Context

Mathematics is a science that is present in our daily lives in many ways. In this project, we will focus on a fascinating concept in geometry, the exterior eccentric angles. Understanding this topic can provide a completely new and exciting view of how we see the world around us.

The exterior eccentric angle is that angle that has as its vertex a point in the exterior region of the circumference, and sides that are secant or tangent to the circumference. Although they may seem complex at first sight, the exterior eccentric angles are key concepts in trigonometry, a branch of mathematics that studies the relationships between the sides and angles of triangles.

It is imperative to understand the relevance of exterior eccentric angles. These concepts are not limited to the classroom. They have essential practical applications in various fields such as engineering, astronomy, and even art. For example, engineers use these concepts when drawing lines for buildings and bridges. Astronomers use them to calculate the position and trajectory of celestial bodies. Artists, in turn, use exterior eccentric angles to create perspectives and optical illusions in their works.

We recommend the following sources to deepen your understanding of the topic:

• Khan Academy: Section on angles (available in Portuguese)
• Book "Geometry and Trigonometry", by Elon Lages Lima
• Website "Mundo Educação: Section on angles".

We hope that through this project, you will not only learn but also have fun with mathematics. After all, math is not just a science, but a universal language that helps decipher the world around us.

Practical Activity: "The Eccentric Exterior Angles Trail"

Project Objective:

The objective of this project is to create a "board game" where victory will be achieved by solving problems involving exterior eccentric angles. In addition to applying the concept of exterior eccentric angles, students will have to use their teamwork, communication and problem solving skills to plan and execute the project, ensuring that the game is educational, fun and playable.

Detailed Project Description:

In groups of 3 to 5 students, you must develop a board game in which players advance by solving mathematical challenges involving the concept of exterior eccentric angles. Each group will be free to define the rules of the game, as long as they meet the established criteria.

Materials Required:

• Cardboard or paperboard for the game board base.
• Colored pencils, markers or paint for decoration.
• Paper for questions and answers to the challenges.
• Dice and pieces for the players (can be made of paper).
• Ruler and protractor for accurate measurements.

Detailed Step by Step:

1. Start by understanding the concept of exterior eccentric angles by studying the theory and solving some exercises.

2. Discuss in a group and determine the rules of the game. This should include the game board layout, the mathematical challenges, and how players advance on the board.

3. Draw the game board layout on the cardboard or paperboard, using colored pencils, markers or ink.

4. Write down the questions and answers to the challenges on separate pieces of paper. These will be the challenges that players will have to solve to advance in the game.

5. Make the dice and the players' pieces.

6. Play the game in a group to test if it is fun and educational. Make any necessary adjustments to the rules of the game, the game board layout or the challenges.

Project Delivery:

At the end of the project, all groups must deliver the finished board game, along with a written document containing:

• Introduction: Explain the concept of exterior eccentric angles, their relevance, real-world application and the objective of this project.

• Development: Describe the theory on eccentric exterior angles, the activity carried out (description of the game, rules, creation process), the methodology used and the results obtained (whether they learned the concept, whether the game worked as expected).

• Conclusion: Reflect on what was learned, the challenges encountered and overcome, and how teamwork contributed to understanding the concept and creating the project.

• Bibliography: List the sources you used to support the work done.

This project will require each team member two to four hours to complete and is due in one week. In addition to technical learning, it is also expected to develop socio-emotional skills such as teamwork, time management, creative thinking, among others.