The Earth and Its Representations. Explorations, Perceptions, and Projections.

This innovative teaching unit combines the fundamental principles of geography with active learning, 'learning by doing,' placing students at the center of the learning process. Through a series of engaging hands-on experiences, students will discover the most fascinating aspects of our planet Earth, from its actual shape to its cartographic representation.

The expected learning objectives for this teaching activity can encompass a range of theoretical and practical skills. Here are some expected learning outcomes:

1. Understanding the shape of the Earth: Students should be able to explain the differences between the ellipsoid and the geoid and understand why the geoid represents the most accurate shape of the Earth.
2. Familiarity with the concepts of latitude and longitude: Students should be able to define meridians and parallels and explain how they are used in mapping the Earth.
3. Interpreting the Mercator projection: Students should be able to recognize the distortions introduced by the Mercator projection and understand how this projection affects cartographic representation.
4. Practical skills: Students should be able to use tools such as 3D printers, paper models, and vector graphics software to create models and three-dimensional representations of the Earth and its geographical concepts.
5. Critical thinking: Students should develop critical thinking skills by questioning traditional cartographic representations and gaining a deeper understanding of the complexity of geography.
6. Collaboration: Students should work in groups to complete practical activities, enhancing their collaboration and communication skills.
7. Practical application: Students should be able to apply the knowledge acquired during practical activities to interpret maps and recognize cartographic distortions in various real-world situations.
8. Creativity: Students should be able to express their creativity in the creation of three-dimensional models and other geographical representations.

These learning outcomes reflect the goal of combining theory and practice, allowing students to develop a comprehensive understanding of geographical concepts and practical skills to explore and accurately represent the world.

Funded by the European Union – Next Generation EU

Supplies

Paper

Scissors

Markers

Color world map

Cutting plotter and self-adhesive vinyl

3D printer + PLA filament

Ink printer

Micro:bit + servo SG90 + expansion board + 3 AAA batteries (4,5v) (or 5v power bank)

Thingiverse.com

Tinkercad.com

Cura software

thetruesize.com

Templatemaker.nl

Inkscape software

Makecode

Step 1: Authors

This teaching unit was designed and developed by Massimiliano Ferré as part of the educational program created on behalf of VCO Formazione, in collaboration with We Do Fablab and the Beltrami Comprehensive Institute of Omegna (Italy).

Step 2: Tasks for Teachers

To properly develop the content of this teaching unit, it is helpful to reflect on some theoretical concepts:

1. What is the true shape of the Earth?
2. What are parallels and meridians?
3. Have North and South always been "Up" and "Down"?
4. What is the Mercator Projection, and what issues does it present?
5. What are the true sizes of countries compared to what we’re used to seeing on two-dimensional maps? Is Greenland really as large as it seems? Africa, on the other hand, is truly enormous!
6. What is the difference between geographic north and magnetic north?

Teachers should consider the following key actions to integrate STEAM disciplines and typical school workshop equipment into subjects like geography and science:

1. Use 3D printing to demonstrate the true shape of the Earth
2. Find an online tool that allows the creation of a simplified Earth model with meridians and parallels using basic materials
3. Identify an online tool that provides an interactive understanding of the Mercator projection's effects and the true sizes of countries
4. Create a challenge that compares the size of countries relative to Africa using 3D printing
5. Use micro:bit to relate the magnetic north to the geographic north of the 3D printed elements
6. Plan a feedback session

Step 3: Content Slides

The teaching unit is developed around in-depth theoretical discussions, starting with the study of the Earth's shape, moving through the explanation of the meaning of latitude and longitude, and understanding how the Mercator projection works. Each theoretical phase is accompanied by experiments involving the use of common materials, a 3D printer, and vector graphics software. Attached are the explanatory slides.

The content of the slides is in Italian.

Step 4: The Earth Is Not Flat, But It’s Not a Sphere Either

Starting from the time it was established that the Earth is round, the alternative to representing it on paper was to preserve its spherical reproduction through globes. However, these illustrated spheres, due to their small size, were so lacking in detail that they had little practical use.

Maps, in fact, are not scale reproductions of reality but projections—representations that aim to be as realistic as possible of the Earth's irregular surface relief.

The geometric figure that best describes our planet is not a sphere but an ellipsoid, a shape obtained by slightly flattening a sphere at the poles. This deformation is caused by the Earth's rotation, as the equator, being farther from the Earth's axis, experiences a stronger centrifugal acceleration compared to regions near the poles.

The effect is similar to how a pizza chef stretches pizza dough by spinning it. The flattening is very slight—just 21 km. That might seem like a lot, but it’s negligible when compared to the Earth’s radius of over 6,300 km.

