# Difference between revisions of "Curves"

From GeoGebra Manual

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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]]. | + | 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]]).}} | * 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. |

==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 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.

## 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`