Reuleaux pentagon: Difference between revisions
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<html> | <html> | ||
<form> | <form> | ||
<input type="button" value="start" onclick=" | <input type="button" value="start" onclick="start();"> | ||
<input type="button" value="stop" onclick=" | <input type="button" value="stop" onclick="stop();"> | ||
<input type="button" value="one step" onclick=" | <input type="button" value="one step" onclick="rol5.rolling();rol3.rolling();"> | ||
</form></html> | </form></html> | ||
<jsxgraph width="600" height="600" box="jxgbox"> | <jsxgraph width="600" height="600" box="jxgbox"> | ||
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5, | var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,7,5,-3]}); | ||
brd.renderer.container.style.backgroundColor = '#3d1c24'; // background color board | |||
brd.suspendUpdate(); | brd.suspendUpdate(); | ||
// Pentagon | |||
var A = brd.create('point',[-2,-2]); | |||
var B = brd.create('point',[2,-2]); | |||
var pol5 = brd.create('regularpolygon',[A,B,5], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0}); | |||
for (var i=0;i<5;i++) pol5.vertices[i].setProperty({color:'#3d1c24'}); | |||
var diagPentagon = (1+Math.sqrt(5))*0.5*A.Dist(B); | |||
// Triangle | |||
var C = brd.create('point',[-2,-2]); | |||
var D = brd.create('point',[C.X()+3/5*diagPentagon, C.Y()]); | |||
var pol3 = brd.create('regularpolygon',[C,D,3], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0}); | |||
for (i=0;i<3;i++) pol3.vertices[i].setProperty({color:'#3d1c24'}); | |||
// Heptagon | |||
var E = brd.create('point',[-2,-2]); | |||
// | |||
// Side length of the heptagon depending on the diagonal of the pentagon: | |||
// r_7 = 7/5*r_5 | |||
var diagHeptagon = 7/5*diagPentagon; | |||
// s_7 = r_7*sqrt(2)*sqrt(1-cos(pi/7)) (law of cosines) | |||
var sideHeptagon = Math.sqrt(2*(1-Math.cos(Math.PI/7)))*diagHeptagon; | |||
// | |||
var F = brd.create('point',[E.X()+sideHeptagon, E.Y()]); | |||
var pol7 = brd.create('regularpolygon',[E,F,7], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0}); | |||
for (i=0;i<7;i++) pol7.vertices[i].setProperty({color:'#3d1c24'}); | |||
// Create the Reuleauc curves | |||
var reuleauxHeptagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol7.vertices, 7), | |||
{strokeWidth:6, strokeColor:'#d66d55', fillColor:'#d6bb55', highlightFillColor:'#d6bb55'}); | |||
var reuleauxPentagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol5.vertices, 5), | |||
{strokeWidth:6, strokeColor:'#d66d55', fillColor:'#ad5544', highlightFillColor:'#ad5544'}); | |||
var reuleauxTriangle = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol3.vertices, 3), | |||
{strokeWidth:6, strokeColor:'#d66d55', fillColor:'#703545', highlightFillColor:'#703545'}); | |||
brd.unsuspendUpdate(); | |||
var | var rol5 = brd.createRoulette(reuleauxHeptagon, reuleauxPentagon, 6*Math.PI/5, Math.PI/45, 1, 50, [A,B,C,D]); | ||
var rol3 = brd.createRoulette(reuleauxPentagon, reuleauxTriangle, 6*Math.PI/5, Math.PI/45, -1, 50, [C,D]); | |||
var rollIt = function() { | |||
rol5.rolling(); | |||
rol3.rolling(); | |||
}; | |||
var interval; | |||
var start = function() { | |||
interval = setInterval(rollIt,10); | |||
}; | |||
var stop = function() { | |||
clearInterval(interval); | |||
} | |||
</jsxgraph> | |||
===The underlying JavaScript code=== | |||
<source lang="javascript"> | |||
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,7,5,-3]}); | |||
brd.renderer.container.style.backgroundColor = '#3d1c24'; // background color board | |||
brd.suspendUpdate(); | |||
// Pentagon | // Pentagon | ||
var A = brd.create('point',[-2,-2]); | var A = brd.create('point',[-2,-2]); | ||
var B = brd.create('point',[2,-2]); | var B = brd.create('point',[2,-2]); | ||
var | var pol5 = brd.create('regularpolygon',[A,B,5], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0}); | ||
var | for (var i=0;i<5;i++) pol5.vertices[i].setProperty({color:'#3d1c24'}); | ||
var diagPentagon = (1+Math.sqrt(5))*0.5*A.Dist(B); | |||
// Triangle | // Triangle | ||
var C = brd.create('point',[-2,-2]); | var C = brd.create('point',[-2,-2]); | ||
var D = brd.create('point',[ | var D = brd.create('point',[C.X()+3/5*diagPentagon, C.Y()]); | ||
var pol3 = brd.create('regularpolygon',[C,D,3], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0}); | |||
