The Sequence Command
The sequence command of geogebra, combined with other commands, yields some fun diagrams!
The sequence command:
Let’s make a sequence of points, with coordinates , for values of
between
and
. That is,
To generate this sequence of points, we type in:
Which yields the graph:
You can try that out on the geogebra applet below. You many be able to copy, paste this command:
Sequence[(n,n^2),n,1,5,1]
Sequences of Circles
Now suppose we want to draw a sequence of circles. The circle command requires a centre and a radius.
Suppose we make a sequence of circles with centre and with radius
.
Try out the following command in the geogebra applet below:
To copy paste use: Sequence[Circle[(10,5),n],n,1,5]
Geogebra applet:
If that worked for you, try out
Sequence[Circle[(10,5), n], n, 1, 5, 0.1]
The final parameter changes the increment of from the default value 1 to 0.1. More steps between 1 and 5 – more circles.
Make some of your own
Use the geogebra applet to generate your own sequence of circles.
- Make a sequence where the centre of the circle is constant, but the radius changes.
- Make a sequence where the centre of the circle changes, but the radius is constant.
- Make a sequence where the centre and the radius both change.
Figure out the sequence command
Now see if you can reproduce the following diagrams:
Project 1
Project 2
ProJect 3
Sequences of Line Segments
The following diagram uses the command Segment[<point>,<point>] to create a sequence of line segments. Observe the start/end point to a few of line segments to see the pattern of start and end points.
Draw your own sequence diagrams!
Return to Sequences and Series Menu