Difference between revisions of "OsculatingCircle Command"

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(* This command is for 2D objects only. For 3D, you can make a custom tool for example https://www.geogebra.org/m/tan7dxjt)
 
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<noinclude>{{Manual Page|version=4.2}}</noinclude>{{command|other}}
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|other}}
;OsculatingCircle[ <Point>, <Function> ]
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;OsculatingCircle( <Point>, <Function> )
 
:Yields the osculating circle of the function in the given point.
 
:Yields the osculating circle of the function in the given point.
:{{example|1=<code><nowiki>OsculatingCircle[(0, 0), x^2]</nowiki></code> yields ''x² + y² - y = 0''.}}
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:{{example|1=<code><nowiki>OsculatingCircle((0, 0), x^2)</nowiki></code> yields ''x² + y² - y = 0''.}}
;OsculatingCircle[ <Point>, <Curve> ]
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;OsculatingCircle( <Point>, <Curve> )
 
:Yields the osculating circle of the curve in the given point.
 
:Yields the osculating circle of the curve in the given point.
:{{example|1=<code><nowiki>OsculatingCircle[(1, 0), Curve[cos(t), sin(2t), t, 0, 2π]]</nowiki></code> yields ''x² + y² + 6x = 7''.}}
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:{{example|1=<code><nowiki>OsculatingCircle((1, 0), Curve(cos(t), sin(2t), t, 0, 2π))</nowiki></code> yields ''x² + y² + 6x = 7''.}}
  
  
;OsculatingCircle[ <Point>, <Object> ]
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;OsculatingCircle( <Point>, <Object> )
 
: Yields the osculating circle of the object (function, curve, conic) in the given point.
 
: Yields the osculating circle of the object (function, curve, conic) in the given point.
 
:{{examples|1=<div>
 
:{{examples|1=<div>
:*<code><nowiki>OsculatingCircle[(0, 0), x^2]</nowiki></code> yields ''x² + y² - y = 0''
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:*<code><nowiki>OsculatingCircle((0, 0), x^2)</nowiki></code> yields ''x² + y² - y = 0''
:*<code><nowiki>OsculatingCircle[(1, 0), Curve[cos(t), sin(2t), t, 0, 2π]]</nowiki></code> yields ''x² + y² + 6x = 7''
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:*<code><nowiki>OsculatingCircle((1, 0), Curve(cos(t), sin(2t), t, 0, 2π))</nowiki></code> yields ''x² + y² + 6x = 7''
:*<code><nowiki>OsculatingCircle[(-1, 0), Conic[{1, 1, 1, 2, 2, 3}]]</nowiki></code> yields ''x² + y² + 2x + 1y = -1''</div>}}
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:*<code><nowiki>OsculatingCircle((-1, 0), Conic({1, 1, 1, 2, 2, 3}))</nowiki></code> yields ''x² + y² + 2x + 1y = -1''</div>}}
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{{note| 1=<div>
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* This command is for 2D objects only. For 3D, you can make a custom tool for example https://www.geogebra.org/m/tan7dxjt
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</div>}}

Latest revision as of 16:15, 28 September 2019


OsculatingCircle( <Point>, <Function> )
Yields the osculating circle of the function in the given point.
Example: OsculatingCircle((0, 0), x^2) yields x² + y² - y = 0.
OsculatingCircle( <Point>, <Curve> )
Yields the osculating circle of the curve in the given point.
Example: OsculatingCircle((1, 0), Curve(cos(t), sin(2t), t, 0, 2π)) yields x² + y² + 6x = 7.


OsculatingCircle( <Point>, <Object> )
Yields the osculating circle of the object (function, curve, conic) in the given point.
Examples:
  • OsculatingCircle((0, 0), x^2) yields x² + y² - y = 0
  • OsculatingCircle((1, 0), Curve(cos(t), sin(2t), t, 0, 2π)) yields x² + y² + 6x = 7
  • OsculatingCircle((-1, 0), Conic({1, 1, 1, 2, 2, 3})) yields x² + y² + 2x + 1y = -1


Note:
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