Difference between revisions of "Curves"
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| − | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|geometric}} |
| − | {{objects|geometric}} | + | GeoGebra supports the following types of curves: |
| − | |||
==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]]. | + | 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''. | ||
| − | * | + | * 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 | + | 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 = | + | 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
Point or command Point. Since the endpoints a and b are dynamic you can use slider variables as well (see tool 
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