for (i=0;i<3;i++) pol3.vertices[i].setProperty({color:'#3d1c24'}); | |||
var pol3 = brd.create('regularpolygon',[C,D,3], {withLines:false, fillColor:' | |||
// Heptagon | |||
var E = brd.create('point',[-2,-2]); | |||
// | |||
// Side length of the heptagon depending on the diagonal of the pentagon: | |||
// r_7 = 7/5*r_5 | |||
var diagHeptagon = 7/5*diagPentagon; | |||
// s_7 = r_7*sqrt(2)*sqrt(1-cos(pi/7)) (law of cosines) | |||
var sideHeptagon = Math.sqrt(2*(1-Math.cos(Math.PI/7)))*diagHeptagon; | |||
// | |||
var F = brd.create('point',[E.X()+sideHeptagon, E.Y()]); | |||
var pol7 = brd.create('regularpolygon',[E,F,7], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0}); | |||
for (i=0;i<7;i++) pol7.vertices[i].setProperty({color:'#3d1c24'}); | |||
// Create the Reuleauc curves | |||
var reuleauxHeptagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol7.vertices, 7), | |||
{strokeWidth:6, strokeColor:'#d66d55', fillColor:'#d6bb55', highlightFillColor:'#d6bb55'}); | |||
var reuleauxPentagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol5.vertices, 5), | |||
{strokeWidth:6, strokeColor:'#d66d55', fillColor:'#ad5544', highlightFillColor:'#ad5544'}); | |||
var reuleauxTriangle = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol3.vertices, 3), | |||
{strokeWidth:6, strokeColor:'#d66d55', fillColor:'#703545', highlightFillColor:'#703545'}); | |||
brd.unsuspendUpdate(); | brd.unsuspendUpdate(); | ||
=== | var rol5 = brd.createRoulette(reuleauxHeptagon, reuleauxPentagon, 6*Math.PI/5, Math.PI/45, 1, 50, [A,B,C,D]); | ||
var rol3 = brd.createRoulette(reuleauxPentagon, reuleauxTriangle, 6*Math.PI/5, Math.PI/45, -1, 50, [C,D]); | |||
var rollIt = function() { | |||
rol5.rolling(); | |||
rol3.rolling(); | |||
}; | |||
var interval; | |||
var start = function() { | |||
interval = setInterval(rollIt,10); | |||
}; | |||
var stop = function() { | |||
clearInterval(interval); | |||
} | |||
</source> | </source> | ||
Latest revision as of 15:50, 20 February 2013
The underlying JavaScript code
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,7,5,-3]});
brd.renderer.container.style.backgroundColor = '#3d1c24'; // background color board
brd.suspendUpdate();
// Pentagon
var A = brd.create('point',[-2,-2]);
var B = brd.create('point',[2,-2]);
var pol5 = brd.create('regularpolygon',[A,B,5], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
for (var i=0;i<5;i++) pol5.vertices[i].setProperty({color:'#3d1c24'});
var diagPentagon = (1+Math.sqrt(5))*0.5*A.Dist(B);
// Triangle
var C = brd.create('point',[-2,-2]);
var D = brd.create('point',[C.X()+3/5*diagPentagon, C.Y()]);
var pol3 = brd.create('regularpolygon',[C,D,3], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
for (i=0;i<3;i++) pol3.vertices[i].setProperty({color:'#3d1c24'});
// Heptagon
var E = brd.create('point',[-2,-2]);
//
// Side length of the heptagon depending on the diagonal of the pentagon:
// r_7 = 7/5*r_5
var diagHeptagon = 7/5*diagPentagon;
// s_7 = r_7*sqrt(2)*sqrt(1-cos(pi/7)) (law of cosines)
var sideHeptagon = Math.sqrt(2*(1-Math.cos(Math.PI/7)))*diagHeptagon;
//
var F = brd.create('point',[E.X()+sideHeptagon, E.Y()]);
var pol7 = brd.create('regularpolygon',[E,F,7], {withLines:false, fillColor:'none', highlightFillColor:'none', fillOpacity:0.0});
for (i=0;i<7;i++) pol7.vertices[i].setProperty({color:'#3d1c24'});
// Create the Reuleauc curves
var reuleauxHeptagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol7.vertices, 7),
{strokeWidth:6, strokeColor:'#d66d55', fillColor:'#d6bb55', highlightFillColor:'#d6bb55'});
var reuleauxPentagon = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol5.vertices, 5),
{strokeWidth:6, strokeColor:'#d66d55', fillColor:'#ad5544', highlightFillColor:'#ad5544'});
var reuleauxTriangle = brd.create('curve', JXG.Math.Geometry.reuleauxPolygon(pol3.vertices, 3),
{strokeWidth:6, strokeColor:'#d66d55', fillColor:'#703545', highlightFillColor:'#703545'});
brd.unsuspendUpdate();
var rol5 = brd.createRoulette(reuleauxHeptagon, reuleauxPentagon, 6*Math.PI/5, Math.PI/45, 1, 50, [A,B,C,D]);
var rol3 = brd.createRoulette(reuleauxPentagon, reuleauxTriangle, 6*Math.PI/5, Math.PI/45, -1, 50, [C,D]);
var rollIt = function() {
rol5.rolling();
rol3.rolling();
};
var interval;
var start = function() {
interval = setInterval(rollIt,10);
};
var stop = function() {
clearInterval(interval);
}