Sequences of Points, Circles and Line Segments

To create a sequence of points, circles or line segments on, we use the sequence command.

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 may be able to copy and paste this command:


Sequences of Circles

To draw a sequence of circles we use the circle command. The circle command requires a center and a radius.

Lets make sequence of circles with center (10,5) and with radius n.

Try out the following command in the geogebra applet below:

Copy& paste: Sequence[Circle[(10,5),n],n,1,5]

Now try:

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.

Now see if you can reproduce the following diagrams:

Project 1

Project 2

ProJect 3

Sequence 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!

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