Contextualization

Mathematics is a science that is present in our daily lives. Several topics studied in the classroom have real practical applications that are not always evident. One of these topics is the study of regular polygons in geometry. But what are regular polygons?

Regular polygons are closed flat geometric figures that have all their sides and internal angles equal. The most well-known examples are the equilateral triangle, the square, and the regular hexagon. Understanding their composition and construction is fundamental for the study of geometry and its application in various areas of study.

The construction of regular polygons with a ruler and compass, basic tools of geometry, is ancient knowledge. Since Ancient Greece, mathematicians sought ways to construct regular polygons with these tools. This knowledge was fundamental for the development of various areas, such as architecture, engineering, and art.

But why is the study of regular polygons so important?

Regular polygons are present in various aspects of our lives. In nature, for example, it is possible to observe their presence in elements such as crystals and snowflakes. In architecture and design, regular polygons are used for the construction of structures and objects due to their stability and symmetry. Moreover, they are fundamental in the study of geometry and help in understanding more advanced concepts.

To delve even deeper into the study of regular polygons, we recommend the following sources:

1. "Mathematics and its Technologies" - High School textbook
2. YourTutor - Regular Polygons
3. World Education - Regular Polygons
4. YouTube Channel - Matemática Rio

Practical Activity - Building Regular Polygons

Title: Construction and Analysis of Regular Polygons

Project Objective

The objective of this project is for students to be able to construct, analyze, and understand the concept of regular polygons, as well as their properties, through a practical, playful, and collaborative activity. By the end of the project, it is expected that students will be able to apply the concept of regular polygons in real situations and also develop skills in teamwork, time management, effective communication, problem-solving, creative thinking, and proactivity.

Detailed Project Description

Students will be divided into groups of 3 to 5 members. Each group will be tasked with building three different types of regular polygons (for example: an equilateral triangle, a regular hexagon, and a regular decagon), using both a ruler and compass, as well as graphic design software.

The step-by-step instructions on how to make the construction will be described in an algorithm, which must be presented in both written form and in a flowchart. The group must also research where regular polygons appear in our world and how they are applied in practical situations.

After the construction, the groups must collect the measurements of the sides and internal angles of the constructed polygons and verify if they are correct (all sides and internal angles must be equal). They must then discuss the importance and application of regular polygons in the real world.

Required Materials

1. Ruler
2. Compass
3. Paper
4. Pencil
5. Access to graphic design software (e.g. Google SketchUp, AutoCAD, CorelDRAW).

Detailed Step-by-Step for Activity Execution

1. Divide the class into groups of 3 to 5 students.
2. Each group must choose three different types of regular polygons to build.
3. The group must research and study the chosen polygons, including their properties and how they are used in practice.
4. The students must then build the chosen polygons using a ruler and compass on a sheet of paper.
5. After manual construction, the students must recreate the same polygons using graphic design software.
6. Upon completing manual and digital construction, the group must measure and collect the lengths of the sides and the internal angles of the constructed polygons, and verify if they are all equal.
7. Based on the construction and the collected data, the students must prepare a detailed report, described in the next topic.

Project Delivery

Each group will deliver a dossier containing:

• The regular polygons constructed manually and digitally.
• A written algorithm and a flowchart of how the polygons were constructed.
• The measurements of the sides and angles of the constructed polygons, accompanied by verification that they are all equal.
• A report with four main sections: Introduction, Development, Conclusions, and Bibliography.

The report must follow the following pattern:

1. Introduction: The group must contextualize regular polygons, their relevance and practical application in the real world, and the objective of this project.

2. Development: The group must explain the theory behind the construction of the polygons, describe in detail the activity carried out, indicate the methodology used, and present and discuss the results obtained.

3. Conclusion: The group must summarize the main points of the project, explain what they learned about regular polygons and their applications, and conclude on what was taken from the project.

4. Bibliography: The group must indicate the sources used to work on the project, such as books, web pages, videos, etc.

This project will last for one month, and each student must spend five to ten hours in total to complete it.