Sequences of Points, Circles and Line Segments

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 (n, n^2), for values of n between 1 and 5. That is,

    \[\{(1,1), \quad (2,4), \quad (3,9), \quad (4,16), \quad (5,25)\} \]

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 (10,5) and with radius n.

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 n 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.

  1. Make a sequence where the centre of the circle is constant, but the radius changes.
  2. Make a sequence where the centre of the circle changes, but the radius is constant.
  3. 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

  1. Sequence[Circle[(n, n), n], n, 1, 5, 0.1]
  2. Sequence[Circle[(n, 5), n], n, 1, 5, 0.05]
  3. Sequence[Circle[(12 + n, 5), n], n, 1, 5, 0.05]


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