Contextualization

Mathematics is a discipline that transcends what we see in the classroom, and it is always a challenge to find ways to apply it to the world around us. The study of the angles of regular polygons presents itself exactly like that, an opportunity to appreciate mathematics in a creative and visual way.

Regular polygons can be found in many structures present in our daily lives, such as the architecture of buildings, furniture design, tile patterns, crystal shapes, and many more. Relating these mathematical concepts to tangible and visible things can help make learning more concrete and engaging.

Understanding the relationship between the internal and external angles of regular polygons is fundamental for many areas of mathematics and other related sciences. In geometry, this relationship is the basis for understanding the behavior of polygons, while in trigonometry we have the study of functions related to angles.

In engineering and architecture, understanding these principles is essential for the design and construction of various structures. To cite an example, Roman architects used the concept of regular polygons to create ornamental mosaics in their constructions, and even today, these concepts are used in graphic design and computer games.

To deepen your knowledge about the angles of regular polygons, we recommend using the book "Fundamentos de Matemática Elementar: Geometria Plana" by Gelson Iezzi and Carlos Murakami, and also utilizing the online resources available on Khan Academy and YouTube, where there are many tutorial videos covering this subject.

Practical Activity: "Mathematical Mosaics"

Project Objective

The main idea of this project is to integrate mathematical concepts, such as the angles of regular polygons, with an interesting and engaging artistic product: mosaics. Through this project, you will explore, understand, and apply the relationships between the internal and external angles of regular polygons in the elaboration of a mosaic.

Detailed Project Description

Each group of students will be tasked with creating a mosaic of regular polygons. To do this, students must first calculate the internal angles of each polygon they plan to use in their mosaic.

Additionally, students must also consider the external angle, which is necessary to ensure that the polygons fit perfectly, without leaving empty spaces. This project requires students to apply their mathematical knowledge in a way that is both playful and challenging.

Required Materials

• Cardboard paper in various colors
• Compass
• Ruler
• Pencil and eraser
• Scissors
• Glue
• Calculator

Step by Step

1. Students must decide which type of regular polygon they want to use in their mosaic. It can be a single type of polygon or a combination of several.

2. Once the type of polygon is decided, students must calculate the internal angle of each polygon using their acquired knowledge. Remember, the goal is for them to make this calculation without the aid of ready-made formulas. This step is essential to understand the relationship between the number of sides of a polygon and its internal angle.

3. After calculating the internal angles, students must calculate the external angles of the chosen polygons. This step is vital to ensure that the polygons fit properly in the mosaic.

4. After the calculations are done, students must draw and cut out the polygons on the cardboard paper. Ensure that all sides of the polygons are equal so that they fit perfectly.

5. Now comes the fun part: assembling the mosaic! Organize the polygons in a way that there are no spaces between them. Glue them on a piece of cardboard or other sturdy material.

Project Deliverables

After completing the assembly of the mosaic, each group must produce a report that addresses the following topics:

1. Introduction: Contextualize the theme of polygon angles, its relevance and application in the real world, and your initial expectations for the project.

2. Development: Describe the theory behind polygon angles, how to calculate the internal and external angles, the methodology used in assembling the mosaic, and the challenges encountered during execution.

3. Conclusions: Review the main points, summarize the lessons learned during the project execution, and discuss how the results correspond or differ from the initial expectations.

4. Bibliography: List all reference sources used during the project, including books, videos, websites, etc.

Remember, the goal of this activity is not only to demonstrate your understanding of polygon angles but also to practice important skills such as teamwork, problem-solving, and creative thinking. We believe this project will enrich everyone with a new perspective on the practical application of polygon angles in creating mosaics.