Difference between revisions of "Curves"

From GeoGebra Manual
Jump to: navigation, search
m (Text replace - "<div class="box info"> 48px|left This page is part of the official manual for print and pdf. For structural reasons normal users can't edit this page. If you found any errors on this page please contact )
m (→‎Polar curves: spacing)
 
(7 intermediate revisions by 3 users not shown)
Line 1: Line 1:
<noinclude>{{Manual Page|version=4.2}}</noinclude>
+
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|geometric}}
{{objects|geometric}}
+
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]], [[Point Command]] and [[Intersect Command]] (GeoGebra 4.2).
+
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.<code>(t^2,t^3)</code>. <br>
 +
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 [[Image:Tool New Point.gif]] [[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 [[Image:Tool Slider.gif]] [[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.
+
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| <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 using the [[Input Bar]].
+
Implicit curves are polynomials in variables ''x'' and ''y''. The can be entered directly using the [[Input Bar]]. <br>
{{example|1=<code>x^4 + y^3 = 2x*y</code>}}
+
The [[ImplicitCurve Command|ImplicitCurve]] command generates an implicit curve through a list of points.
 +
{{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
© 2021 International GeoGebra Institute