Following the rules. Most geometry used in everyday life is the geometry of flat spaces, or Euclidean geometry, so called because the Greek mathematician Euclid wrote down many of its principles ...

Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in ...

So much for parental encouragement. Undeterred, János went on to hammer out rules for what we now call non-Euclidean geometries. In Euclidean geometry, the angles of a triangle add to 180 degrees and ...

Euclidean geometry is the kind of geometry we normally study at school, whereas non-Euclidean geometries are all those that reject one or more of Euclid's five postulates. A geometry that unfolds ...

Before his early death, Riemann freed geometry from Euclidean prejudices. ... it was important to grasp the ideas behind the calculations, not merely accept the rules and follow standard procedures.

This "non-Euclidean" example, where the formal rules of geometry as most people learn them do not hold true, seems to suggest that our geometry education may actually mislead us, Dr Pica said.