Step 5: The Geoid

To be precise, the shape that most closely resembles the Earth is the geoid, an irregular solid that is defined by a surface always perpendicular to a plumb line, which is the direction of the gravitational force. The geoid thus accounts for gravitational irregularities caused by the presence of mountain ranges or less dense materials, such as the water in the oceans. One might expect the resulting figure to be quite bumpy. In reality, however, the extent of these deformations in relation to the overall size of the Earth is so small that the final result looks like a slightly rippled surface, smoother than the skin of an orange.

Johann Benedict Listing defined the ideal shape of the Earth, the "geoid," in the second half of the 19th century.

Step 6: 3D Model of the Geoid

A 3D model of the geoid represents the Earth's surface based on its gravitational field, showing variations in elevation caused by uneven mass distribution. Unlike a perfect sphere or ellipsoid, the geoid reflects the "bumpy" reality of Earth's shape, influenced by features such as mountains, ocean trenches, and density anomalies within the planet.

Purpose: Create a tactile, creative, and inclusive experience.

The 3D printing activity can be carried out either by the teacher, producing a model of significant size, or by each student, resizing the object and verifying printing times in advance.

For a more realistic effect, the printed model can be painted using acrylic inks.

You can find a 3d model of geoid on Thingiverse (please read "thing details"!).

Step 7: Let's 3D Print the Geoid!

Problem Solving

Questions:

1. Can I print the entire geoid?
2. If I choose to print the two hollow halves, already available in .STL format, what precautions should I take?

Answers:

1. Printing the entire model is not recommended. I can split it in half using Tinkercad (possibly aligning with the equator!) and then print the two parts to glue together afterward.
2. Problem: The .STL file of the entire geoid cannot be imported into Tinkercad.
3. Cause: The model is too complex or excessively large.
4. Solution: Use an online tool to simplify and reduce its size (e.g., "Mesh Simplification").
5. I can decide to enable support structures if no specific instructions are provided.

Step 8: Meridians and Parallels

The abstract figure of the "reference ellipsoid" is used to define projections that map each point on the ellipsoid to a point on the two-dimensional plane of a map. The first step in transferring data from the Earth's surface to a flat plane involves drawing a geographic grid that virtually wraps around the Earth's surface.

The grid consists of elements with two familiar names: meridians and parallels.

1. Meridians are semicircles of equal length (about 20,000 kilometers) that connect the two poles. While theoretically infinite, by convention, 360 meridians are considered, one for each degree of the Earth's complete rotation.
2. Parallels, on the other hand, are circles that connect points equidistant from the poles. They have different lengths but exist in pairs—one in the northern hemisphere and one in the southern hemisphere. Like meridians, parallels are infinite, but starting from the Equator, which is the largest parallel, 90 parallels are numbered in the northern hemisphere and another 90 in the southern hemisphere.

Every point on Earth is intersected by a meridian and a parallel that define its position. Each point can be identified using geographic coordinates:

1. Latitude, which is the angular distance of a point from the Equator, measured north or south.
2. Longitude, which is the angular distance from a prime meridian. By convention, the prime meridian is the Greenwich Meridian, near London, home to a famous astronomical observatory.

Each point on Earth is thus represented by a pair of angular coordinates.

Step 9: Latitude and Longitude

How are latitude and longitude measured? How does the GPS in our phones work?

1. Latitude is measured in degrees (from 0 to 90 degrees) with a precision of arcseconds (1/3600 of a degree). Zero degrees latitude is found at the Equator, while 90 degrees latitude is at the poles.
2. Longitude is measured from zero degrees at the Prime Meridian, located at the Greenwich Observatory in London, to 180 degrees at the Antimeridian.

Traditionally, latitude was calculated by observing the Sun or a star.

Today, geographic positioning is determined using GPS (Global Positioning System). GPS is a global navigation system based on radio signals sent from satellites orbiting the Earth. GPS receivers use these signals to determine their exact position on the Earth with high precision.

A point on Earth is identified by a pair of values expressed in sexagesimal notation: degrees° minutes' seconds'' (e.g., 41°55'27.851'').

1. Latitude values range from 0 to 90 (North/South, or N/S).
2. Longitude values range from 0 to 180 (East/West, or E/W).

Step 10: Pencil, Paper, and Scissors!

Objective: Explore meridians and parallels creatively while developing analytical skills, using simple materials.

How can I create a (simplified) sphere using paper?

To build a paper sphere, it’s essential to consider its 2D development (the flattened version of the shape). Together with the students, we brainstorm which geometric profiles can be used to construct a sphere. These can include:

1. Strips or bands arranged in a globe-like structure.
2. Circular or petal-like segments that, when assembled, create a 3D form.

