# Project: Sequences of Circles, Line Segments, Polygons

A sequence of polygons

For this project you need to create 3 or 4 of your own sequence diagrams. The first two can be the product of experiment – try different things out. The third (and fourth) you are to first draw with paper and pencil, and then try to reproduce your idea with a sequence of circles/line segments/polygons etc.

Page 1: Title, Name, Date, Introduction

Page 2: The first sequence screenshot with command

Page 3: The second sequence screenshot with command

Page 4: A hand drawn diagram, with calculations

Page 5: The geogebra diagram for your third idea

(Page 6, 7 – again, but with some other shape)

The following sequences are to get you started.

To begin, open a geogebra classic page, (close the keyboard) then open a long input bar at the bottom as follows:

For each command given as an example, either type carefully to include all brackets or copy and paste into the input bar on the geogebra page.

# A Sequence

A squence until now has simply been a list of numbers. The sequence command in geogebra is as follows:

Fill in the input options as follows:

Sequence(2n+1,n,1,10,1)

Press enter, to generate a simple sequence of numbers:

# Sequences of Circles

The circle command requires a point for the centre, and a radius.

Example 1. Clear your geogebra screen and type in the following set of circles, one at a time:

Circle((1,1),1)

Circle((2,2),1)

Circle((3,3),1)

Circle((4,4)1)

This should give four circles, all with different centres but radius 1.

What they have in common is that the centres are at the point (n,n) between and

Now, clear the screen and enter all of them together with one sequence command:

Sequence(circle((n,n),1),n,1,4,1)

This means, circle centre (n,n) with radius 1, for all values of n between 1 and 4, going up in 1s.

Example 2.

Now enter

Sequence(circle((n,n),1),n,1,4,0.1)

Which means, circle centre (n,n) with radius 1, for all values of n between 1 and 4, going up in 0.1s – which draws a total of 31 circles!

Example 3. Suppose we make a sequence of circles with centre and with radius .

Try out the following command:

Sequence[Circle[(10,5),n],n,1,5]

Example 4. Now let’s add the ‘increment parameter’ and make it 0.1, to draw many more circles.

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

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:

# Sequences of Line Segments

The following diagram uses the sequence command along with the command Segment[<point>,<point>] to create a sequence of line segments.

Example 1. What will the following command produce? Try it out.

Example 2. Observe the start/end point to a few of line segments to see the pattern of start and end points.