Like let’s say that we start on the cape of goodwill for example and follow the coast.
Represent each 1km with 1mm for example on our map (map size isn’t a problem just for the sake of the argument). Getting the directions of drawing off a compass exactly. And just walk around all the coasts of the world.
What type of map do we end up with in this hypothetical?
In: 5
How do you intend to transcribe your motion onto paper?
By simple angle change?
The allow me to give you a simple path that should demonstrate the problem. You start at the north pole, and follow the prime meridian south. You turn 90 degrees left at the equator, and travel a quarter of the way around the Earth. You then turn left 90 degrees again, and walk another quarter.
You’re back at the north pole, having followed a ‘triangular’ path. Each corner is 90 degrees. If you were to draw this path on flat paper, your map would have two north poles on it. Your path would look like 3 sides of a square, since each corner is 90 degrees, and each side would be 10 meters long. Your start point and end point were both the north pole, but on paper they’re a quarter world (10 meters) apart.
If you were to try and trace a country using this system, walking its border, you would walk the full length and your drawing on paper would not be a full loop; your start and end points would be in different spots on your paper despite them being in the same place on Earth.
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