Contextualization

Theoretical Introduction

Polygons are flat geometric figures, bounded by line segments that together form a closed contour. These line segments are called the sides of the polygon. Among polygons, there are several categories including triangles, squares, pentagons, hexagons, and so on, all classified by their number of sides. Furthermore, polygons can be differentiated by their regularity, that is, whether all their sides and angles are equal, being classified as regular, or not, being classified as irregular.

Polygons can also be classified as convex or concave. A polygon is said to be convex if, when we join any two internal points of the polygon, the line segment formed by these points is entirely inside the polygon. Otherwise, the polygon is said to be concave.

The classification and study of polygons are fundamental for the understanding of various concepts in geometry and are frequently applied in many other areas of Mathematics, including Analytical Geometry and Trigonometry.

The Importance of Polygons

The importance of polygons goes beyond the boundaries of the academic world and the discipline of Mathematics, finding practical applications in various areas of our daily lives. In Engineering and Architecture, for example, the design of plans and structural projects often involves the use of regular and irregular polygons.

Furthermore, in the field of Computer Science, polygons play a fundamental role in three-dimensional modeling, graphic rendering, and simulation systems. In Nature, we can find several examples of polygons, from the hexagonal structure of beehives to the shapes of starfish.

Finally, understanding polygons is essential for the development of logical reasoning and spatial vision, skills widely required in today's job market.

Practical Activity: Polygons in the Real World

Project Objective

The objective of the project is to explore the application and classification of polygons in the real world, allowing students to understand the importance of studying polygons and how they are applied in various areas of life and different disciplines.

Project Description

In this project, students will build a model of a real-world object composed of polygons. They should select an object, identify the polygons present in it, classify them, and explain their characteristics. In addition, students should research the application of polygons in the structure or functioning of the chosen object.

The project should start with the research and identification of a real-world object that can be represented by polygons. Once the object has been selected, students should gather information about the object, including the shapes and sizes of the polygons that compose it. With this information in hand, students should classify the polygons, indicating the type of polygon (triangle, square, pentagon, etc.), whether they are regular or irregular, and whether they are convex or concave.

Having classified the polygons, students will move on to the model construction phase. In this phase, they can use various materials such as paper, cardboard, styrofoam, etc. They should recreate the chosen object, making accurate representations of the polygons that compose it.

Once the model is built, students should prepare a presentation explaining the characteristics of the polygons used, their classification, and how this applies to the object. They should also discuss the importance of polygons in the chosen object and in their real-world applications.

Required Materials

• Paper, cardboard, or styrofoam;
• Pencils, pens, and rulers;
• Glue;
• Scissors;
• Computer with internet access for research.

Project Step-by-Step

1. Formation of groups of 3 to 5 students.
2. Research and selection of a real-world object that can be represented by polygons.
3. Research and collection of information about the characteristics and types of polygons present in the chosen object.
4. Classification of the identified polygons in the object.
5. Construction of a model of the chosen object, accurately representing the polygons that compose it.
6. Preparation of a presentation explaining the project, the classification of polygons, their characteristics, and practical applications in the object chosen.

Project Deliverables and Document Writing

• Physical Model of the Object: Students must deliver the model of the chosen object, which will be evaluated for the accuracy of the representation of polygons and the overall quality of construction.
• Oral Presentation: Students must present their project to the class. During the presentation, they should explain the chosen object, the polygons that compose it, the classification of polygons, their characteristics, and the practical application of these polygons in the object.
• Written Report: After completing the project, students must produce a written report containing all the main topics: Introduction, Development, Conclusions, and Bibliography used. This should reflect in writing all the work and research carried out during the project, as well as document the results and learnings obtained.