Difference between revisions of "Curves"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|geometric}}
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GeoGebra supports the following types of curves:
There are two types of curves in geogebra.
 
 
==Parametric curves==
 
==Parametric curves==
Parametric curves of the form a(t)=(f(t),g(t)) where ''t'' is real parameter within certain range can be created using the [[Curve Command]]. They can be used in [[Tangent Command]] and [[Point Command]].
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Parametric curves of the form ''a(t)'' = ''(f(t), g(t))'' where ''t'' is real parameter within a certain range can be created:
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* using the [[Curve Command]] or
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* by typing their expression directly in the ''input bar'', e.g.<code>(t^2,t^3)</code>. <br>
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Parametric curves can be used as arguments in the following commands: [[Tangent Command|Tangent]], [[Point Command|Point]], [[Intersect Command|Intersect]], [[Derivative Command|Derivative]], [[Length Command|Length]], [[Curvature Command|Curvature]], [[CurvatureVector Command|CurvatureVector]] and [[OsculatingCircle Command|OsculatingCircle]].
  
 
{{note|1=* Parametric curves can be used with pre-defined functions and arithmetic operations.  For example, input <code>c(3)</code> returns the point at parameter position 3 on curve ''c''.  
 
{{note|1=* Parametric curves can be used with pre-defined functions and arithmetic operations.  For example, input <code>c(3)</code> returns the point at parameter position 3 on curve ''c''.  
* Using the mouse you can also place a point on a curve using tool [[New Point Tool|New Point]] or command [[Point Command|Point]]. Since the endpoints ''a'' and ''b'' are dynamic you can use slider variables as well (see tool [[Slider Tool|Slider]]).}}
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* You can also place a point on a curve using tool [[File:Mode point.svg|link=|24px]] [[Point Tool|Point]] or command [[Point Command|Point]]. Since the endpoints ''a'' and ''b'' are dynamic you can use slider variables as well (see tool [[File:Mode slider.svg|link=|24px]] [[Slider Tool|Slider]]).}}
  
Creating parametric curve going through given points is not possible. You can however try e.g. [[FitPoly Command]] to get a function going through these points.
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Creating a parametric curve through some given points is not possible. You can however try e.g. [[FitPoly Command]] to get a function going through these points.
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==Polar curves==
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In order to draw a curve defined using polar coordinates, it is possible to use one of the following (equivalent) syntaxes:
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{{example| <code>ρ=sin(2 θ)</code>, or <code>sin(2 θ)</code>, or <code>f(t)=(sin(2*t); t)</code>, or <code>(sin(2*t); t)</code>, or <code>f(t)=(sin(2*t); t), 0< t < pi</code>, or <code>(sin(2*t); t), 0 < t < pi</code>, or <code>Curve[(sin(2*t); t), t, 0, 2pi]</code>. }}
  
 
==Implicit curves==
 
==Implicit curves==
Implicit curves are polynomials in variables ''x'' and ''y''. The can be entered directly into [[Input Bar]].
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Implicit curves are polynomials in variables ''x'' and ''y''. The can be entered directly using the [[Input Bar]]. <br>
{{example|1=x^4+y^3=2xy}}
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The [[ImplicitCurve Command|ImplicitCurve]] command generates an implicit curve through a list of points.
{{description}}
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{{example|1=<code>x^4 + y^3 = 2xy</code>}}

Latest revision as of 10:29, 16 March 2017


GeoGebra supports the following types of curves:

Parametric curves

Parametric curves of the form a(t) = (f(t), g(t)) where t is real parameter within a certain range can be created:

  • using the Curve Command or
  • by typing their expression directly in the input bar, e.g.(t^2,t^3).

Parametric curves can be used as arguments in the following commands: Tangent, Point, Intersect, Derivative, Length, Curvature, CurvatureVector and OsculatingCircle.

Note:
  • Parametric curves can be used with pre-defined functions and arithmetic operations. For example, input c(3) returns the point at parameter position 3 on curve c.
  • You can also place a point on a curve using tool Mode point.svg Point or command Point. Since the endpoints a and b are dynamic you can use slider variables as well (see tool Mode slider.svg Slider).

Creating a parametric curve through some given points is not possible. You can however try e.g. FitPoly Command to get a function going through these points.

Polar curves

In order to draw a curve defined using polar coordinates, it is possible to use one of the following (equivalent) syntaxes:

Example: ρ=sin(2 θ), or sin(2 θ), or f(t)=(sin(2*t); t), or (sin(2*t); t), or f(t)=(sin(2*t); t), 0< t < pi, or (sin(2*t); t), 0 < t < pi, or Curve[(sin(2*t); t), t, 0, 2pi].


Implicit curves

Implicit curves are polynomials in variables x and y. The can be entered directly using the Input Bar.
The ImplicitCurve command generates an implicit curve through a list of points.

Example: x^4 + y^3 = 2xy
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