Contextualization
Introduction
Polygons are closed geometric figures formed by line segments, which we call sides, that have all ends connected to each other. When we talk about polygon angles, we are referring to structures that are widely used in our daily lives. From architecture to space engineering, polygons and their interior and exterior angles are fundamental concepts for the understanding and development of many disciplines.
The interior angles of a polygon are the angles formed by consecutive sides. The exterior angles are complementary to the interior angles, that is, the angles that, added to the interior angles, correspond to 180º. In regular polygons, which are those that have all sides and angles equal, the calculation of interior and exterior angles becomes more simplified due to their symmetry.
The study of these angles is essential for the understanding of many phenomena and their application in different areas of knowledge. Through it, it is possible, for example, to calculate routes and trace digital maps, design building structures and even develop electronic games.
Contextualization
Imagine that you are involved in creating a new video game. During the design process, you need to create regular polygons to represent the characters. A solid understanding of the interior and exterior angles of the polygons can help you create more realistic graphics and more balanced characters.
Now, imagine that you are in charge of designing the new school building. You would need a deep understanding of the interior and exterior angles to ensure that the foundations are strong, that the building's structure is safe, and that all spaces are well used.
Thus, it becomes clear how the theory of polygon angles applies to real world situations. Mathematics, specifically geometry, is all around us, even if we often don't notice it.
Recommended Reading
To delve into the topic and acquire a more comprehensive understanding, we recommend some readings and videos:
- Book: "Mathematics and its technologies", by Editora Moderna.
- Khan Academy website, which has a section dedicated to plane geometry and polygons. Link
- Só Matemática website, which offers a direct and practical explanation about angles. Link
Practical Activity
Activity Title: "Polygon Architects: Building with Angles"
Project Objective
The objective of this project is to apply the knowledge acquired about internal and external angles of regular polygons in the construction of a city model using cardboard, ruler, protractor, scissors and glue. In addition, students will also have to prepare a report detailing the construction process, the theory of polygon angles and the application of this theory in the construction of the city.
Detailed Project Description
The work will be done in groups of 3 to 5 students, and each group will be responsible for creating a city model using regular polygon shapes. Students must apply their knowledge of interior and exterior angles of regular polygons to design and build the city's buildings, thus setting up a practical activity of applying polygons in civil construction. In addition, they must prepare a report detailing the planning and construction process of the city, as well as the theory of polygon angles.
Materials Needed
- Cardboard of various colors
- Ruler
- Pencil
- Protractor
- Scissors
- Glue
- Markers of various colors
- A4 paper for the report
Detailed Step-by-Step Project
- Planning: Each group should plan their city, thinking about which buildings it will have and how these buildings will be represented by regular polygons.
- Drawing the Polygons: Using the ruler and protractor, students should draw the polygons on the cardboard that will represent the buildings in the city. Remember that they must be regular polygons, that is, with all sides and angles equal.
- Cutting and Assembly: Using scissors, students should cut out the polygons and start assembling the city, gluing the buildings in the desired place.
- Decoration: With markers, students can customize the buildings, adding windows, doors and other details.
- Report: Each group must prepare a report detailing the process of building the city, the theory of polygon angles and how this theory was applied in the construction. The report should be divided into four sections: Introduction, Development, Conclusions and Bibliography.
In the report, students must:
- In the introduction, contextualize the theme, its relevance and application in the real world as well as the objective of this project.
- In the development, explain the theory behind the angles of polygons, explain the activity in detail, indicate the methodology used and finally present and discuss the results obtained.
- In the conclusion, resume the main points of the work, explain the lessons learned and the conclusions drawn about the project.
- In the bibliography, indicate the sources on which they relied to work on the project, such as books, web pages, videos, etc.
Project Duration: 2 to 4 hours per student. Delivery Time: One week.
