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Activity 2 - Concreção 5732

Author:Cláudia Oliveira de Almeida Santos
[i]Concreção 5732, 1957[/i] Luiz Sacilotto Synthetic enamel on aluminum, c.i.e. 40.90 cm x 81.70 cm Collection of the Museum of Contemporary Art of the University of São Paulo Source: Enciclopédia Itaú Cultural.
Concreção 5732, 1957 Luiz Sacilotto Synthetic enamel on aluminum, c.i.e. 40.90 cm x 81.70 cm Collection of the Museum of Contemporary Art of the University of São Paulo Source: Enciclopédia Itaú Cultural.
Using the GeoGebra Translate command, reproduce part of the artwork Concreção 5732 following the steps below. The chosen part will be the one formed by black squares on a yellow background.
  1. Open the GeoGebra online app by clicking on the link https://www.geogebra.org/classic.
  2. Create a square ABCD (q1) with one unit of side length.
  3. Remove the labels of the points, segments, and polygon. Hide the vertices A, B, C, and D of the square.
  4. Start by creating a vector u indicating the horizontal direction and a vector v indicating the vertical direction (remove the labels), both with the same length as the side of the original square.
  5. Using the Translate command, create squares from the original square ABCD. For example, type q1_{2} = Translate(q1, 2u) in the input field of the Algebra menu. This command will represent the square A'B'C'D' obtained from the translation of square ABCD in the direction of u and displaced by 2 units from the original square.
  6. Continue creating the other 3 squares, following the naming convention, and complete the first row of the artwork Concreção 5732.
Alternatively, instead of creating the first row square by square, you can create a button named "First Row." After creating this button and accessing the Configuration option, choose "Scripting" and, in the "On Click" tab, type all the squares to be obtained by translating ABCD in the direction of vector u. q1_{2}=Translate(q1,2u) q1_{3}=Translate(q1,4u) q1_{4}=Translate(q1,6u) q1_{5}=Translate(q1,8u)

Question 1

What do you observe when clicking the "First Row" button in your activity?

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Question 2

To create the second row of squares, what could be a sequence of Translate commands to be programmed in a new button? Consider the translation of the squares in the first row in the direction of the vector v created initially.

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Question 3

To create the third row of squares, what could be a sequence of commands to be programmed?

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Create the last two rows of the first part of the artwork Concreção with what you have learned about the Translate command.

Question 4

The second part of the artwork, that is, the yellow squares on a black background, can be obtained using which isometric transformation?

Select all that apply
  • A
  • B
  • C
  • D
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Question 5

Justify the choice made in the previous question.

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In addition to the Translate command, by using the Reflection command, it was possible to create a reinterpretation of Concreção 5732. Interact with the proposed activity, using the indicated buttons, and complete the creation of this reinterpretation by following these steps:
  1. Create each row of black squares by clicking the First Row, Second Row, and so on.
  2. Create the symmetry axis of the artwork by clicking the Symmetry Axis button.
  3. Reflect the background square by clicking Reflection Background, and then change the color so that the background becomes black. To do this, click the Change Background Color button.
  4. Reflect each row created previously, always clicking Change Color immediately after reflecting each row.
    Return to the activity you were creating and, using the Reflection command, try to complete your reinterpretation of the artwork Concreção 5732, since the right side of the artwork corresponds to the reflection of the first part, with alternating colors. Suggested steps to follow:
    1. To reflect each square you created, it will be necessary to create a line (line) that represents the axis of symmetry of the artwork. For example, using the Reflect command, define q'1_{1} = Reflect(q1, line) in the programming tab of the Reflection q1 button. The object thus defined, q'1_{1}, represents the reflection of square q1, present in the first row of squares of the artwork. By clicking the Reflect q1 button, you will be able to see the reflection of square q1 with respect to the line, with the same color as the original. Using a naming convention that identifies each square is important for organization.
    2. To change the color of objects in GeoGebra, you can also use GeoGebraScript commands like SetColor or SetBackgroundColor. In this activity, the command was inserted into the programming tab of the Change Background Color button with the following command: SetColor(POL', Black). Here, POL represents the larger yellow square on the left side of the artwork, and POL' is the larger black square resulting from the reflection: POL'=Reflect(POL,line). Similarly, buttons were created to define the colors of other geometric objects present in the artwork.
    3. Try to organize your programming when reflecting objects. You can choose to reflect an entire row, such as in the following sequence of commands:
    q'1_{2}=Reflect(q1_{2},line) q'1_{3}=Reflect(q1_{3},line) q'1_{4}=Reflect(q1_{4},line) q'1_{5}=Reflect(q1_{5},line) q'1_{1}=Reflect(q1,line) This sequence of commands was inserted into the programming of the Reflection First Row button.

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