The individual parts can then be glued or taped together.

Steps to Experiment:

1. Visualize the Shape: Begin by drawing simple shapes that can form a sphere when folded or assembled.
2. Cut and Assemble: Use scissors to cut out the chosen profiles and experiment with joining them into a spherical shape.
3. Refine the Structure: Test different patterns and learn from any imperfections.

Personalization with TemplateMaker.nl:

After experimenting with hand-drawn designs, introduce TemplateMaker.nl, a powerful online tool to generate geometric templates.

1. Students can discover how parameters (like the number of strips or petals) affect the shape.
2. The activity shows the value of customization and the impact of precise measurements in creating functional designs.

Ready? 1, 2, 3... Let’s experiment!

Step 11: The Perception of the World

What is a projection?

A projection is a method used to represent the spherical surface of the Earth—three-dimensional and curved—on a flat surface, such as a map. However, this transformation inevitably causes distortions. Imagine flattening half an orange peel onto a table: it will tear, leaving gaps.

Projections influence how we perceive the world!

The Mercator Projection

One of the most commonly used projections, invented in the 16th century by Gerardus Mercator, represents parallels and meridians as a grid of perpendicular lines. It became popular for its navigational usefulness, as it preserves directions.

However, due to distortions inherent in the projection:

1. The relative size of landmasses is misrepresented. For example, Africa appears much smaller compared to Europe than it actually is.
2. The farther a region is from the Equator, the larger and more exaggerated its size becomes. For instance, Greenland, Canada, and Antarctica appear much larger on Mercator maps than they are in reality.
3. Areas near the Equator are depicted more realistically in terms of proportions.

This distortion profoundly affects our perception of the relative sizes of countries and continents.

Experiment: Measure Distances

Have you ever tried measuring the distance between two points on a sphere?

1. Use Google Maps to measure the airline distance between Milan and Beijing.
2. Observe if the trajectory shown on the map is straight or curved.

This exercise highlights how the shortest path between two points on a sphere—a great circle route—differs from our intuition on a flat map.

What other types of globe projections exist?

There is no absolute correct way to draw a map of the world. The world map we are familiar with is the result of political and cultural choices that are not shared by all countries.

From elementary school, we have all used and memorized the same map of the world, with Europe at the top and center of the map. This is the Mercator map: Europe in the center, the Americas to the left, Asia to the right, and Africa below. While the world remains the same for everyone, when people from other countries are asked to think about the map of the world, not everyone immediately envisions the same image. The Mercator map as we know it is not universal and is not used everywhere. Which countries represent the world differently, and why do they do so?

In the United States, the American continent is placed at the center, appearing as an island in the middle of the world. On this map, Russia, China, and India are not only on the periphery but are divided and represented with one part in the east and another in the west, making it difficult for the observer to perceive them as single territories.

The Chinese world map uses an equidistant projection, which, unlike the Mercator projection, alters the shapes of the continents but preserves their sizes. Additionally, the Chinese map is centered on China, placing the territory of the People's Republic of China at the center of the map.

Similarly, some countries south of the Equator tend to place themselves at the center of the map but with a significant difference compared to the maps seen so far: they reverse the positions of north and south. The fact that north is at the top of the map is merely a convention, which has led people to develop the notion that northern countries are better and wealthier (partly due to associations in other contexts where "up" equates to good and "down" equates to bad).

In the early 1900s, countries such as Australia, South Africa, or Chile developed this unique approach called the “south-up” technique, meaning "south on top." Rotating the projection by 180 degrees is technically simple, and this practice has helped eliminate the north-south bias, restoring dignity to the representation of countries located south of the Equator.

Why are there different representations? Comparison and discussion among students

It is evident that various countries represent the world differently, primarily for political and cultural reasons, to assert their identity and portray themselves as more significant. Each map is correct in its own way, and understanding it requires evaluating the perspective from which the map's creator views the world. Lastly, all the elements of the world map that we take for granted and consider established are the result of conventions (for example, north being at the top), but they are not universally correct: every representation can stem from choices influenced by historical, political, or cultural factors.

Step 12: The True Size Of…

Let’s use an interactive online platform to make the distortions caused by the Mercator Projection more understandable and fun.

TheTrueSize.com allows us to identify countries on the map and move them freely. The closer a country is dragged toward the equator, the more its true proportions are revealed.

For example, let’s compare the actual size of Greenland to that of the African continent. At first glance, they may seem similar, but in reality, Africa is over 14 times larger! Let’s try the same with the United States of America!

Tricks:

1. By hovering the mouse over a country, you can see its actual area in square kilometers.
2. By right-clicking on a previously selected country, you can remove it from the map.
3. Each country can be rotated to align with a different reference system by using the compass at the bottom left.

