Contextualization

Theoretical Introduction

Regular polygons are present in our daily lives in various ways, although we often overlook them. Whether in the form of everyday objects or complex structures, regular polygons are key elements of geometry, and understanding their properties opens up a new world of possibilities for understanding the world around us.

A regular polygon is a flat geometric figure that has all its sides and angles equal. These two properties - all equal sides and all equal angles - form the essence of what we call regular polygons. The most common examples we can find are the equilateral triangle, the square, and the regular hexagon.

But beyond theory, how can we calculate some important properties of regular polygons? For example, we can calculate the number of diagonals that pass through the center of a regular polygon, or calculate its internal and external angles. In our project, we will explore these and other properties in order to deepen our understanding of regular polygons.

Connection to the Real World

Regular polygons are found in various fields and practical situations. In Architecture, regular shapes provide a pleasant and coherent aesthetic, as well as enabling better organization of spaces. In Engineering, especially in Civil and Mechanical Engineering, regular polygons are used in the design of structures and parts. Even in nature, we find examples of regular shapes, such as in the cells of a honeycomb, formed by perfect hexagons.

Therefore, understanding the mathematics behind these shapes is not only an academic exercise but also a way to better understand the real world around us. This work will provide the necessary knowledge on the subject and its practical applicability.

Practical Activity

Activity Title: Exploring and Understanding Regular Polygons

Project Objective

This project aims to lead students to a better understanding of the characteristics and properties of regular polygons through practical activities, collaborative study, and problem-solving.

Students will learn to calculate the number of diagonals passing through the center, as well as calculate the internal and external angles of regular polygons. The proposal is that, through teamwork, students can synthesize the information and present it in a well-structured report.

Detailed Project Description

Students will create physical models of regular polygons using simple materials such as barbecue sticks and modeling clay, in groups of 3 to 5 members.

Required Materials

• Barbecue sticks
• Modeling clay
• Ruler
• Calculator
• Graph paper
• Colorful pens
• Pencils and erasers
• Scissors

Project Steps

1. Theoretical Study: Each group should start by conducting a theoretical study on Regular Polygons using the suggested resources and through additional research.

2. Ideas Brainstorming: Students, in groups, should discuss and sketch the model they will build. Each group member should draw a different regular polygon, from three to seven sides.

3. Building the Models: Students will use barbecue sticks and modeling clay to build the models.

4. Exploring the Models: Using the constructed models, students must calculate the number of diagonals passing through the center and the internal and external angles of each regular polygon. They should record their calculations for future use.

5. Problem Solving: Each group will create a problem related to the polygon they built and solve it.

6. Report: Finally, students must write a report with the results of the activities carried out.

The project should last one week, with an estimated working time of 2 to 4 hours per student.

Project Deliverables

The group must submit a written report following the same proposed structure:

1. Introduction: The group must contextualize the theme, explain the relevance of regular polygons and their application in the real world. The objective of this project should also be explicitly stated in this section.

2. Development: In this section, the group must explain in detail the theory behind regular polygons, the activities that were carried out, the methodology used, and present the results obtained. The conclusions drawn from the process should also be included here.

3. Conclusion: The group must summarize the main points of the introduction and development, analyze the results obtained, offer interpretations, and provide final conclusions on the project.

4. Bibliography: The group must present the references used during the project.