Euclidean geometry has been the foundation of mathematics for millennia. But the philosopher and mathematician Jules Henri Poincaré shows that it is not an absolute truth, but a convenient convention. Conventionalism claims that different types of geometries can be valid depending on the context.
For example, Euclidean geometry works well for measurements of the Earth’s surface, but non-Euclidean geometries, such as those developed by Lobachevsky and Riemann, are used in space. In Einstein’s theory of relativity, space and time are distorted, making Euclidean geometry inappropriate.
Euclid’s geometry remains relevant today – for example, in the architecture of the Sagrada Familia in Barcelona, where geometric shapes play a key role. However, conventionalism teaches us that we can expand our perceptions by considering other possibilities.
Next time you draw a triangle, think: what would it look like on the surface of a sphere or in the depths of space?
