Context

Theoretical Introduction

Mathematics is a discipline that teaches us to decipher the cosmos through the power of numbers and shapes. Among these shapes, regular polygons hold a special place. Regular polygons are closed flat figures, with all sides and angles equal. They are fundamental in various areas of mathematics, including geometry and trigonometry.

Regular polygons are extremely symmetrical. Think of a square or a regular hexagon - you can rotate these shapes at certain angles and they will still look the same. This reflects the regularity and symmetry of these figures. Furthermore, all points of the regular polygon are at the same distance from the center, something that does not occur with irregular polygons.

But what is the impact of regular polygons in our lives? In addition to their evident importance in mathematics and other areas of science such as physics, chemistry, and biology, regular polygons are fundamental in areas such as engineering and architecture. They also have profound implications in our understanding of the universe, from the distribution of planets to the structure of crystals.

Context

In practical applications, regular polygons can be found everywhere around us. In the world of architecture, the use of polygonal shapes is a common practice for creating resilient and visually appealing structures. Engineers use regular polygons in the planning and development of various structures, from the design of simple machines to the architecture of complex electronic circuits.

On a smaller scale, in nature, various polygonal shapes are visible, from the hexagons of beehives to the crystalline structure of minerals. These seemingly simple structures are extremely efficient and can serve as inspiration and a model for various solutions in our society.

Practical Activity

Activity Title

"The World Around Us Through Polygons"

Activity Objective

The objective of this activity is to create a model of a real-world structure, such as a building, a bridge, or even a simpler object, using regular polygons. This should be combined with a study on the number of diagonals and internal and external angles of these polygons.

Detailed Activity Description

1. Group Formation: To start the project, students must divide into groups of 3 to 5 members. Each group will work together throughout the project.

2. Research and Decision: Groups should research different real-world structures and choose one to focus on for the project. Remember that the chosen structure must have at least one regular polygon in its design.

3. Structure Drawing: After choosing the structure to work on, students should draw it on paper or using digital drawing software. In this drawing, the regular polygons used should be clearly highlighted.

4. Polygon Study: With the drawings in hand, students must identify the regular polygons used, calculate the number of diagonals passing through the center of these polygons, and calculate the internal and external angles. This will allow students to better understand the structure and symmetry of the polygons.

5. Model Construction: Using craft materials such as toothpicks, cardboard, colored paper, etc., students will create a scale model of the chosen structure.

6. Project Report: Finally, each group should write a detailed report on the project, covering the research conducted, choice of structure, polygon study, model construction process, and the results obtained.

Required Materials

• Paper or digital drawing software
• Drawing instruments (pencils, ruler, protractor, etc.)
• Craft materials (toothpicks, cardboard, colored paper, etc.)

Detailed Steps

1. Divide students into groups of 3 to 5 people.
2. Each group chooses a real-world structure to study.
3. Draw the chosen structure, highlighting the regular polygons.
4. Identify the regular polygons in the drawing and calculate the number of diagonals and internal and external angles.
5. Using craft materials, build a physical model of the structure.
6. Finally, prepare a detailed report covering the entire process.

Project Deliverables

The project deliverables include:

• The drawing of the structure with highlighted regular polygons.
• Calculations of the number of diagonals and internal and external angles of the polygons.
• The scale model of the chosen structure.
• The final report, including:
  • Introduction: Summary of the chosen structure and its relevance.
  • Development: Detailed explanation of the process, including drawing, polygon identification, diagonal and angle calculations, model construction.
  • Conclusion: Reflections on the project, the learnings obtained, and the conclusions.
  • Bibliography: References used throughout the project.