Contextualization

Theoretical Introduction

Pythagoras' theorem is one of the main concepts found in mathematics. It is named after Pythagoras, a Greek philosopher and mathematician who lived between 570 and 495 BC. According to this theorem, in every right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² = b² + c².

This may seem like a simple concept, but it is fundamental for many calculations in geometry, physics, and even engineering. Pythagoras' theorem also connects to many other mathematical concepts, such as trigonometric functions, areas of geometric figures, and distance measurements.

Moreover, Pythagoras' theorem is an excellent example of how a simple mathematical concept can have profound and far-reaching implications. For example, the theorem is used in diverse areas such as construction, quantum physics, string theory, and even art!

Contextualization of the Theme and Its Importance

Pythagoras and his theorem are essential for extremely relevant areas of our daily lives. Through it, for example, we can determine distances. Imagine you want to find the shortest route between two points on a map, or the distance between two objects in space. Pythagoras' theorem can assist us in that!

Similarly, in construction, many problems involving distance and measurement calculations are solved with the help of Pythagoras' theorem. Not to mention its application in physics, where it is used to calculate the distance between two points in a coordinate system, or in engineering for calculating stresses in materials, among many other examples.

To delve deeper into the subject, we suggest consulting the following resources:

• Book: 'The Life and Work of Pythagoras', by Laura Fermi. This book, available in various libraries, presents the life of Pythagoras and his main contributions to mathematics.
• Website: Just Mathematics (link). This site offers a great summary of Pythagoras' theorem, with practical examples and solved exercises.
• Video: YouTube Channel Matemática Rio (link). This YouTube channel offers excellent videos on various mathematical topics, including Pythagoras' theorem.

Practical Activity: 'Pythagoras in the Real World'

Project Objective

The objective of this project is to apply Pythagoras' theorem to a real-life situation to help students understand how this theorem can be useful for solving everyday problems.

Detailed Project Description

We will divide the class into groups of 3 to 5 students. Each group will choose a profession (for example, architect, engineer, geographer, etc.) and develop a project where the application of Pythagoras' theorem will be necessary to solve a specific problem or challenge in that profession.

Necessary Materials

1. Paper and pencil for drawing and calculations;
2. Ruler, tape measure, or measuring tape;
3. Internet access for research;
4. Computer with text editing software for the preparation of the final report.

Detailed Step-by-Step

1. Choosing the Profession: Each group must choose a profession in which Pythagoras' Theorem can be applied.

2. Problem Identification: The groups must identify a specific problem or challenge, within the chosen profession, that requires Pythagoras' Theorem for its solution.

3. Research: The groups must research how Pythagoras' Theorem is used in the chosen profession and how it can be applied to solve the identified problem.

4. Problem Solving: After the research, the groups must make the necessary calculations to solve the problem using Pythagoras' Theorem.

5. Report Preparation: Based on the research and calculations performed, the students must produce a report detailing the entire process.

This report should include:

1. Introduction: an explanation of what Pythagoras' Theorem is, a description of the chosen profession, and a statement of the problem to be solved.

2. Development: a detailed description of the research conducted by the students, explaining how Pythagoras' Theorem is used in the chosen profession and how it was applied to solve the problem. The calculations performed should also be included in this section.

3. Conclusions: in this section, the students should summarize the main points described in the introduction and development, emphasizing what they learned from the project, as well as the conclusions they were able to draw from the experience.

4. Bibliography: the students should indicate the sources they used for the research and the project solution.

It is expected that each student dedicates between five and ten hours to the execution of this project, including research, calculations, and report preparation. The project deadline is one month.

Finally, this project should serve as a way not only to deepen students' knowledge of Pythagoras' Theorem but also to develop their socio-emotional skills, such as teamwork, problem-solving, communication, and time management.