You may not be familiar with the name Euclid, but you're probably familiar with his ideas. More than two thousand years ago in Ancient Greece, Euclid laid down the foundations of basic geometry, such as the idea that two parallel lines never cross, and that the angles inside a triangle always add up to a constant number.
Many of us will have learned these basic principles of geometry at school, although some philosophers have suggested that we actually get most of our grasp of geometry from looking at the world around us and moving about in it. For example, figuring out that the shortest way home is in a straight line rather than a curved or wiggly one.
To find out whether this idea is correct, some French psychologists took a field trip to the Amazon, to find out how well the Mundurucu, a tribe of indigenous people who have no formal schooling in maths, grasp the principles of Euclidean geometry.
The researchers developed a series of tasks for adults and children from the tribe, asking them about lines drawn on a flat surface, or on a sphere. For example, they asked whether lines could be drawn between two points, or whether parallel or non-parallel lines would cross. To set the scene, they explained that the points were villages and the lines were paths between the two – a concept very familiar to the Mundurucu, who are experts at navigating around the landscape. They also asked them to estimate the third angle in an incomplete triangle, to see whether the Mundurucu understood that the angles inside a triangle always added up to a constant number.
When completing the tasks, the tribespeople did almost exactly as well as French or American adults and children given the same tasks, who would have had formal education in geometry. This suggests that just figuring out the environment, and learning to get from place to place gives you a pretty good grounding in Euclidean principles, without having to learn about it in the classroom.
But, intriguingly, when the researchers tested very young children – aged 5 or 6 – they found that their grasp of geometry was a bit shakier. They still had some of it right, but hadn't quite figured it out. So overall, it looks like we have an intuitive grasp of the principles of basic geometry, shaped by our learning and interactions with the world around us as we grow up.
This doesn’t mean that we should stop learning geometry in the classroom as maths lessons teach you a lot more than the basics. But it does tell us that we develop a lot of our sense of geometry through our experience of the world around us, and that it fits in with Euclid's principles. But what's still not explained is the observation that the Mundurucu, as well as Western people with maths training, can understand concepts that are outside the sphere (pardon the pun) of what they can see or do. So that's something that still needs exploring.