O GeoGebra
GeoGebra is a dynamic mathematics software that combines geometry, algebra, tables, graphs, calculus, and statistics in a simple and easy-to-use environment. It is widely used by students, teachers, and professionals to visualize mathematical concepts interactively and exploratorily. With GeoGebra, it is possible to create mathematical constructions, explore relationships, solve problems, and visualize results in a dynamic way.
Main components of the software:
Input Field:
- The input field is an area where the user can directly type commands and mathematical expressions. It allows the entry of formulas, functions, equations, and specific GeoGebraScript commands to create and manipulate mathematical objects. For example, by typing y = 2x + 3 and pressing Enter, GeoGebra will draw the corresponding line on the Cartesian plane, which is a geometric representation of the set .
Tools Menu:
- The tools menu contains a variety of icons that represent different operations and geometric constructions. The tools are organized into categories such as points, lines, polygons, transformations, and measurements. Each tool allows you to create and manipulate geometric objects, such as drawing segments, constructing triangles, measuring angles, and performing geometric transformations. For example, the "Point" tool
allows you to place points on the Cartesian plane, while the "Line" tool 
allows you to draw lines.
Cartesian Plane:
- The Cartesian plane is the main workspace in GeoGebra, where geometric objects and function graphs are visualized. It consists of a coordinate axis system (x and y) that facilitates the graphical representation of points, lines, curves, and other geometric figures. The objects placed or drawn on the Cartesian plane can be dynamically manipulated, allowing for visual and interactive exploration of mathematical properties.
In this chapter, we will explore the application of GeoGebra in the context of geometric transformations, aiming to familiarize the reader with the specific commands related to these transformations. In this context, we will use the Cartesian Plane representation, although GeoGebra also has other functionalities and the possibility of representation in three-dimensional space and polar coordinate systems.
We will cover isometric transformations (rotation, reflection, and translation) and homothety, which are frequently found in the works of the artist Luiz Sacilotto. This chapter will serve as a foundation for reinterpreting the works of this artist, providing an introduction to the practical use of these tools in GeoGebra software.
The reader can use the download buttons for the GeoGebra Calculator app (Apple Store and Google Play), available in the bottom right corner of the pages of this material. Alternatively, they can access GeoGebra online through this link .