View source for Spirograph - geometric construction

=== Double speed ===
The speed of <math>C</math> is twice the speed of <math>B</math>.
<jsxgraph width="600" height="600">
(function() {
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5], keepaspectratio:true});

var O = brd.create('point',[0,0],{name:'O',fixed:true, fillColor:'blue', strokeColor:'blue'});
var A = brd.create('point',[2,0],{name:'A'});
var k = brd.create('circle',[O,A],{name:'k'});
var B = brd.create('glider',[0.7,1,k],{name:'B drag me'});
var g1 = brd.create('line',[O,B], {strokeColor:'lightgray'});
var C = brd.create('reflection',[A, g1],{name:'C', fillColor:'blue', strokeColor:'blue'});

var M = brd.create('glider',[2,2,g1], {name:'M', fillColor:'red', strokeColor:'red'});
var k2 = brd.create('circle',[M,B],{name:'k'});  

var gpar = brd.create('parallel',[O,C,M], {name:"g", strokeColor:'lightgray'});
var Cprime = brd.create('intersection',[gpar,k2,0], {name:"C'", fillColor:'blue', strokeColor:'blue'});

var g2 = brd.create('line',[M,Cprime], {strokeColor:'lightgray'});
var Cstern = brd.create('glider',[1,1,g2], {name:"C*", trace:true, fillColor:'green', strokeColor:'green'});
})();
</jsxgraph>
====The JavaScript code====
<source lang="javascript">
(function() {
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,5,5,-5], keepaspectratio:true});

var O = brd.create('point',[0,0],{name:'O',fixed:true, fillColor:'blue', strokeColor:'blue'});
var A = brd.create('point',[2,0],{name:'A'});
var k = brd.create('circle',[O,A],{name:'k'});
var B = brd.create('glider',[0.7,1,k],{name:'B drag me'});
var g1 = brd.create('line',[O,B], {strokeColor:'lightgray'});
var C = brd.create('reflection',[A, g1],{name:'C', fillColor:'blue', strokeColor:'blue'});

var M = brd.create('glider',[2,2,g1], {name:'M', fillColor:'red', strokeColor:'red'});
var k2 = brd.create('circle',[M,B],{name:'k'});  

var gpar = brd.create('parallel',[O,C,M], {name:"g", strokeColor:'lightgray'});
var Cprime = brd.create('intersection',[gpar,k2,0], {name:"C'", fillColor:'blue', strokeColor:'blue'});

var g2 = brd.create('line',[M,Cprime], {strokeColor:'lightgray'});
var Cstern = brd.create('glider',[1,1,g2], {name:"C*", trace:true, fillColor:'green', strokeColor:'green'});
})();
</source>

=== Threefold speed ===
The speed of <math>C_2</math> is three times the speed of <math>B</math>.
<jsxgraph width="600" height="600" box="jxgbox2">
(function() {
var brd = JXG.JSXGraph.initBoard('jxgbox2',{boundingbox:[-5,5,5,-5], keepaspectratio:true});

var O = brd.create('point',[0,0],{name:'O',fixed:true, fillColor:'blue', strokeColor:'blue'});
var A = brd.create('point',[2,0],{name:'A'});
var k = brd.create('circle',[O,A],{name:'k'});
var B = brd.create('glider',[0.7,1,k],{name:'B drag me'});
var g1 = brd.create('line',[O,B], {strokeColor:'lightgray'});
var C = brd.create('reflection',[A, g1],{name:'C', fillColor:'blue', strokeColor:'blue'});

var g1a = brd.create('line',[O,C], {strokeColor:'lightgray'});
var C2 = brd.create('reflection',[B, g1a],{name:'C_2', fillColor:'blue', strokeColor:'blue'});

var M = brd.create('glider',[2,2,g1], {name:'M', fillColor:'red', strokeColor:'red'});
var k2 = brd.create('circle',[M,B],{name:'k'});  

var gpar = brd.create('parallel',[O,C2,M], {name:"g", strokeColor:'lightgray'});
var Cprime = brd.create('intersection',[gpar,k2,0], {name:"C'", fillColor:'blue', strokeColor:'blue'});

var g2 = brd.create('line',[M,Cprime], {strokeColor:'lightgray'});
var Cstern = brd.create('glider',[1,1,g2], {name:"C*", trace:true, fillColor:'green', strokeColor:'green'});
})();
</jsxgraph>
====The JavaScript code====
<source lang="javascript">
(function() {
var brd = JXG.JSXGraph.initBoard('jxgbox2',{boundingbox:[-5,5,5,-5], keepaspectratio:true});

