FLASHCARDS! Google Maps, Waze, and the Science of Map Distortion

We use maps all day, including Google Maps, Waze, Apple Maps. We use them without even noticing that every one of them distorts reality. In this episode, Gabrielle explains why flattening a round Earth always bends the truth, how classic projections (like Mercator) live inside today’s apps, and why those distortions shape our mental picture of the world. Practical, visual, and myth-busting, this is cartography you can feel on your daily commute. 

To hear the podcast on Marie Tharp, visit: Math Science History with Gabrielle Birchak

Three Coordinates to Remember

1. Why distortion is unavoidable when projecting a 3D globe onto a flat screen (thanks, Gauss).
2. How Web Mercator powers Google Maps/Waze, great for street-level navigation, misleading at global scales.
3. How projection choices shape perception, from Greenland vs. Africa to who appears “big” or “central” on a map.

Resources & Visuals

• Gall–Peters (equal-area) projection:
  Peters Projection Map: Everything Your Ever Wanted To Know
• Compare Map Projections:
  https://map-projections.net/compare.php
• Buckminster Fuller’s Dymaxion map (unfolded globe):
  https://www.bfi.org/about-fuller/dymaxion-map
• “The True Size Of…” (drag countries to compare real sizes):
  https://thetruesize.com

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Episode Transcript

(00:02):
It's Flashcards Fridays at Math! Science! History! where we explore big ideas in math,
science, and history, all in the time it takes to enjoy a cup of coffee. I'm Gabrielle
Birchak, and today, in a follow-up to Tuesday's podcast about Marie Tharp and her mapping
of the Atlantic Ridge under the Atlantic Ocean, I thought we would take a look at something

(00:24):
familiar that you probably really don't even think about, a map. But first, a word from
my advertisers. Think back to the last time you used a map. It was probably this morning
when you were probably trying to find your way through traffic to get to work on time.
Whether it's Google Maps, Apple Maps, Waze, or the GPS in your car, we trust these tools

(00:48):
to get us from point A to point B in the quickest way possible. But did you know that each one
of these maps, as well as the globes in your home or classrooms, have been distorted?
And it's not because the engineers or cartographers are bad at their jobs, but because maps have
to bend for accuracy. When you look at a globe and see a country like Greenland that looks

(01:11):
nearly twice the size of Africa, consider that Africa could fit 14 Greenlands inside
of it. That's the distortion that you are seeing. And these aren't mistakes. They're
the unavoidable side effects of flattening a round world onto a flat surface. The Earth
is spherical, but maps are flat. Turning one into the other is like peeling an orange and

(01:35):
trying to press the peel perfectly flat. Somewhere, the peel has to stretch, rip, or budge. That
is distortion. In 1827, mathematician Carl Friedrich Gauss proved in his Theorema Egregium
that you cannot take a curved surface and flatten it without changing something. On

(01:57):
a map, those somethings are shape, area, distance, or direction. You can preserve some, but never
all four at the same time. Every map you look at is a compromise. The only question is,
what did the mapmaker decide to keep accurate, and what did they choose to let go? One of

(02:18):
the most famous projections is the Mercator, created in 1569 by Gerardus Mercator. It became
a hit with sailors because it preserved angles perfectly, making navigation simple. Draw
a straight line on a Mercator map, follow that compass bearing, and you'd reach your
destination. The tradeoff? As you move away from the equator, the map stretches everything

(02:43):
vertically. Greenland looks huge. Alaska rivals Brazil. Canada looms like a giant hat over
the northern hemisphere. In reality, they are much smaller. This wasn't political trickery.
It was geometry. But because Mercator maps hung in classrooms for decades, they subtly

(03:05):
reinforced an inflated sense of the size, and perhaps the importance of certain northern
countries. By the 1970s, some geographers wanted something fairer. The Gall-Peters projection
keeps the area of countries proportional. On this map, Africa and South America appear
as massive as they truly are. But the shapes look stretched and a bit odd. People weren't

(03:32):
used to seeing the world that way. It felt so wrong, even though the math was right.
That's the power of habit. Once you are used to one kind of distortion, another kind of
feels like a mistake. Not all projections serve the same purpose. Airline route maps
often use azimuthal projections, which preserve direction from one point. Many regional maps

(03:56):
use conic projections, balancing shape and area for mid-latitude countries. The Robinson
projection, which National Geographic adopted in the late 1980s, is a compromise that doesn't
preserve any single quality perfectly. It looks good overall. Then, this one's really
cool. There's the Buckminster Fuller's Dymaxion map, which unfolds the globe into triangles

(04:22):
to minimize distortion and tosses the whole north on top idea out the window. I will post
an image of this on my website at mathsciencehistory.com. And while you're there, please feel free to
click on that coffee button and make a donation to Math Science History. Because every donation
that you make keeps this free educational podcast and blog up and running. We always

(04:48):
appreciate your generosity. And if you're looking for that image, click on the link
that says the transcriptorium. We've moved a few things around and put the podcast on
the front page just to make the podcast easier to find. But the blog can be found under
the transcriptorium link. So back to mapping. You might think digital maps have solved this,

(05:11):
but not quite. Most online maps, including Google Maps, use Web Mercator, a variation
of the Mercator that's easy for computers to process. At street level, it's accurate
enough that you won't notice. But zoom out to see the whole earth and you will find
Greenland is still way too big. So why does distortion matter? Well, map distortion isn't

(05:37):
just a trivia fact. It shapes how we think about the world. Maps can make some countries
look larger and more central, subtly influencing how we see their importance. Even deciding
which part of the world gets placed in the center of a map can reflect the map maker's
culture and perspective. Maps are not neutral. They are both tools and stories, revealing

(06:03):
not just where things are, but how someone chose to show them. So here's an easy trick.
The next time you look at a world map, compare Greenland to Africa. If they look close in
size, you're looking at a projection that values shape over area. And that's fine as
long as you know it. So what are the three flashcards we can use as takeaways? Well, first,

(06:27):
all maps distort. It's mathematically impossible to make a perfectly accurate flat map of around
earth. Second, the projection a map maker chooses tells you what they value, whether
it's navigation, proportional size, or a pleasing overall look. Third, the way a map is drawn

(06:47):
can influence your perception of geography, culture, and even politics. Awareness is your
best defense. So that's your Flashcards Friday episode. I'm Gabrielle, and if you enjoyed
today's episode, subscribe to Math! Science! History! on your favorite podcast player. And
until next time, carpe diem.