Difference between revisions of "Reuleaux pentagon"

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(36 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
<jsxgraph width="0" height="0" box="nix"></jsxgraph>
 
 
<html>
 
<html>
−
<script type="text/javascript" src="/~alfred/jsxgraph/trunk/src/Roulette.js"></script>
 
 
<form>
 
<form>
−
<input type="button" value="start" onclick="rol.start(); rol3.start();">
+
<input type="button" value="start" onclick="start();">
−
<input type="button" value="stop" onclick="rol.stop(); rol3.stop();">
+
<input type="button" value="stop" onclick="stop();">
−
<input type="button" value="one step" onclick="rol.rolling()">
+
<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:[-5,7,5,-3]});
 
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
 
// Pentagon
Line 15: Line 15:
 
var B = 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});
 
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
 
// Triangle
 
var C = brd.create('point',[-2,-2]);
 
var C = brd.create('point',[-2,-2]);
−
var D = brd.create('point',[C.X()+3/5*(1+Math.sqrt(5))*0.5*A.Dist(B), C.Y()]);
+
var D = brd.create('point',[C.X()+3/5*diagPentagon, C.Y()]);
−
var pol3 = brd.create('regularpolygon',[C,D,3], {withLines:false, fillColor:'#e8501f', highlightFillColor:'#e8501f', fillOpacity:0.0});
+
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
 
// Heptagon
 
var E = brd.create('point',[-2,-2]);
 
var E = brd.create('point',[-2,-2]);
−
var F = brd.create('point',[E.X()+7/5*A.Dist(pol5.vertices[2]), E.Y()]);
 
−
var pol7 = brd.create('regularpolygon',[E,F,7], {withLines:false, fillColor:'#e8501f', highlightFillColor:'#e8501f', fillOpacity:0.0});
 
  
−
var reuleauxHeptagon = brd.create('curve', JXG.Math.Numerics.reuleauxPolygon(pol7.vertices, 7),  
+
//
−
       {color:'#e8501f', highlightFillColor:'#e8501f'});
+
// Side length of the heptagon depending on the diagonal of the pentagon:
−
var reuleauxPentagon = brd.create('curve', JXG.Math.Numerics.reuleauxPolygon(pol5.vertices, 5),  
+
// r_7 = 7/5*r_5
−
       {color:'#093083', highlightFillColor:'#093083'});
+
var diagHeptagon = 7/5*diagPentagon;
−
var reuleauxTriangle = brd.create('curve', JXG.Math.Numerics.reuleauxPolygon(pol3.vertices, 3),  
+
// s_7 = r_7*sqrt(2)*sqrt(1-cos(pi/7)) (law of cosines)
−
       {color:'#e8501f', highlightFillColor:'#e8501f'});
+
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 rol = JXG.Math.Numerics.createRoulette(reuleauxHeptagon, reuleauxPentagon, 6*Math.PI/5, Math.PI/90, -1, 10, [A,B])();  
+
var rol5 = brd.createRoulette(reuleauxHeptagon, reuleauxPentagon, 6*Math.PI/5, Math.PI/45, 1, 50, [A,B,C,D]);  
−
var rol3 = JXG.Math.Numerics.createRoulette(reuleauxPentagon, reuleauxTriangle, 6*Math.PI/5, Math.PI/90, 1, 10, [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>
 
</jsxgraph>
  
Line 41: Line 66:
 
<source lang="javascript">
 
<source lang="javascript">
 
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-5,7,5,-3]});
 
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
 
// Pentagon
Line 46: Line 73:
 
var B = 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});
 
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
 
// Triangle
 
var C = brd.create('point',[-2,-2]);
 
var C = brd.create('point',[-2,-2]);
−
var D = brd.create('point',[C.X()+3/5*(1+Math.sqrt(5))*0.5*A.Dist(B), C.Y()]);
+
var D = brd.create('point',[C.X()+3/5*diagPentagon, C.Y()]);
−
var pol3 = brd.create('regularpolygon',[C,D,3], {withLines:false, fillColor:'#e8501f', highlightFillColor:'#e8501f', fillOpacity:0.0});
+
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
 
// Heptagon
 
var E = brd.create('point',[-2,-2]);
 
var E = brd.create('point',[-2,-2]);
−
var F = brd.create('point',[E.X()+7/5*A.Dist(pol5.vertices[2]), E.Y()]);
 
−
var pol7 = brd.create('regularpolygon',[E,F,7], {withLines:false, fillColor:'#e8501f', highlightFillColor:'#e8501f', fillOpacity:0.0});
 
  
−
var reuleauxHeptagon = brd.create('curve', JXG.Math.Numerics.reuleauxPolygon(pol7.vertices, 7),  
+
//
−
       {color:'#e8501f', highlightFillColor:'#e8501f'});
+
// Side length of the heptagon depending on the diagonal of the pentagon:
−
var reuleauxPentagon = brd.create('curve', JXG.Math.Numerics.reuleauxPolygon(pol5.vertices, 5),  
+
// r_7 = 7/5*r_5
−
       {color:'#093083', highlightFillColor:'#093083'});
+
var diagHeptagon = 7/5*diagPentagon;
−
var reuleauxTriangle = brd.create('curve', JXG.Math.Numerics.reuleauxPolygon(pol3.vertices, 3),  
+
// s_7 = r_7*sqrt(2)*sqrt(1-cos(pi/7)) (law of cosines)
−
       {color:'#e8501f', highlightFillColor:'#e8501f'});
+
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 rol = JXG.Math.Numerics.createRoulette(reuleauxHeptagon, reuleauxPentagon, 6*Math.PI/5, Math.PI/90, -1, 10, [A,B])();  
+
var rol5 = brd.createRoulette(reuleauxHeptagon, reuleauxPentagon, 6*Math.PI/5, Math.PI/45, 1, 50, [A,B,C,D]);  
−
var rol3 = JXG.Math.Numerics.createRoulette(reuleauxPentagon, reuleauxTriangle, 6*Math.PI/5, Math.PI/90, 1, 10, [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 17:50, 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);
}
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