Difference between revisions of "Curves"

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(→‎Parametric curves: added new syntax and related commands)
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There are two types of curves in GeoGebra:
 
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]], [[Point Command]] and [[Intersect 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''.  
 
* 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]]).}}
 
* 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.
  
 
==Implicit curves==
 
==Implicit curves==
 
Implicit curves are polynomials in variables ''x'' and ''y''. The can be entered directly using the [[Input Bar]].
 
Implicit curves are polynomials in variables ''x'' and ''y''. The can be entered directly using the [[Input Bar]].
 
{{example|1=<code>x^4 + y^3 = 2x*y</code>}}
 
{{example|1=<code>x^4 + y^3 = 2x*y</code>}}

Revision as of 12:39, 25 October 2015


There are two types of curves in GeoGebra:

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.

Implicit curves

Implicit curves are polynomials in variables x and y. The can be entered directly using the Input Bar.

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