Contextualization

Since ancient times, regular polygons have been the subject of study and admiration. They possess a perfect symmetry that makes them a fascinating example of what mathematics can describe. But what is a regular polygon? It is a polygon with all sides and angles equal. The hexagon, for example, is a regular polygon with six equal sides.

Geometric drawing, a discipline that studies the construction of geometric figures using tools such as ruler and compass, is one of the contexts where regular polygons take on a prominent role. In this project, we will become familiar with the construction of regular polygons using different techniques and tools.

Importance of Regular Polygons

Regular polygons play a fundamental role in many areas, including graphic design, architecture, engineering, and even in nature. To illustrate this, think about the honeycomb of bees: perfect hexagons that make up an incredibly efficient structure. In civil engineering, regular polygons are often used in the construction of structures such as bridges and buildings, due to their strong structure and symmetry.

In this context, learning to construct regular polygons is not just an academic activity, but a practical skill that can be applied in various real-world situations.

Practical Activity: Regular Polygons Construction

Project Objective

Learn to construct regular polygons, using theory combined with practice. Explore mathematics and geometry in a playful way, applying concepts learned in the classroom and collaborating in small groups of 3 to 5 students.

Detailed Project Description

In this project, groups will be challenged to construct regular polygons using different methods and tools. Each group will choose two different types of regular polygons (for example, a pentagon and a decagon) and must build them through two approaches:

1. Manual: Ruler and compass will be used to draw the polygons on a sheet of paper.
2. Digital: Using the GeoGebra software, students must replicate the polygons they built manually.

The activity also requires the development of a flowchart that explains the step-by-step algorithm used in the construction of the chosen regular polygons.

Required Materials

1. A4 size white paper;
2. Ruler and compass;
3. Pencil and eraser;
4. Access to GeoGebra software;
5. Computer with internet access for research and report writing.

Detailed Step-by-Step for Activity Execution

1. Divide students into groups of 3 to 5 members.
2. Each group must choose two different types of regular polygons to construct.
3. With the help of a ruler and compass, students must draw the chosen polygons on the paper.
4. Next, the groups must replicate the drawings of the polygons using the GeoGebra software.
5. Students must develop a flowchart, explaining the algorithm used in the construction of the regular polygons.
6. Finally, the groups will prepare a final report addressing the theory behind regular polygons, the process of constructing the polygons, the methodology used, and discuss the results obtained.

Project Deliverables

At the end of the project, each group must deliver:

1. The drawings of the polygons constructed manually and digitally.
2. The flowchart explaining the construction process.
3. A written report with the following structure:
   • Introduction: The group must contextualize the theme, its relevance, application, and the objective of this project.
   • Development: The group must explain the theory behind regular polygons, explain the activity in detail, indicate the methodology used, and present and discuss the results obtained.
   • Conclusion: The group must conclude the work by summarizing its main points, explaining the learnings obtained, and drawing conclusions about the project.
   • Bibliography: The group must indicate the sources they relied on to work on the project.

The report should be presented in digital document format, with a minimum of 15 pages. Remember that the goal is to apply the concepts of regular polygons, as well as to develop social and emotional skills, such as time management, communication, and creative thinking.