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 11:39, 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