Difference between revisions of "OsculatingCircle Command"

Revision as of 08:26, 25 August 2014

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.

Following text is about a feature that is supported only in GeoGebra 5.0.

Note: From GeoGebra 5, this command will work with conics as well.

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

@@ Line 2: / Line 2: @@
 ;OsculatingCircle[ <Point>, <Function> ]
 :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''.}}
+:{{example|1=<code><nowiki>OsculatingCircle[(0, 0), x^2]</nowiki></code> yields ''x² + y² - y = 0''.}}
 ;OsculatingCircle[ <Point>, <Curve> ]
 :Yields the osculating circle of the curve in the given point.
@@ Line 11: / Line 11: @@
 : Yields the osculating circle of the object (function, curve, conic) in the given point.
 :{{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), Conic[{1, 1, 1, 2, 2, 3}]]</nowiki></code> yields ''x² + y² + 2x +1y = -1''</div>}}
+:*<code><nowiki>OsculatingCircle[(-1, 0), Conic[{1, 1, 1, 2, 2, 3}]]</nowiki></code> yields ''x² + y² + 2x + 1y = -1''</div>}}
 }}