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Some rules in geometry are not "absolute truth" but conventions chosen because they are the most practical — we could, in theory, have chosen others.

Henri Poincaré · Science and Hypothesis · 19021 minute readpublic domain
Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.Henri Poincaré · Science and Hypothesis · 1902

Geometry is a practical convention, not an absolute truth, chosen to simplify calculations.

Poincaré showed you can describe the same world using different geometries, just like you can map the same city on a flat sheet or on a globe. We pick ordinary geometry not because it is the only true one, but because it makes calculations simplest. The choice matters, even if invisible.

Why it mattersThis idea helped Einstein, a few years later, to think beyond ordinary geometry.

Simple EuclideanOther geometries
Comparing geometry usefulness

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