curve', [[0],[0]],{strokecolor:'red', strokeWidth:1});  
         c2.updateDataArray = function() {
         c2.updateDataArray = function() {
                 var r = 1, n = Math.floor(N.Value()),  
                 var r = 1, n = Math.floor(N.Value()),  
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             }
             }
             board.update();
             board.update();
</jsxgraph>
</source>
</source>


[[Category:Examples]]
[[Category:Examples]]
[[Category:Geometry]]
[[Category:Geometry]]

Latest revision as of 10:56, 17 March 2020

The underlying JavaScript code

        board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1.5,2,8,-3], keepaspectratio:true, axis:true});
        var N = board.create('slider', [[0,1.5],[3,1.5],[1,3,40]], {name:'n',snapWidth:1});
        var circ = board.create('circle',[[4,-1.5],1],{strokeWidth:1, strokecolor:'black', strokeWidth:2, fillColor:'#0055ff13'});
        
        var c = board.create('curve', [[0],[0]],{strokecolor:'red', strokeWidth:2}); 
        c.updateDataArray = function() {
                var r = 1, n = Math.floor(N.Value()), 
                    x = [0], y = [0],
                    phi = Math.PI/n,
                    h = r*Math.cos(phi),
                    s = r*Math.sin(phi),
                    i, j, 
                    px = 0, py = 0, sgn = 1, 
                    d = 16, 
                    dt = phi/d, 
                    pt;
                    
                for (i=0;i<n;i++) {
                    for (j=-d;j<=d;j++) {
                        pt = dt*j;
                        x.push(px+r*Math.sin(pt));
                        y.push(sgn*r*Math.cos(pt)-(sgn-1)*h*0.5);
                    }
                    px += s;
                    sgn *= (-1);
                }
                x.push((n-1)*s);
                y.push(h+(sgn-1)*h*0.5);
                this.dataX = x;
                this.dataY = y;
            }

        var c2 = board.create('curve', [[0],[0]],{strokecolor:'red', strokeWidth:1}); 
        c2.updateDataArray = function() {
                var r = 1, n = Math.floor(N.Value()), 
                    px = circ.midpoint.X(), py = circ.midpoint.Y(),  
                    x = [px], y = [py],
                    phi = Math.PI/n,
                    s = r*Math.sin(phi),
                    i, j, 
                    d = 16, 
                    dt = phi/d, 
                    pt = Math.PI*0.5+phi;
                    
                for (i=0;i<n;i++) {
                    for (j=-d;j<=d;j++) {
                        x.push(px+r*Math.cos(pt));
                        y.push(py+r*Math.sin(pt));
                        pt -= dt;
                    }
                    x.push(px);
                    y.push(py);
                    pt += dt;
                }
                this.dataX = x;
                this.dataY = y;
            }
            board.update();