Contextualization

What are Polygons?

Our world is full of shapes - some complex, some simple. In mathematics, we learn to describe these shapes systematically and understand their properties. A class of shapes that we frequently encounter are polygons.

A polygon is a closed flat geometric figure bounded by straight segments, called sides. The term comes from Greek, where 'poly' means many and 'gonia' means angle. Therefore, polygons are 'many angles'. Polygons have a variety of properties that make them useful in many areas of mathematics and everyday life.

Classification of Polygons

Polygons are classified according to the number of their sides or vertices. Additionally, they can be grouped based on other properties such as the length of their sides (equilateral polygons have sides of equal length) and the measure of their internal angles (equiangular polygons have equal angles). When a polygon is both equilateral and equiangular, it is called a regular polygon.

The Importance of Polygons in Our Everyday Life

Polygons are all around us. You can find them in art, architecture, engineering, and nature. They are the basis of many shapes in our three-dimensional world. They are used to create computational models, to understand the structure of crystals and molecules, and much more.

Architecture, for example, uses polygons to create floor plans of buildings and house designs. Furthermore, the use of polygons in graphic design and 3D modeling is almost ubiquitous. In nature, polygons can be found in shapes such as the hexagonal structure of a honeycomb or the pentagonal shape of certain flowers and starfish.

To delve deeper into the topic, the following sources are recommended:

1. Book: Elements of Geometry, by Euclid. It is one of the oldest and most comprehensive books on the subject.
2. Website: Brazil School - Mathematics - Polygons. This is a good online resource to understand the basic concepts.
3. Video: Mathematics Rio - Polygons. This YouTube channel is known for its clear and visual explanations of mathematics.

Practical Activity

Activity Title: 'Polygons Around the World'

Project Objective

The objective of this activity is to allow students to expand their understanding of polygons through the study of their real-world applications, while developing teamwork, communication, time management, creative thinking, and problem-solving skills.

Detailed Project Description

Students will identify and classify polygons in their communities, photograph these polygons, and document their findings in a detailed and creative way. Additionally, students need to research practical applications of these polygons in a specific field of interest (e.g., architecture, engineering, art, nature, etc.) and present this research to the group.

Required Materials

1. Camera or smartphone with a camera
2. Notebook for documentation and research
3. Text editing software (e.g., Microsoft Word, Google Docs, etc.)
4. Internet access for research

Detailed Step-by-Step

Each group should follow the following steps:

1. Identification and Classification: Go out to your community (it can be a neighborhood, a park, a shopping center, etc.) and identify up to 10 polygons. Take clear photos of these polygons. Then, classify each polygon according to the number of sides and whether they are equilateral, equiangular, regular, or irregular.

2. Documentation: Create a document where you will include the photos, the classification of each polygon, and a brief description of where the polygon was found and why you chose that shape.

3. Research: Choose a field of application for polygons and research more deeply on how polygons are used in that field. Document your findings in the same document created in the previous step.

4. Final Report: Finally, the report should be written, where the Introduction should present the topic of polygons, their relevance, real-world application, and the project's objective. In the Development, explain the theory behind the topic, describe the activity in detail, include the methodology used, and present and discuss the results obtained. In the Conclusion, summarize the main points, explain what was learned, and draw conclusions from the project. And finally, in the Bibliography, include the sources used during the research.

5. Presentation: Prepare a presentation of your work for the class. The presentation should be clear, informative, and engaging.

The activity is expected to last for one month, with groups of 3 to 5 students. Each student should dedicate between five to ten hours to the project.

Project Delivery

The project delivery will consist of two main parts:

1. Written Report: This is a detailed document, contextualizing the topic, the project's objectives, the methodology used, the results obtained, and the project's conclusions. This document should include images of the identified polygons and a detailed description of each of them. The chosen field of application and the research conducted should also be detailed in the report.

2. Oral Presentation: This is a classroom presentation where the group exposes their findings and shares what they have learned throughout the project.

The evaluation will take into account both the written report and the oral presentation, as well as teamwork, the quality and diversity of the identified polygons, the quality of the research conducted, the clarity and organization of the documentation and presentations, and finally, the reflection and understanding demonstrated of the concepts related to polygons.