# Difference between revisions of "Curves"

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==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 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`