How many countries can we fit into Africa?

Using the website TheTrueSize.com, let’s place as many countries as we can within the African continent, orienting them as we like. Let’s fit them together like a puzzle!

From the document published at this link, we can realize a possible optimal solution... and just how large Africa really is!

Step 13: Let's Create a 3D Printed Model That Showcases the Experience

PHASE 1: Save the image

Using the website TheTrueSize.com, place as many countries as you can within the African continent, orienting them as you like, but be careful not to overlap them in any way.

Take a screenshot of the screen and import the saved file into Inkscape.

PHASE 2: Trace the outlines

In Inkscape, using the PEN tool, trace the outline of Africa, then create an Offset (a parallel path to the original) by using the command PATH / LINKED OFFSET. With the NODE tool, you can drag the outline to create a new contour.

Using the PEN tool, trace the outlines of all the states that were placed. This time, only one outline per state is needed.

It is recommended to save an SVG file for each profile/state.

Important: during these operations, it is essential not to resize the background map.

STEP 3: Creating the 3D models

1. Import the individual SVG files into Tinkercad.
2. Build the game by adjusting the heights of the shapes and adding any custom text as needed.
3. You can modify the height of each state profile and make any other adjustments to suit your design.
4. Once all elements are assembled, resize ALL of them so that the largest model fits within the available printing area, while the smallest model remains proportional in size.
5. After adjusting the sizes, export each 3D model as an STL file for 3D printing.

STEP 4: Simulate and Print

1. Import the STL files into the Ultimaker Cura software without resizing them.
2. Arrange the models optimally, creating different print sessions based on the colors you wish to use.
3. Perform the prints and then assemble your geographical puzzle.

STEP 5: Some of the Activities to Do:

1. Display the works and present the different solutions identified.
2. Calculate the total square kilometers achieved.
3. Exchange projects and try to reassemble them.
4. Recognize the states based on their shapes.
5. Use the pen tool to write the names of the states or their identification numbers.

Here you cand find the online 3d model project on Tinkercad.

Step 14: The Difference Between the Geographic and Magnetic North Pole

The axis of rotation intersects the surface of the planet at two points: the geographic North Pole and the geographic South Pole. To visualize them in our minds, these are the points on the globe where the pins are fixed that allow it to rotate.

But where exactly are the two geographic poles located? The North Pole is located in the middle of the Arctic Ocean, at a point permanently covered by a layer of ice several meters thick. The South Pole, on the other hand, is situated in Antarctica. Simply put, these two points can be considered fixed.

Our planet can be considered as a giant magnet. Like all magnets, it has a positive pole and a negative pole: the positive is called "north," and the negative is called "south." To clarify, the north pole is the one indicated by the compass needle when we use it to orient ourselves.

Since the Earth's magnetic field changes over time, the magnetic north does not remain fixed. Periodically, a phenomenon known as magnetic reversals occurs. This means that the magnetic north pole flips with the south pole.

Step 15: Let's Build a Compass With Micro:bit

As a final practical exercise, let's build an electronic compass: every time you move the micro:bit, the servo motor automatically rotates to always point towards magnetic north, reflecting the direction detected by the compass sensor.

First of all, with the cardboard, we built the fixed base of the compass and decorated it with the north, east, and west directions. We attached a stick to the servo motor's axle, which represents the compass needle. With a bit of creativity, we managed to secure the micro:bit and servo motor to the cardboard.

Considering that the SG90 servo motor operates at 5V and its connection cables are jumper-style rather than alligator clips, it is recommended to use an expansion board that allows connecting the electronic system to a 5V power bank or three AAA batteries (totaling 4.5V). The servo motor should be connected to the 5V and GND pins of the expansion board and can use a digital PIN as the signal output (angle). Connections can be made using three jumper wires. In this example, PIN12 has been used.

Attached are the graphical blocks that make up the functional program.

Step 16: Conclusions

Through this activity, students gained a deeper understanding of the complexities of representing the Earth's surface on maps and the influence of politics, culture, and conventions in cartography. By engaging with interactive tools and hands-on projects, such as creating 3D models and building a magnetic compass with Micro:bit, they developed practical skills and critical thinking. These exercises emphasized the importance of perspective in interpreting geographical data and fostered creativity, problem-solving, and collaboration.

Step 17: Example of a Learning Unit

Here an example of a learning unit developed for the explained topic. It is important to define the number of hours to be dedicated to each phase of the work and the methods of practice. How long does this lesson last in total? What role should the teacher play in each phase? What challenges are encountered? Use this template as a guide to develop your own lesson!