Circle approximation

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The JavaScript code

var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-6, 6, 6, -6], grid: true});
var n = brd.createElement('slider',[[-5,5],[4.5,5],[3,4,96]],{name:'n',snapWidth:1});
 
var p0 = brd.create('point',[0,0],{strokeColor:'black',fillColor:'white',name:''});
var p1 = brd.create('point',[4,0],{strokeColor:'black',fillColor:'white',name:''});
var rot = brd.create('transform', [function() {return Math.PI*2.0/n.Value();},p0], {type:'rotate'}); // angle, rotation center
var ptmp = brd.create('point',[0,0],{visible:false,withLabel:false}); // dummy point for the rotation
var cOut = brd.create('curve',[[0],[0]],{fillColor:'#5e9abf',highlightFillColor:'#5e9abf',fillOpacity:1,highlightFillOpacity:1,strokeColor:'black',highlightStrokeColor:'black'});
var circ = brd.create('circle',[p0,p1],{fillColor:'#fefd4c',highlightFillColor:'#fefd4c',fillOpacity:0.5,highlightFillOpacity:0.5,strokeColor:'black',highlightStrokeColor:'black'});
var cIn = brd.create('curve',[[0,1,2],[0,1,2]],{fillColor:'#d769a3',highlightFillColor:'#d769a3',fillOpacity:1,highlightFillOpacity:1,strokeColor:'black',highlightStrokeColor:'black'});
 
var tCirc = brd.create('text',[-5,-4.0,function(){
return 'Area of the circle = ' + (0.0625*circ.getRadius()*circ.getRadius()*Math.PI).toFixed(5);
}],{fontSize:20});
var tIn = brd.create('text',[-5,-4.5,function(){
return 'Area of the inscribed ' +n.Value().toFixed(0)+ '-polygon = ' + (0.0625*n.Value()*circ.getRadius()*circ.getRadius()*Math.sin(Math.PI/n.Value())).toFixed(5);
}],{fontSize:20});
var tOut = brd.create('text',[-5,-5,function(){
return 'Area of the circumscribed ' +n.Value().toFixed(0)+ '-polygon = ' + (0.0625*n.Value()*circ.getRadius()*circ.getRadius()*Math.tan(Math.PI/n.Value())).toFixed(5);
}],{fontSize:20});
 
cIn.updateDataArray = function() {
var i, len = n.Value();
this.dataX = [p0.X()+circ.getRadius()];
this.dataY = [p0.Y()];
ptmp.setPositionDirectly(JXG.COORDS_BY_USER, [p0.X()+circ.getRadius(), p0.Y()]);
for (i=0;i<len;i++) {
rot.applyOnce(ptmp);
this.dataX.push(ptmp.X());
this.dataY.push(ptmp.Y());
}
}
 
cOut.updateDataArray = function() {
var i, len = n.Value();
var s = circ.getRadius()/Math.cos(Math.PI/n.Value());
this.dataX = [p0.X()+s];
this.dataY = [p0.Y()];
ptmp.setPositionDirectly(JXG.COORDS_BY_USER, [p0.X()+s,p0.Y()]);
for (i=0;i<len;i++) {
rot.applyOnce(ptmp);
this.dataX.push(ptmp.X());
this.dataY.push(ptmp.Y());
}
}
 
brd.update();
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