Contextualization

Introduction

Pythagoras of Samos was a Greek philosopher and mathematician who lived in the 6th century BC. He is best known in mathematics for his theorem that bears his name, the Pythagorean Theorem. The Pythagorean Theorem establishes that in a right triangle (one that has a 90-degree angle), the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In simpler terms, if you know the lengths of two sides of a right triangle, you can calculate the length of the third side using this theorem.

This theorem is one of the fundamental tools of geometry and is used in many areas of mathematics and physics. For example, it is used in trigonometry, analytic geometry, and physics to calculate distances. Furthermore, it is essential for understanding the concept of Euclidean distance, which is a fundamental concept in mathematics and computer science.

Contextualization

The Pythagorean Theorem has several practical applications in everyday life and in various professions. Architects and engineers use it to calculate distances and to design buildings and structures. Additionally, it is used in navigation, astronomy, geography, among others.

For example, if you want to know the direct distance between two points on a map or a graph, the Pythagorean Theorem can be applied. Similarly, if you need to calculate the width of a river without crossing it, or the height of a building or a tree without climbing it, you can apply the Pythagorean Theorem. Therefore, understanding this theorem can provide students with a new perspective on the world around them and strengthen their analytical and problem-solving skills.

Practical Activity

Activity Title: "Pythagoras in the Real World: Investigating and Applying the Pythagorean Theorem in Everyday Situations"

Project Objective

To learn about the Pythagorean Theorem in a deep and practical way, investigating how it is applied in real-world situations and solving a practical problem using the theorem.

Detailed Project Description

This project will be carried out by groups of 3 to 5 students and should last at least two weeks. The goal is for each group to research situations where the Pythagorean Theorem is used, in professions, everyday life, or in sciences like physics and astronomy. After identifying these situations, each group must select one situation to investigate further and solve a practical problem related to that situation using the Pythagorean Theorem.

Required Materials

• Computer with internet access for research
• Notebook for jotting down ideas and calculations
• Ruler, protractor, and compass for making drawings
• Geometric drawing or 3D modeling software (optional)

Detailed Step-by-Step Activity Execution

1. Research and Situation Selection: Each group should research on the internet and in books about real situations where the Pythagorean Theorem is used. The situations can be from various areas such as architecture, engineering, geography, astronomy, physics, among others. After the research, each group should choose a situation to investigate further.

2. Study of the Situation and Problem Identification: Students must study the chosen situation and identify a problem that can be solved using the Pythagorean Theorem. For example, if the chosen situation is the construction of a ramp, the problem could be to calculate the ideal slope of the ramp.

3. Problem Solving: Using the Pythagorean Theorem, students must solve the identified problem. They should document all the steps of the solution, including calculations and drawings. Important: Students should do the calculations manually, not using calculators or math software.

4. Project Presentation: Each group should prepare a presentation for the class explaining the chosen situation, the identified problem, and the problem solution. The presentation should include a clear explanation of how the Pythagorean Theorem was used to solve the problem.

5. Final Report: At the end of the project, each group must write a detailed report, containing:

• Introduction: This should include a brief explanation of the Pythagorean Theorem, the chosen situation, and the relevance of this theorem to solving the problem.
• Development: Detailed description of all project stages. How the research was done, how the situation was chosen and the problem defined, how the problem was solved, and the methodology used to solve the problem.
• Conclusions: What was learned from the project, how the Pythagorean Theorem was applied, and how it could be used in other similar situations.
• Bibliography: All research sources must be cited in the report.

Students should strive to connect all the project learning with the theoretical part studied, and describe it succinctly in the report. Additionally, they should comment on the collaboration among group members, the challenges encountered, and how they overcame these challenges.