# 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|* 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 | + | Implicit curves are polynomials in variables ''x'' and ''y''. The can be entered directly using the [[Input Bar]]. <br> |

− | {{example|< | + | 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`