Contextualization

Mathematics is present in all areas of our lives. And geometric algorithms are a powerful tool that allows us to solve everyday problems involving geometric shapes.

Let's think about a very practical situation: Have you ever played video games? In many games, characters need to move in a three-dimensional environment. For this, game programmers use geometric algorithms to calculate the path that each character should follow to avoid obstacles and reach the goal.

Project Introduction

Throughout this project, you will investigate, learn, and apply fundamental concepts of geometric algorithms, which are mathematical methods used to solve problems related to geometry.

There are several types of geometric algorithms, but the main focus of this project will be on building algorithms that allow us to create and move geometric shapes systematically, as if they were instructions in a recipe.

It is an interesting and very useful topic because with geometric algorithms we can, for example, create complex folding patterns, draw perfect geometric figures, or even program a robot to move in an environment.

Connection to the Real World

Geometric algorithms are extremely relevant in the real world and used in various areas, such as computer game programming, robotics, electronic circuit design, architecture, and many other applications.

For example, engineers who design autonomous robots, such as Roomba, small robots that clean the house, use geometric algorithms to program the robot's movement so that it can cover the entire area of a room, avoiding obstacles.

Practical Activity

Activity Title: Building and Navigating a Geometric Maze

Project Objective:

The objective of the project is to apply the concepts of geometric algorithms to build and navigate a maze. For this, students should create an algorithm, that is, a set of step-by-step instructions for building the maze and then another algorithm for solving it.

Detailed Project Description:

Students, in groups of 3 to 5, should first conduct a detailed research on geometric algorithms. Then, they should use their knowledge to create a two-dimensional (flat) maze and a set of rules to navigate through it.

The maze can be represented physically, for example, on a board or through drawings on a piece of paper, or digitally, for example, using drawing programs.

The idea is for students to create a step-by-step sequence of instructions (an algorithm) that anyone (or even a machine) can follow to build the maze and then create a resolution algorithm that allows a player to find the way out of the maze.

Required Materials:

• Paper and pen or drawing software (depending on the chosen format for the maze).
• Research material, such as books and access to online resources.

Detailed Step-by-Step for the Activity:

1. Research: Research geometric algorithms and how they can be applied to real-world problems. Understand the concept of an algorithm, its parts, and how it is used to solve problems.

2. Maze Planning: Plan the format of your maze. This maze should be two-dimensional and should have an entry point and an exit point. The maze can be as simple or complex as the group desires, but remember that you will also have to create an algorithm to solve the maze.

3. Maze Creation: Draw the maze as planned. If you choose to make the maze digitally, you can use simple drawing programs like Paint or more complex tools.

4. Construction Algorithm Creation: Write a set of step-by-step instructions for building the maze. Anyone who reads these instructions should be able to recreate the maze exactly as you designed it.

5. Resolution Algorithm Creation: Write a set of step-by-step instructions to solve the maze. Again, anyone who reads these instructions should be able to follow the maze path from the entrance to the exit.

6. Review and Test: Review your algorithms and test them. Ask another group to try to build and solve the maze based solely on your instructions.

7. Report: Write a detailed report on the project, including an introduction to the topic, the development of the project, conclusions, and bibliography. The development section should include a discussion on the theory of geometric algorithms, a detailed description of the activity, and the results obtained.

Project Deliverables:

• A written algorithm for building the maze.
• A written algorithm for solving the maze.
• The constructed maze (physically or digitally).
• A written report containing:
  1. Introduction: Contextualization of the topic, its relevance and application in the real world, as well as the objective of this project.
  2. Development: The theory behind geometric algorithms, detailed explanation of the activity, the methodology used, and the results obtained.
  3. Conclusion: Recap of the main points of the work, the learnings obtained, and the conclusions about the project.
  4. Bibliography: Sources used to work on the project such as books, web pages, videos, etc.