Semicubical parabola - Revision history

A WASSERMANN at 09:39, 13 January 2011

2011-01-13T09:39:56Z

← Older revision		Revision as of 09:39, 13 January 2011
Line 21:		Line 21:
	</jsxgraph>		</jsxgraph>

	~~====~~From Wikipedia:~~====~~		* '''From Wikipedia:'''
	The semicubical parabola was discovered in 1657 by William Neile who computed its arc length; it was the first algebraic curve (excluding the line) to be rectified. It is unique in that a particle following its path while being pulled down by gravity travels equal vertical intervals in equal time periods.		The semicubical parabola was discovered in 1657 by William Neile who computed its arc length; it was the first algebraic curve (excluding the line) to be rectified. It is unique in that a particle following its path while being pulled down by gravity travels equal vertical intervals in equal time periods.
	~~====~~From MathDL:~~====~~		* '''From MathDL:'''
	1659:Hendrik van Heuraet sent van Schooten his rectification of the semi-cubical parabola. This was published---his only publication---in the second Latin edition of Descartes' Geometrie. This broke the spell of Aristotle's dictum that curved lines could not in principle be compared with straight lines.		1659: Hendrik van Heuraet sent van Schooten his rectification of the semi-cubical parabola. This was published---his only publication---in the second Latin edition of Descartes' Geometrie. This broke the spell of Aristotle's dictum that curved lines could not in principle be compared with straight lines.

	===References===		===References===
	* [http://en.wikipedia.org/wiki/Semicubical_parabola Wikipedia on semicubical parabola]		* [http://en.wikipedia.org/wiki/Semicubical_parabola Wikipedia on semicubical parabola]

A WASSERMANN at 09:38, 13 January 2011

2011-01-13T09:38:57Z

← Older revision		Revision as of 09:38, 13 January 2011
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	-2, 2		-2, 2
	],		],
	{strokeWidth:2, strokeColor:'black'});		{strokeWidth:1, strokeColor:'black'});
	brd.unsuspendUpdate();		brd.unsuspendUpdate();
	})();		})();
	</jsxgraph>		</jsxgraph>

			====From Wikipedia:====
			The semicubical parabola was discovered in 1657 by William Neile who computed its arc length; it was the first algebraic curve (excluding the line) to be rectified. It is unique in that a particle following its path while being pulled down by gravity travels equal vertical intervals in equal time periods.
			====From MathDL:====
			1659:Hendrik van Heuraet sent van Schooten his rectification of the semi-cubical parabola. This was published---his only publication---in the second Latin edition of Descartes' Geometrie. This broke the spell of Aristotle's dictum that curved lines could not in principle be compared with straight lines.
	===References===		===References===
	* [http://en.wikipedia.org/wiki/Semicubical_parabola Wikipedia on semicubical parabola]		* [http://en.wikipedia.org/wiki/Semicubical_parabola Wikipedia on semicubical parabola]
			* [http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Heuraet.html The MacTutor History of Mathematics archive]
	* [http://mathdl.maa.org/mathDL/?pa=historicalEvent&sa=browseFrontEnd&month=0&day=13 MathDL, the MAA Mathematical Sciences Digital Library]		* [http://mathdl.maa.org/mathDL/?pa=historicalEvent&sa=browseFrontEnd&month=0&day=13 MathDL, the MAA Mathematical Sciences Digital Library]

Line 29:		Line 34:
	var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-1,2,3,-2], keepaspectratio:true, axis:true});		var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-1,2,3,-2], keepaspectratio:true, axis:true});
	brd.suspendUpdate();		brd.suspendUpdate();
	var a = brd.create('slider',[[-1,1.8],[1,1.8],[-5,0.20,5]], {name:'a'});		var a = brd.create('slider',[[-0.5,1.8],[1,1.8],[-5,0.20,5]], {name:'a'});

	var p = brd.create('curve',		var p = brd.create('curve',
	[function(t){ return t*t;},		[function(t){ return t*t;},
	function(t){ return a.Value()tt*t;}		function(t){ return a.Value()tt*t;},
			-2, 2
	],		],
	{strokeWidth:2, strokeColor:'black'});		{strokeWidth:1, strokeColor:'black'});
	brd.unsuspendUpdate();		brd.unsuspendUpdate();
	</source>		</source>

