Contextualization

Geometric algorithms are an essential part of computer science that deals with algorithms designed to solve problems based on geometry. They are the building blocks for a variety of applications in different fields, such as robotics, pattern recognition, computer design, and, of course, video games! Furthermore, we need to understand the fundamentals of computing and computational thinking, such as basic algorithm concepts, to be good problem solvers in our everyday, academic, and future professional lives.

Although we are dealing with a concept typically from computing, we can develop this reasoning skill in a playful and dynamic way through practical activities that explore space and geometry. It is common to think that an 'algorithm' is a very advanced concept, but it is present in our daily lives when we follow a cake recipe, when we assemble a puzzle, when we follow a route on GPS, etc.

The importance of understanding geometric algorithms is directly reflected in the ability to solve problems. More and more, we are challenged by problems that require not only linear thinking but also the ability to deal with multiple dimensions, spaces, and shapes. From solving engineering problems to programming computer games, geometric algorithms are essential tools that provide a systematic methodology to face these challenges.

To deepen knowledge, students can refer to some reliable sources. For a more general understanding of what algorithms are, it is recommended to read the article 'What is an algorithm and why are they important' (available at: https://blog.betrybe.com/tecnologia/o-que-e-algoritmo/). Additionally, the chapter 'Geometric Algorithms' from the book 'Algorithms: Theory and Practice' by Thomas H. Cormen provides a detailed approach to the topic (book available in many libraries and bookstores).

Practical Activity

Title: Construction of a Geometric Maze

Project Objective

This project aims to apply geometric algorithms in a playful and practical way through the construction of a cardboard maze. As a way to stimulate teamwork, this project should be carried out by groups of 3 to 5 students, with a total duration of approximately two to four hours per student.

Project Description

Students will design and create a physical maze from cardboard, using geometry and algorithms to guide an object (a small ball, for example) from the beginning to the end of the maze. The maze should have at least one valid path, containing curves, straight lines, and 90-degree corners/geometries.

Required Materials

• Cardboard (can be reused from packaging boxes)
• Pencil and eraser
• Ruler
• Scissors
• Glue
• A small ball (e.g., a marble)

Step-by-Step for Activity Execution

1. Planning: As a group, plan the maze. Decide on the size, shape, and how the maze path will be. Draw the sketch of your maze on a piece of paper.
2. Path Algorithm: In the sketch of your maze, create a step algorithm that describes the path of the ball from the entrance to the exit of the maze.
3. Material Preparation: Measure and cut the cardboard according to your maze planning.
4. Assembly: Place the cardboard parts according to the created sketch and let it dry. Make sure the ball can travel the entire planned path.
5. Testing: Test the maze with the ball and check if it can reach the exit following the created algorithm. Make adjustments if necessary.

Project Delivery

After constructing the maze, each group must produce a report with the following topics:

1. Introduction: Description of the project, relevance of geometric algorithms in real life, and the project's objective.
2. Development: Explanation of geometric algorithms concept, detailed description of the activity performed, explanation of the methodology used, and presentation of results (with photos of the maze, if possible). Show the created algorithm in a step-by-step list format.
3. Conclusion: Recap of the main points of the work, explanation of the learnings obtained, conclusions about the project, and possible ways to improve or expand it.
4. Bibliography: Indication of the sources used for theoretical foundation and project execution.