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.

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

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

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

[list=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.[/*][*]In the [i]Translation Sector 1[/i] button, in the [i]Scripting[/i] tab, the following commands were inserted:[/*][/list][*][code]c_1=Translate(c,u)[br][/code][/*][*][code]c_2=Translate(c,2u)[/code][/*][*][code]c_3=Translate(c,v)[/code][/*][*][code]c_4=Translate(c,2v)[/code][/*][*][code]c_5=Translate(c,u + v)[/code][/*][*][code]c_6=Translate(c,2u + 2v)[/code][/*][*][code]c_7=Translate(c,u + 2v)[/code][/*][*][code]c_8=Translate(c,2u + v)[/code][/*]

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