Introduction

Welcome to this math project! Let's dive together into the exciting world of geometry, specifically the concept of 'orthogonal view'.

Geometry is a branch of mathematics that studies shapes, measurements, and properties of space. An important part of geometry is 'descriptive geometry', which studies three-dimensional shapes and how these shapes can be represented in two dimensions. 'Orthogonal view' is a key concept in this area, where a three-dimensional image is projected onto two orthogonal planes (90-degree angle).

To understand it, imagine a cube: if you view this shape from different angles, you will see different faces of the cube. The orthogonal view tries to describe these different faces through projections on two-dimensional planes. Therefore, the orthogonal view tries to describe a three-dimensional object using only two dimensions.

Context

But why does this matter? Well, the orthogonal view is extremely important in technical design, architecture, and civil engineering. If you have ever seen a construction drawing, you have probably seen orthogonal views. They are used to create a 'plan' of the construction, which represents the building construction project in two dimensions but gives a complete view of the building. This way, it is possible to understand how the building will look when completed without necessarily seeing a real three-dimensional perspective.

Furthermore, the orthogonal view is also used in other fields such as graphic design, video games, and film production. When game designers create a new character, for example, they can use orthogonal views to show how the character should look from different angles, facilitating 3D modeling.

Of course, to master this technique, it is necessary to understand the concept well and know how to implement it. Therefore, this project will help you understand and apply the orthogonal view in practical situations.

To start, think of real-life examples where the orthogonal view is used, such as the blueprint of your house, the technical drawings of a machine, or a character from a video game that you like.

Below are some reliable sources in Portuguese for you to base yourself on and delve deeper into the topic:

1. Descriptive Geometry: orthogonal projections (UOL Educação)
2. Descriptive Geometry: orthogonal views (InfoEscola)
3. Orthogonal Views (Toda Matéria)

Practical Activity

Activity Title: Orthogonal 3D Modeling with Modeling Clay

Project Objective

In this activity, you and your team members (3 to 5 members) should:

1. Create a three-dimensional object with modeling clay.
2. Make the orthogonal projections of this object on paper.
3. Prepare a detailed report on the process.

Detailed Project Description

Let's put into practice the theoretical concept of orthogonal view! This project consists of modeling a 3D object with modeling clay, making its orthogonal projections, and presenting all of this in a detailed report. This work will help you better understand the concept of orthogonal view and how it is used in different contexts.

The activity will last approximately one month, with a workload of five to ten hours per participating student.

Required Materials

• Modeling clay
• Graph paper
• Pencil and eraser
• Ruler

Step-by-Step Guide for the Activity

1. Planning: As a team, decide on the object you will model. The object should be something with an interesting shape that can be viewed from different angles. For example: a house, a car, a chair, or an abstract sculpture.

2. Modeling: Use the modeling clay to create the object. Remember, you are creating a three-dimensional object, so you need to think about how it looks from different angles.

3. Drawing the orthogonal views: After modeling the object, draw it in orthogonal projection on the graph paper. Three drawings should be made representing the front, top, and side views of the object.

4. Report: Write a detailed report on the project. This report should include:

   a. Introduction: Explain the concept of orthogonal view and its importance in various areas. Talk about the object you chose and why you made this choice.

   b. Development: Describe in detail the modeling process, the difficulties encountered, and how they were overcome. Discuss the drawing of orthogonal projections and how practice connected with theory. This topic should include images of the different work stages.

   c. Conclusion: Here, students should reflect on the process, what they learned from the activity, and how they believe this knowledge can be useful in the future.

   d. Bibliography: Indicate the sources used to learn about the topic and to develop the project.

At the end of the project, each group should present the modeled object, the drawn orthogonal projections, and the written report.