Difference between revisions of "Polynomial curve of constant width"
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+ | The curve defined by | ||
+ | |||
+ | :<math> p(\phi) = a\cdot cos(k\cdot\phi/2)+b </math> | ||
+ | |||
+ | in polar form is smooth and of constant width for odd values of <math>k</math>. | ||
+ | |||
<jsxgraph width="600" height="600"> | <jsxgraph width="600" height="600"> | ||
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-2,2,2,-2], keepaspectratio:true}); | var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-2,2,2,-2], keepaspectratio:true}); | ||
Line 15: | Line 21: | ||
var co = Math.cos(kk*phi*0.5); | var co = Math.cos(kk*phi*0.5); | ||
return aa*co*co+bb; | return aa*co*co+bb; | ||
− | },[0,0], 0,Math.PI*2], {curveType:'polar', strokeWidth:6, strokeColor:'# | + | },[0,0], 0,Math.PI*2], {curveType:'polar', strokeWidth:6, strokeColor:'#ad5544'}); |
brd.unsuspendUpdate(); | brd.unsuspendUpdate(); | ||
</jsxgraph> | </jsxgraph> | ||
+ | |||
+ | ===References=== | ||
+ | * [http://www.mathpropress.com/stan/bibliography/ Stanley Rabinowitz, A Polynomial Curve of Constant Width. Missouri Journal of Mathematical Sciences, 9(1997)23-27.] | ||
+ | |||
+ | ===The underlying JavaScript code=== | ||
+ | var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-2,2,2,-2], keepaspectratio:true}); | ||
+ | brd.suspendUpdate(); | ||
+ | var a = brd.create('slider',[[-1,1.8],[1,1.8],[-5,0.20,5]], {name:'a'}); | ||
+ | var b = brd.create('slider',[[-1,1.6],[1,1.6],[-5,1.15,10]], {name:'b'}); | ||
+ | var k = brd.create('slider',[[-1,1.4],[1,1.4],[1,1,11]], {name:'k\'', snapWidth:1}); | ||
+ | |||
+ | var p = brd.create('curve',[function(phi, suspendUpdate){ | ||
+ | var kk, aa, bb; | ||
+ | if (!suspendUpdate) { | ||
+ | aa = a.Value(); | ||
+ | bb = b.Value(); | ||
+ | kk = 2*k.Value()+1; | ||
+ | } | ||
+ | var co = Math.cos(kk*phi*0.5); | ||
+ | return aa*co*co+bb; | ||
+ | },[0,0], 0,Math.PI*2], {curveType:'polar', strokeWidth:6, strokeColor:'#ad5544'}); | ||
+ | brd.unsuspendUpdate(); | ||
[[Category:Examples]] | [[Category:Examples]] | ||
[[Category:Curves]] | [[Category:Curves]] |
Revision as of 15:39, 6 October 2010
The curve defined by
- [math] p(\phi) = a\cdot cos(k\cdot\phi/2)+b [/math]
in polar form is smooth and of constant width for odd values of [math]k[/math].
References
The underlying JavaScript code
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-2,2,2,-2], keepaspectratio:true}); brd.suspendUpdate(); var a = brd.create('slider',[[-1,1.8],[1,1.8],[-5,0.20,5]], {name:'a'}); var b = brd.create('slider',[[-1,1.6],[1,1.6],[-5,1.15,10]], {name:'b'}); var k = brd.create('slider',[[-1,1.4],[1,1.4],[1,1,11]], {name:'k\, snapWidth:1});
var p = brd.create('curve',[function(phi, suspendUpdate){
var kk, aa, bb; if (!suspendUpdate) { aa = a.Value(); bb = b.Value(); kk = 2*k.Value()+1; } var co = Math.cos(kk*phi*0.5); return aa*co*co+bb; },[0,0], 0,Math.PI*2], {curveType:'polar', strokeWidth:6, strokeColor:'#ad5544'});
brd.unsuspendUpdate();