Complete the theorem and its consequence.
A sphere cannot be flattened without distortion, so every projection is a bargain: Mercator preserves ______, making a constant compass bearing a straight line, and pays in ______, which inflates toward the poles. There is therefore no ______ map, and the choice of projection is always an argument.
Word bank: angles · area · neutral · distance · accurate
Hints
- A curved surface cannot be flattened without loss.
- No projection can therefore be neutral.
Show the answer
A sphere cannot be flattened without distortion, so every projection is a bargain: Mercator preserves angles, making a constant compass bearing a straight line, and pays in area, which inflates toward the poles. There is therefore no neutral map, and the choice of projection is always an argument.
Angles, area, neutral. Not a failure of cartography but a theorem about geometry, which is why the only real question is whether the bargain was struck deliberately.
Practise Maps and Projections
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