# Tutorial:Conditional Visibility & Sequences

## Visualizing Integer Addition on the Number Line

In this activity you can either use the following tools or corresponding commands. Make sure you know how to use them before you begin.

Slider | |

Point | |

Vector | |

Move | |

Segment Between Two Points | |

Insert Text | |

Checkbox |

### Construction Steps

1. Open a new GeoGebra window and hide the Algebra View. Set the labeling option to *All new objects* (Options Menu).

2. Open the Properties dialog for the Graphics View. On tab *yAxis*, uncheck *Show yAxis*. On tab *xAxis*, set the distance of tick marks to *1* by checking the box *Distance* and entering *1* into the text field. On tab *Basic* set the *minimum* of the x-Axis to *-21* and the *maximum* to *21*.

3. Create sliders a and b (interval -10 to 10; increment 1). Show the value of the sliders instead of their names (Properties dialog).

4. Create points *A = (0 , 1)* and *B = A + (a , 0)*.

5. Create vector *u = Vector[A, B]* which has the length a.

6. Create points *C = B + (0 , 1)* and *D = C + (b , 0)* as well as vector *v = Vector[C , D]* which has the length b.

7. Create point *R = (x(D) , 0)*.

**Hint:**x(D) gives you the x-coordinate of point D. Thus, point R shows the result of the addition.

8. Create point *Z = (0, 0)* as well as the following segments: *g = Segment[Z, A]*, *h = Segment[B, C]*, *i = Segment[D, R]*.

9. Use the Properties Dialog to enhance your construction (e.g. change color, line style, fix sliders, hide labels).

### Insert dynamic text

Enhance your interactive figure by inserting dynamic text that displays the corresponding addition problem.

10. Calculate the result of the addition problem: *r = a + b*

11. In order to display the parts of the addition problem in different colors you need to insert the dynamic text step by step. a. Insert text1: Select a from Objects b. Insert text2: + c. Insert text3: Select b from Objects d. Insert text4: = e. Insert text5: Select r from Objects

12. Match the color of text1, text3, and text5 with the color of the corresponding sliders and point R. Hide the labels of the sliders and fix the text (Properties Dialog).

13. Export the interactive figure as a dynamic worksheet.

## Conditional Formatting – Inserting Checkboxes

### Construction Steps

Insert a checkbox into the Graphics View that allows you to show or hide the result of the addition problem (text5, point R, and segment i).

1. Activate tool Checkbox to show and hide objects.

2. Click on the graphics view next to the result of the addition problem.

3. Enter *Show result* into the *Caption* text field.

4. From the drop down menu successively select all objects whose visibility should be controlled by the checkbox (text5, point R, and segment i).

5. Click *Apply* to create the checkbox.

6. In *Move* mode check and uncheck the checkbox to try out if all three objects can be hidden / shown.

7. Fix the checkbox so it can’t be moved accidentally any more (Properties dialog).

8. Export this new interactive figure as a dynamic worksheet.

**Hint:**You might want to use a different name for this worksheet.

### Boolean variables

A Check Box to Show / Hide Objects is the graphical representation of a Boolean variable in GeoGebra. It can either be true or false which can be set by checking (Boolean variable = true) or unchecking (Boolean variable = false) the checkbox.

1. Open the *Properties* dialog. The list of Boolean values only contains one object called j, which is represented graphically as your checkbox.

2. Select *text5* from the list of objects in the *Properties* dialog.

3. Click on tab *Advanced* and look at the text field called *Condition to Show Object*. It shows the name of your checkbox j.

**Hint:**This means that the visibility of

*text5*depends on the status of the checkbox.

4. Select point R from the list of objects in the Properties dialog. Click on tab *Advanced*. The text field Condition to Show Object is empty.

5. Enter j into the text field *Condition to Show Object*. The visibility of point R is now connected to the checkbox as well.

6. Repeat steps 4 and 5 for segment i which connects the second vector with point R on the number line.

**Hint:**Now the checkbox controls three objects of your dynamic figure:

*text5*(which shows the result of the addition), point R and segment i (which show the result on the number line).

## The Sierpinski Triangle

You will now learn how to create a custom tool that facilitates the construction of a so called Sierpinski triangle.

### Preparations

- Open a new GeoGebra window.
- Switch to Perspectives – Geometry.
- In the
*Options menu*set the Labeling to*New Points Only*.

### Construction Steps

### Conditional Visibility

Insert checkboxes that allow you to show and hide the different stages of the Sierpinski triangle.

## Introducing Sequences

GeoGebra offers the command Sequence which produces a list of objects. Thereby, the type of object, the length of the sequence (that’s the number of objects created) and the step width (e.g. distance between the objects) can be set using the following command syntax:
*Sequence[<expression>, <variable>, <from>, <to>, <step>]*

Explanations:

- <expression>: Determines the type of objects created. The expression needs to contain a variable (e.g. (i, 0) with variable i).
- <variable>: Tells GeoGebra the name of the variable used.
- <from>, <to>: Determine the interval for the variable used (e.g. from 1 to 10).
- <step>: Is optional and determines the step width for the variable used (e.g. 0.5).

### Examples for sequences

- Sequence[(n, 0), n, 0, 10]
- Creates a list of 11 points along the x-axis.
- Points have coordinates (0, 0), (1, 0), (2, 0), …, (10, 0).

- Sequence[Segment[(a, 0), (0, a)], a, 1, 10, 0.5]
- Creates a list of segments with distance 0.5.
- Each segment connects a point on the x-axis with a point on the yaxis (e.g. points (1, 0) and (0, 1); points (2, 0) and (0, 2).

- If s is a slider with interval from 1 to 10 and increment 1, then command Sequence[(i, i), i, 0, s]
- creates a list of s + 1 points whose length can be changed dynamically by dragging slider s.
- Points have coordinates (0, 0), (1, 1), …, (10, 10)

## Visualizing Multiplication of Natural Numbers

### Preparations

- Open a new GeoGebra window.
- Switch to Perspectives – Geometry.
- Show the Input Bar (View Menu).
- In the Options menu set the Labeling to
*All New Objects*.

### Construction Steps

## Challenge of the Day: String Art Based on Bézier Curves

Bézier curves are parametric curves used in computer graphics. For example, they are used in order to create smooth lines of vector fonts. Let’s create some ‘string art’ based on Bézier curves.

### Preparations

- Open a new GeoGebra window.
- Switch to Perspectives – Geometry.
- Show the Input Bar (View Menu).
- In the
*Options menu*set the Labeling to*All New Objects*.

### Construction Steps

**Note:**The segments you just created are tangents to a quadratic Bézier curve.

### Task

Create more *string art* with GeoGebra using sequences of points and segments.