Contextualization

Geometry plays a fundamental role in our daily lives, from simple moments like cutting a cake to more complex concepts in architecture, engineering, and art. Based on this principle, the study of geometric constructions serves as a foundation for understanding the world and for the development of logical and abstract reasoning.

Geometric construction is a practice that involves creating precise geometric figures without the aid of numerical measurements, but using geometric concepts. In ancient times, the Greeks were able to create astonishing architectural works using only an unmarked ruler and a compass.

In this project, we will work with some of these constructions: mediatrix, bisector, angles of 90°, 60°, 45°, and 30°, and regular polygons. Each of these constructions has particular characteristics and laws that will be explored during the process.

Our world is full of geometric shapes and patterns that help us understand and organize the space around us. The importance of geometry is evident in various areas of society, such as art, construction, navigation, design, and even city planning.

Understanding geometric constructions can be applied to solve everyday problems and becomes an essential tool for many professionals. Furthermore, there is a hidden beauty in geometry that is often revealed through mathematics and can be appreciated even more as we comprehend it.

In this link, a video has been provided with a teacher explaining and performing some of the constructions that will be studied: Geometric Constructions

Additionally, we also have a website with various explanations and exercises on the topic: Exercises on Geometric Constructions

Enjoy the exploration and happy studies!

Practical Activity

Activity Title: "Unveiling the Shapes: A Journey through Geometric Constructions"

Project Objective:

The objective of this project is for students to learn how to construct geometric figures using algorithms, flowcharts, or other methods, using concepts of mediatrix, bisector, angles of 90°, 60°, 45°, and 30°, and regular polygons. Additionally, the project aims to develop socio-emotional skills such as time management, teamwork, problem-solving, and creative thinking.

Detailed Project Description:

Students should work in groups of 3 to 5 people. The project will be developed over a month, with students meeting weekly to discuss progress and organize tasks.

Students should start the activity with a brief research on geometric constructions, analyzing how they are present in everyday life.

Next, each group should choose two geometric figures (a regular polygon and an angle) to focus on. Each group should create a flowchart or algorithm detailing how to construct their chosen figure.

Then, students should construct the chosen geometric figures on a piece of paper, using only an unmarked ruler and a compass.

Next, each group should give an oral presentation to the class, explaining the steps to construct the figure, presenting the flowchart or algorithm, and explaining the mathematical concepts involved.

Materials Needed:

• Unmarked ruler
• Compass
• Sheets of paper
• Pencils and erasers
• Computer with internet access (for research and report preparation)

Detailed Step-by-Step Guide for the Activity:

1. Formation of groups and task division.
2. Research on geometric constructions and analysis of how they are present in everyday life.
3. Selection of two geometric figures to focus on (a regular polygon and an angle).
4. Creation of a flowchart or algorithm for constructing the chosen figures.
5. Construction of the figures on a piece of paper using an unmarked ruler and compass.
6. Preparation of an oral presentation explaining the construction process of the figures.
7. Presentation to the class.

Project Deliverables:

The project will have two main deliverables:

1. The physical construction of the geometric figures.
2. A detailed report, containing:

• Introduction: Where students contextualize the theme, its relevance, real-world applications, and the objective of this project;
• Development: Where they explain the theory behind the chosen geometric figures, the activity in detail, the methodology used, and present the results obtained;
• Conclusion: Where they summarize the main points, explain the learnings obtained, and draw conclusions about the project;
• Bibliography: Where they indicate the sources used for the project.

Additionally, the group should give an oral presentation to the class, presenting the constructed figures, explaining the steps to build them, showing the flowchart or algorithm, and explaining the mathematical concepts involved.

Each deliverable is expected to add value to the academic development of the students, helping them solidify their knowledge in geometric constructions while enhancing socio-emotional skills.