Contextualization

Projection is a fascinating and extremely useful concept in mathematics. Used in different areas such as engineering, architecture, and especially cartography. The study of projections is fundamental to understanding how we transform the sphericity of our planet into flat maps. Because of this transformation, there are inevitable distortions that occur, and this is what we will explore in this project.

Projections can be classified into different types, understanding these classifications and their properties is essential to understanding how and why certain distortions occur. In particular, we are going to focus on two widely used projections: cylindrical and conic projections. Each of these projections has its unique characteristics and specific applications, and each has implications for how angles and areas are represented.

In the real world, understanding distortions in projections has very practical applications. For example, in cartography, a wrong choice of which type of projection to use can lead to significant errors in maps. Also, it has implications in different areas of our daily lives, like GPS navigation, airplane route design, and in military and defensive strategies, where small errors can have big impacts. Therefore, having a clear understanding of distortions in projections is of utmost importance.

To help you embark on this journey of discovery, we suggest the following reliable sources:

• Cartography Fundamentals - Online class notes with chapters specifically focused on cartographic projections.
• Map Projections - Website with interactive animations showing different types of projections and their properties.
• Book: "GIS Fundamentals", Paul E. Bolstad.

Hands-on Activity

Activity Title: "Projecting the Earth: A study on distortions in cylindrical and conic projections"

Project Objective

This project aims to provide students with the opportunity to explore, understand, and analyze the effect of the distortions that occur when the Earth's sphericity is converted into a flat map, more specifically in cylindrical and conic projections.

Detailed Project Description

Students will work in groups of 3 to 5, with each group having the task of investigating two types of projections that are cylindrical and conic, and the distortion of angles and areas in these projections.

The project will be divided into two main parts. In the first part, students will research and understand the key concepts associated with projections and the inherent distortions for each projection. In the second part, the groups will put their theoretical knowledge into practice, analyzing, and comparing the distortions in different projections.

Materials Required

1. Internet access
2. Stationery: Paper, pens, rulers, protractors, color pencils
3. Cartographic projection software (optional)

Detailed Step-by-Step Activity

1. Initial Research: Each group should start the activity by researching about cylindrical and conic projections using the suggested sources and other reliable sources.

2. Projection Theory: Students need to understand and discuss as a group the fundamentals of cylindrical and conic projections, and the principles, methodology, and types of distortions inherent to each projection.

3. Practical Application: Each group will create two maps, one using cylindrical projection and the other using conic projection of a region of their choice. They should compare and contrast the distortion of angles and areas between the two projections. This can be done manually or using cartographic projection software.

4. Analysis and Discussion: Each group will discuss and analyze the differences and similarities between the two projections focusing on how and why distortions occur.

5. Report Elaboration: Finally, each group is required to prepare a detailed report of their findings, which should include the following sections: Introduction, Development, Conclusions, and Bibliography.

The report should correlate the practice with the theory, demonstrating the knowledge acquired during the project. The report should be submitted one week after the initiation of the project.

Project Deliverables

At the end of the project, each group will submit a report covering:

1. Introduction: Context of the theme, relevance, practical application, and scope of the project.

2. Development: Explanation of the theoretical concepts, detailed description of the project, methodology used, and presentation and discussion of the results obtained.

3. Conclusion: Recapitulation of the key points, lessons learned, and conclusions about the project.

4. Bibliography: List of all sources used throughout the project.

In addition to the report, students have to present the two maps they created during the project.