Contextualization

Mathematics is a vast field, and in this project, we will address a very important and fascinating subject: bisectors and mediatrices. They are fundamental in geometry, an area of mathematics that studies shapes, sizes, and properties of space. They act as a bridge, helping us understand visual abstractions in our everyday world.

These concepts allow us to make important measurements and establish significant relationships between geometric elements. A bisector is a line segment that divides an angle into two equal angles, while a mediatrice is the line perpendicular to a line segment at the midpoint of this segment. These concepts may seem simple, but their application is very broad, and they allow us to unravel many mysteries of geometry.

Importance and Applications

Geometry involving mediatrices and bisectors is not only useful in classrooms but also has many practical applications in the real world. For example, the mediatrice is often used in the field of civil engineering to determine equidistant lines between two specific points, which is very useful in projects such as road and bridge construction.

The bisector, on the other hand, has many applications in the fields of art and design. It is used to create symmetry and balance in a design, as well as to divide angles precisely. In the educational field, it helps in understanding complex concepts of geometry and trigonometry.

Mathematics is a universal language that helps us interpret and interact with the world around us. This project will give you a sense of how mathematical concepts can be challenging and attractive at the same time!

Practical Activity: "Exploring Mediatrices and Bisectors in Geometry and Art"

Project Objective

This project aims to deepen students' knowledge in geometry, specifically in mediatrices and bisectors, through the practical application of these concepts in the construction of a geometric art mosaic. The project should be completed in groups of 3 to 5 students, with a total estimated duration of over twelve hours per student.

Detailed Project Description

This project consists of two phases. First, students will research the concepts of mediatrice and bisector and how they are applied in geometry and art. Next, they will use this research to create a geometric art mosaic, which will be the final product of the project.

Students must deliver two products:

1. A written report containing the four topics as mentioned above
2. The resulting mosaic from their experimentation with bisectors and mediatrices.

Required Materials

• Notebook and pen
• Cardboard paper
• Ruler
• Protractor
• Coloring materials: colored pencils, markers, or crayons
• Computer with Internet access for research and report preparation

Step by Step

1. Research (3-4 hours): Each group starts by researching the definitions and applications of mediatrice and bisector. They should also look for geometric art to inspire them for the second phase of the project. All insights should be documented for later inclusion in the report.

2. Mosaic Planning (2-3 hours): Using information from their research, each group should conceive a project for a mosaic that incorporates mediatrices and bisectors. The project should be drawn on paper, with a written explanation of how mediatrices and bisectors are used.

3. Mosaic Creation (6-8 hours): Now, each group should transfer their project to the cardboard paper, using a ruler and protractor to ensure accuracy. Once the geometry part is ready, they should color their mosaic.

4. Writing the Report (2-3 hours): Finally, each group should compile their findings into a report. This report should include an introduction with the contextualization of the use of bisectors and mediatrices in mathematics and art, detailed development with the theory and experiment conducted, the results obtained and analysis, the conclusion on the learning and experience during the project, and lastly, the bibliography of the resources used for research.

Project Delivery

Students should deliver, in addition to the mosaic, a report with the following topics:

• Introduction: Contextualization of the use of bisectors and mediatrices in everyday life, mathematics, and art.
• Development: Description of the experiment and detailed discussion on the application of the theory in the mosaic project, including the methodology used.
• Results: Presentation and analysis of the results obtained in the project.
• Conclusion: Reflection on the learning obtained during the project, both in terms of mathematical concepts and socio-emotional skills.
• Bibliography: Citation of the resources consulted during the research.