Project: Sequences of Circles, Line Segments, Polygons

A sequence of polygons

For this project you need to create your own sequence diagrams, and figure out a given sequence by drawing by hand before using the command on GeoGebra.

Page 1: Title, Name, Date, Introduction

Page 2: Your own sequence of circles screenshot with command

Page 3: Your own sequence of line segments screenshot with command

Page 4: A hand drawn diagram of a given command for a sequence of circles and/or line segment, with calculations

Page 5: The geogebra diagram for the given sequence

Page 6: Conclusion stating accuracies or errors between pages 4&5.

Before beginning, become acquainted with the various GeoGebra commands by following these instructions:

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

  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:

TUnnel

eye 1

eye 2


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.

 


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