var O = brd.create('point',[0,0],{name:'O',fixed:true, fillColor:'blue', strokeColor:'blue'});
var A = brd.create('point',[2,0],{name:'A'});
var k = brd.create('circle',[O,A],{name:'k'});
var B = brd.create('glider',[0.7,1,k],{name:'B drag me'});
var g1 = brd.create('line',[O,B], {strokeColor:'lightgray'});
var C = brd.create('reflection',[A, g1],{name:'C', fillColor:'blue', strokeColor:'blue'});

var g1a = brd.create('line',[O,C], {strokeColor:'lightgray'});
var C2 = brd.create('reflection',[B, g1a],{name:'C_2', fillColor:'blue', strokeColor:'blue'});

var M = brd.create('glider',[2,2,g1], {name:'M', fillColor:'red', strokeColor:'red'});
var k2 = brd.create('circle',[M,B],{name:'k'});  

var gpar = brd.create('parallel',[O,C2,M], {name:"g", strokeColor:'lightgray'});
var Cprime = brd.create('intersection',[gpar,k2,0], {name:"C'", fillColor:'blue', strokeColor:'blue'});

var g2 = brd.create('line',[M,Cprime], {strokeColor:'lightgray'});
var Cstern = brd.create('glider',[1,1,g2], {name:"C*", trace:true, fillColor:'green', strokeColor:'green'});
})();
</source>

=== Fourfold speed ===
The speed of <math>C_2</math> is four times the speed of <math>B</math>.
<jsxgraph width="600" height="600" box="jxgbox3">
(function() {
var brd = JXG.JSXGraph.initBoard('jxgbox3',{boundingbox:[-5,5,5,-5], keepaspectratio:true});

var O = brd.create('point',[0,0],{name:'O',fixed:true, fillColor:'blue', strokeColor:'blue'});
var A = brd.create('point',[2,0],{name:'A'});
var k = brd.create('circle',[O,A],{name:'k'});
var B = brd.create('glider',[0.7,1,k],{name:'B drag me'});
var g1 = brd.create('line',[O,B], {strokeColor:'lightgray'});
var C = brd.create('reflection',[A,g1],{name:'C', fillColor:'blue', strokeColor:'blue'});

var g1a = brd.create('line',[O,C], {strokeColor:'lightgray'});
var C2 = brd.create('reflection',[A, g1a],{name:'C_2', fillColor:'blue', strokeColor:'blue'});

var M = brd.create('glider',[2,2,g1], {name:'M', fillColor:'red', strokeColor:'red'});
var k2 = brd.create('circle',[M,B],{name:'k'});  

var gpar = brd.create('parallel',[O,C2,M], {name:"g", strokeColor:'lightgray'});
var Cprime = brd.create('intersection',[gpar,k2,0], {name:"C'", fillColor:'blue', strokeColor:'blue'});

var g2 = brd.create('line',[M,Cprime], {strokeColor:'lightgray'});
var Cstern = brd.create('glider',[3,3,g2], {name:"C*", trace:true, fillColor:'green', strokeColor:'green'});
})();
</jsxgraph>
====The JavaScript code====
<source lang="javascript">
(function() {
var brd = JXG.JSXGraph.initBoard('jxgbox3',{boundingbox:[-5,5,5,-5], keepaspectratio:true});

var O = brd.create('point',[0,0],{name:'O',fixed:true, fillColor:'blue', strokeColor:'blue'});
var A = brd.create('point',[2,0],{name:'A'});
var k = brd.create('circle',[O,A],{name:'k'});
var B = brd.create('glider',[0.7,1,k],{name:'B drag me'});
var g1 = brd.create('line',[O,B], {strokeColor:'lightgray'});
var C = brd.create('reflection',[A, g1],{name:'C', fillColor:'blue', strokeColor:'blue'});

var g1a = brd.create('line',[O,C], {strokeColor:'lightgray'});
var C2 = brd.create('reflection',[A, g1a],{name:'C_2', fillColor:'blue', strokeColor:'blue'});

var M = brd.create('glider',[2,2,g1], {name:'M', fillColor:'red', strokeColor:'red'});
var k2 = brd.create('circle',[M,B],{name:'k'});  

var gpar = brd.create('parallel',[O,C2,M], {name:"g", strokeColor:'lightgray'});
var Cprime = brd.create('intersection',[gpar,k2,0], {name:"C'", fillColor:'blue', strokeColor:'blue'});

var g2 = brd.create('line',[M,Cprime], {strokeColor:'lightgray'});
var Cstern = brd.create('glider',[3,3,g2], {name:"C*", trace:true, fillColor:'green', strokeColor:'green'});
})();
</source>

===Literatur===
* W. Neidhardt, Ch. Wurm: ''Arbeitsbuch THALES, Geometrie mit dem Computer'', Dümmler-Verlag 1997. ISBN 3-427-45511-4

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