Difference between revisions of "OsculatingCircle Command"

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;OsculatingCircle( <Point>, <Function> )
 
;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> )
 
;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''.}}
  
  
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: 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''
+
:*<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''
+
:*<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>}}

Revision as of 09:40, 9 October 2017


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
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