Difference between revisions of "OsculatingCircle Command"

Latest revision as of 17:15, 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:

This command is for 2D objects only. For 3D, you can make a custom tool for example https://www.geogebra.org/m/tan7dxjt

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.2}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|other}}
-{{command|other}}
+;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.
-; OsculatingCircle[Point, Curve]: Yields the osculating circle of the curve in the given point.
+:{{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.
+:{{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> )
+: 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((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>}}
+{{note| 1=<div>
+* This command is for 2D objects only. For 3D, you can make a custom tool for example https://www.geogebra.org/m/tan7dxjt
+</div>}}