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 $n=1$ and $n=4$

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 $(10,5)$ and with radius $n$ .

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 $n$ from the default value 1 to 0.1. More steps between 1 and 5 – more circles.

Make some of your own

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.