Difference between revisions of "Tschirnhausen Cubic Catacaustic"
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[function(t){ return a.Value()*6*(t*t-1);}, | [function(t){ return a.Value()*6*(t*t-1);}, | ||
function(t){ return a.Value()*4*t*t*t;}, | function(t){ return a.Value()*4*t*t*t;}, | ||
− | - | + | -4, 4 |
], | ], | ||
{strokeWidth:1, strokeColor:'red'}); | {strokeWidth:1, strokeColor:'red'}); | ||
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[function(t){ return a.Value()*6*(t*t-1);}, | [function(t){ return a.Value()*6*(t*t-1);}, | ||
function(t){ return a.Value()*4*t*t*t;}, | function(t){ return a.Value()*4*t*t*t;}, | ||
− | - | + | -4, 4 |
], | ], | ||
{strokeWidth:1, strokeColor:'red'}); | {strokeWidth:1, strokeColor:'red'}); |
Revision as of 11:06, 13 January 2011
The Tschirnhausen cubic is defined parametrically as
- [math] x = a3(t^2-3) [/math]
- [math] y = at(t^2-3) [/math]
Its catcaustic with radiant point [math](-8a,p)[/math] is the semicubical parabola with parametric equations
- [math] x = a6(t^2-1) [/math]
- [math] y = a4t^3 [/math]
References
The underlying JavaScript code
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-10,10,10,-10], keepaspectratio:true, axis:true});
brd.suspendUpdate();
var a = brd.create('slider',[[-5,6],[5,6],[-5,1,5]], {name:'a'});
var cubic = brd.create('curve',
[function(t){ return a.Value()*3*(t*t-3);},
function(t){ return a.Value()*t*(t*t-3);},
-5, 5
],
{strokeWidth:1, strokeColor:'black'});
var radpoint = brd.create('point',[function(){ return -a.Value()*8;},0],{name:'radiant point'});
var cataustic = brd.create('curve',
[function(t){ return a.Value()*6*(t*t-1);},
function(t){ return a.Value()*4*t*t*t;},
-4, 4
],
{strokeWidth:1, strokeColor:'red'});
brd.unsuspendUpdate();