Circle inversion: Difference between revisions

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The point <math>P'</math> is the result of a circle inversion of <math>P</math> on circle <math>c</math> (black circle line).
<jsxgraph width="600" height="600">
<jsxgraph width="600" height="600">
brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5]});
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5]});
var m = brd.create('point',[0.5,0.3],{name:'M'});
var m = brd.create('point',[0.5,0.3],{name:'M'});
var b = brd.create('point',[3,0]);
var b = brd.create('point',[3,0]);
var c = brd.create('circle',[m,b]);
var c = brd.create('circle',[m,b],{strokeColor:'black',name:'c'});
var m1 = brd.create('point',[-4,2],{name:'M_1'});
var m1 = brd.create('point',[-4,2],{name:'M_1'});
var b1 = brd.create('point',[-4,3],{name:'C_1'});
var b1 = brd.create('point',[-4,3],{name:'C_1'});
var c1 = brd.create('circle',[m1,b1]);
var c1 = brd.create('circle',[m1,b1]);
var p = brd.create('glider',[-4,1,c1],{name:'P'});
var p = brd.create('glider',[-4,1,c1],{name:'P [drag me]'});


// If p is not on c, the tangent is the polar.
var t = brd.create('polar', [c,p], {name:'polar', withLabel:true, strokeColor:'gray', dash:2});  
var t = brd.create('tangent', [c,p], {name:'polar', withLabel:true, strokeColor:'gray', dash:2});  
var l = brd.create('line', [m,p], {name:'', withLabel:false, strokeColor:'gray', dash:2});  
var l = brd.create('line', [m,p], {name:'', withLabel:false, strokeColor:'gray', dash:2});  
var s = brd.create('intersection', [l,t,0], {name:"P'", withLabel:true});  
var s = brd.create('intersection', [l,t,0], {name:"P'", withLabel:true, trace:true});  
</jsxgraph>
</jsxgraph>


===The underlying JavaScript code===
===The underlying JavaScript code===
<source lang="javascript">
<source lang="javascript">
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5]});
var m = brd.create('point',[0.5,0.3],{name:'M'});
var b = brd.create('point',[3,0]);
var c = brd.create('circle',[m,b],{strokeColor:'black',name:'c'});
var m1 = brd.create('point',[-4,2],{name:'M_1'});
var b1 = brd.create('point',[-4,3],{name:'C_1'});
var c1 = brd.create('circle',[m1,b1]);
var p = brd.create('glider',[-4,1,c1],{name:'P [drag me]'});
var t = brd.create('polar', [c,p], {name:'polar', withLabel:true, strokeColor:'gray', dash:2});
var l = brd.create('line', [m,p], {name:'', withLabel:false, strokeColor:'gray', dash:2});
var s = brd.create('intersection', [l,t,0], {name:"P'", withLabel:true, trace:true});
</source>
</source>


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

Latest revision as of 08:01, 15 May 2010

The point [math]\displaystyle{ P' }[/math] is the result of a circle inversion of [math]\displaystyle{ P }[/math] on circle [math]\displaystyle{ c }[/math] (black circle line).

The underlying JavaScript code

var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5]});
var m = brd.create('point',[0.5,0.3],{name:'M'});
var b = brd.create('point',[3,0]);
var c = brd.create('circle',[m,b],{strokeColor:'black',name:'c'});
var m1 = brd.create('point',[-4,2],{name:'M_1'});
var b1 = brd.create('point',[-4,3],{name:'C_1'});
var c1 = brd.create('circle',[m1,b1]);
var p = brd.create('glider',[-4,1,c1],{name:'P [drag me]'});

var t = brd.create('polar', [c,p], {name:'polar', withLabel:true, strokeColor:'gray', dash:2}); 
var l = brd.create('line', [m,p], {name:'', withLabel:false, strokeColor:'gray', dash:2}); 
var s = brd.create('intersection', [l,t,0], {name:"P'", withLabel:true, trace:true});