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Maps and cartography

What is a map? How do we represent a 3D world on a 2D map?

The fundamental problem

Try to peel an orange into a flattened shape that accurately shows what’s on the surface:

Earth 3D map on orange flattened out problem

Image from blogs.lincoln.ac.nz

Map Projections Part 1: Where on Earth are we?

In short – it’s impossible. Or rather it’s impossible to do it in such as way that you retain all the relationships between what’s on the surface. When flattening out the orange peel you have to make some choices about what you’re going to sacrifice.

Is it direction? Is it area? Is it proximity? Any attempt to flatten the peel will mean sacrificing one or more of these relationships.

When making maps, it’s the same set of choices to make. And this is where map projections come in. Projections are methods that translate the three-dimensional surface of the earth (the globe) into flat, two-dimensional spaces (maps) and there are a multitude available.

This section from Map Projections Part 1: Where on Earth are we?, GIS Blog


It’s impossible to transfer the features on the surface of a sphere onto a flat plane without creating some sort of distortion. As soon as we turn the light on (metaphorically speaking) we sacrifice something: area, shape, bearing, or distance.

Another way we can classify projections is what aspect of the surface they preserve. Here are the main categories:

Direction Preserving (azimuthal or zenithal)

Shape Preserving (conformal or orthomorphic)

Area Preserving (equal-area or equiareal or equivalent or authalic)

Distance Preserving (equidistant), or

Shortest Route Preserving (gnomonic)

Often, the choice of which one to use depends on what the maps will be used for. Mercator first drew his map to be used by mariners, so it was designed to preserve bearing (direction) at the cost of shape and area (hence, an overly large Greenland).

Sometimes, a projection can be chosen so that it minimises several distortions at one time, a sort of compromise that has been used on many New Zealand maps (we’ll look at this more closely later on).

This section from “Map Projections Part 2: The Allegory of the Cave”, GIS Blog

Learning Standards

Massachusetts Science and Technology/Engineering Curriculum Framework

4-ESS2-2. Analyze and interpret maps of Earth’s mountain ranges, deep ocean trenches,
volcanoes, and earthquake epicenters to describe patterns of these features and their
locations relative to boundaries between continents and oceans.

Science and Engineering Practices – 4. Analyzing and Interpreting Data – Use graphical displays (e.g., maps, charts, graphs, and/or tables) of large data sets to identify temporal and spatial relationships.

College Board Standards for College Success: Science

Standard SP.3 – Data Analysis – Searching for regularities and patterns in observations and measurements (i.e., data analysis)
Objective SP.3.1 – Analyzing Data for Patterns

Objective SP.4.2 – Models and Representations –  Students construct, use, re-express and revise models and representations of natural and designed objects, systems, phenomena and scientific ideas in the appropriate context and in formulating their explanation.

ELA Common Core State Standards for English Language Arts & Literacy

English Language Arts Standards » Science & Technical Subjects » Grade 9-10

Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics.

Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.

Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem.

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