Difference between revisions of "Curves"

From GeoGebra Manual
Jump to: navigation, search
(added examples for polar curves and link to ImplicitCurve command)
m (→‎Polar curves: spacing)
 
Line 14: Line 14:
 
==Polar curves==
 
==Polar curves==
 
In order to draw a curve defined using polar coordinates, it is possible to use one of the following (equivalent) syntaxes:
 
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>. }}
+
{{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==

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