A WASSERMANN at 09:33, 13 January 2011

2011-01-13T09:33:17Z

← Older revision		Revision as of 09:33, 13 January 2011
Line 13:		Line 13:
	var p = brd.create('curve',		var p = brd.create('curve',
	[function(t){ return t*t;},		[function(t){ return t*t;},
	function(t){ return a.Value()tt*t;}		function(t){ return a.Value()tt*t;},
			-2, 2
	],		],
	{strokeWidth:2, strokeColor:'black'});		{strokeWidth:2, strokeColor:'black'});

A WASSERMANN at 09:32, 13 January 2011

2011-01-13T09:32:34Z

← Older revision		Revision as of 09:32, 13 January 2011
Line 7:		Line 7:
	<jsxgraph width="600" height="600">		<jsxgraph width="600" height="600">
	(function(){		(function(){
	var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-1,2,3,-2], keepaspectratio:true});		var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-1,2,3,-2], keepaspectratio:true, axis:true});
	brd.suspendUpdate();		brd.suspendUpdate();
	var a = brd.create('slider',[[-1,1.8],[1,1.8],[-5,0.20,5]], {name:'a'});		var a = brd.create('slider',[[-0.5,1.8],[1,1.8],[-5,0.20,5]], {name:'a'});

	var p = brd.create('curve',		var p = brd.create('curve',
Line 26:		Line 26:
	===The underlying JavaScript code===		===The underlying JavaScript code===
	<source lang="javascript">		<source lang="javascript">
	var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-1,2,3,-2], keepaspectratio:true});		var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-1,2,3,-2], keepaspectratio:true, axis:true});
	brd.suspendUpdate();		brd.suspendUpdate();
	var a = brd.create('slider',[[-1,1.8],[1,1.8],[-5,0.20,5]], {name:'a'});		var a = brd.create('slider',[[-1,1.8],[1,1.8],[-5,0.20,5]], {name:'a'});

A WASSERMANN: New page: A semicubical parabola is a curve defined parametrically as : $x = t^2$ : $y = at^3$ (function(){ var brd = JXG.JSXGraph.init...

2011-01-13T09:31:31Z

New page: A semicubical parabola is a curve defined parametrically as :<math> x = t^2 </math> :<math> y = at^3 </math> <jsxgraph width="600" height="600"> (function(){ var brd = JXG.JSXGraph.init...

New page

A semicubical parabola is a curve defined parametrically as

:<math> x = t^2 </math>

:<math> y = at^3 </math>

<jsxgraph width="600" height="600">
(function(){
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-1,2,3,-2], keepaspectratio:true});
brd.suspendUpdate();
var a = brd.create('slider',[[-1,1.8],[1,1.8],[-5,0.20,5]], {name:'a'});

var p = brd.create('curve',
[function(t){ return t*t;},
function(t){ return a.Value()*t*t*t;}
],
{strokeWidth:2, strokeColor:'black'});
brd.unsuspendUpdate();
})();
</jsxgraph>

===References===
* [http://en.wikipedia.org/wiki/Semicubical_parabola Wikipedia on semicubical parabola]
* [http://mathdl.maa.org/mathDL/?pa=historicalEvent&sa=browseFrontEnd&month=0&day=13 MathDL, the MAA Mathematical Sciences Digital Library]

===The underlying JavaScript code===
<source lang="javascript">
var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-1,2,3,-2], keepaspectratio:true});
brd.suspendUpdate();
var a = brd.create('slider',[[-1,1.8],[1,1.8],[-5,0.20,5]], {name:'a'});

var p = brd.create('curve',
[function(t){ return t*t;},
function(t){ return a.Value()*t*t*t;}
],
{strokeWidth:2, strokeColor:'black'});
brd.unsuspendUpdate();
</source>

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

Semicubical parabola - Revision history

A WASSERMANN at 09:39, 13 January 2011

A WASSERMANN at 09:38, 13 January 2011

A WASSERMANN at 09:33, 13 January 2011

A WASSERMANN at 09:32, 13 January 2011

A WASSERMANN: New page: A semicubical parabola is a curve defined parametrically as : x = t^2 : y = at^3 (function(){ var brd = JXG.JSXGraph.init...

A WASSERMANN: New page: A semicubical parabola is a curve defined parametrically as : $x = t^2$ : $y = at^3$ (function(){ var brd = JXG.JSXGraph.init...