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Activity 1

Autor:Cláudia Oliveira de Almeida Santos
Luiz Sacilotto was known for his versatile artistic production, which encompassed abstract paintings, geometric sculptures, and innovative collages. In addition to his completed works, the artist's studies and works in progress are also valued and often included in archives and private collections dedicated to him. These studies are fundamental pieces for understanding Sacilotto’s evolution and creative approach, offering valuable insights into his artistic process.

Figure 1 – Study by Luiz Sacilotto featuring the repetition of geometric shapes in gouache.

Figure 1 – Study by Luiz Sacilotto featuring the repetition of geometric shapes in gouache.
Source: Facebook - https://www.facebook.com/luiz.sacilotto

Question 1

In this study by Luiz Sacilotto, we can observe the repetition of certain geometric shapes as well as the presence of geometric transformations. Which geometric shapes do you identify in this study?

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Question 2

Which geometric transformations do you identify in this study?

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In GeoGebra, using the Rotate and Translate commands, it was possible to create a reinterpretation of this study by Sacilotto. Interact with the activity below to understand when these commands were used. Follow the steps provided:
  1. First, create sectors 2, 3, and 4 based on the sector already placed on the screen.
  2. Then, by applying translations, complete the reinterpretation of the artwork.

Using GeoGebraScript in the Reinterpretation of Sacilotto's Study

To create this activity, the Rotate and Translate commands were used in combination with the Button tool. This demonstrates one way to utilize the GeoGebraScript language. The necessary commands for performing translations and rotations were inserted in the Scripting tab of each button.

Steps to Create the Activity

  1. Initially, a circular sector was created with center at point C and endpoints at points D and E, using the command: Sector(Center, Point, Point).
  2. Once the first circular sector was created and named c, the remaining sectors were obtained through translation and rotation. To achieve this, directional vectors were created to indicate the required translations: u and v, where u represents the horizontal direction, v represents the vertical direction, both vectors have a magnitude equal to the diameter of the circular sector.
  3. For the Setor 2 button to translate the first sector after a 90° rotation about its center, the following command was inserted in the Scripting tab of the button: d=Translate(Rotate(c,-90°,C),3v).
  4. For the Setor 3 button, the following command was inserted: e=Translate(Rotate(c,-180°, C),3v + 3u).
  5. For the Setor 4 button, the following command was inserted: f=Translate(Rotate(c,-270°,C),3u).

Question 3

Explain what the command d=Translate(Rotate(c,-90°,C),3v) does.

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Question 4

Explain what the command e=Translate(Rotate(c,-180°,C),3v+3u) does.

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Question 5

Explain what the command f=Translate(Rotate(c,-270°,C),3u) does.

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Step 2 – Translations of Circular Sectors.

  1. After creating the four circular sectors, translations were applied to these sectors to complete the reinterpretation. To achieve this, four additional buttons were created.
  2. In the Translation Sector 1 button, in the Scripting tab, the following commands were inserted:
  • c_1=Translate(c,u)
  • c_2=Translate(c,2u)
  • c_3=Translate(c,v)
  • c_4=Translate(c,2v)
  • c_5=Translate(c,u + v)
  • c_6=Translate(c,2u + 2v)
  • c_7=Translate(c,u + 2v)
  • c_8=Translate(c,2u + v)

    • Question 6

    Explain each command inserted in the Translation Sector 1 button.

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    Question 7

    What should the commands be for the Translation Sector 2 button?

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    Question 8

    What should the commands be for the Translation Sector 3 button?

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    Question 9

    What should the commands be for the Translation Sector 4 button?

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    Question 10

    Justify why an error occurs in the execution of the programming when clicking any of the translation buttons before clicking the buttons to create sectors 2, 3, or 4.

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    Following the same reasoning for construction presented here, create an activity to reinterpret Sacilotto's study using GeoGebra Online by accessing the link https://www.geogebra.org/classic

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