Contextualization
Geometry is a branch of mathematics that studies the properties and characteristics of physical objects in space. Within this universe, there are fascinating concepts, among them, geometric transformations. Geometric transformations are movements or changes made to a figure on the plane without altering its basic properties and characteristics. Among the most important geometric transformations are translation, reflection, and rotation.
Reflection is the transformation we will discuss in this project. It is considered an isometric transformation, which means it preserves distances and angles. In reflection, a figure is mirrored in relation to an axis or a point, producing an image that is the exact reflection of the original. The line or point of reflection acts as a mirror, duplicating the figure.
To better understand these concepts, think of the symmetries we find around us: the reflection of a mountain in a lake, the face of a tiger, the structure of a snowflake. Or, if we want to be more abstract, fractal structures or shapes found in art, such as Escher's mosaics and Salvador Dalí's paintings. The notion of reflection is, therefore, something with very real application and provides us with a new perspective on how we see the world.
All these manifestations of the concept of reflection that I mentioned are within our reach, and we often don't even notice them. With a little knowledge and creativity, however, we can look at our environment and see a world full of mathematics and symmetry.
The following resources may be useful for studying the concepts involved in this project:
- Geometric Transformations - OBMEP Mathematics Portal
- Transformations on the Plane - Brasil Escola
- Reflection - Basic Mathematics
