All humans exhibit an intuitive knowledge of geometry no matter their cultural or educational background. A team of researchers has concluded that this ability develops when children become aware that they exist in three dimensional space.
Euclidean geometry makes it possible to describe space using planes, spheres, straight lines, points, etc. Can geometric intuitions emerge in all human beings, even in the absence of geometric training?
To answer this question, a team of cognitive science researchers elaborated two experiments aimed at evaluating geometric performance, whatever the level of education. The first test consisted in answering questions on the abstract properties of straight lines, in particular their infinite character and their parallelism properties. The second test involved completing a triangle by indicating the position of its apex as well as the angle at this apex.
To carry out this study correctly, it was necessary to have participants that had never studied geometry at school, the objective being to compare their ability in these tests with others who had received training in this discipline. The researchers focused their study on Mundurucu Indians, living in an isolated part of the Amazon Basin: 22 adults and 8 children aged between 7 and 13. Some of the participants had never attended school, while others had been to school for several years, but none had received any training in geometry. In order to introduce geometry to the Mundurucu participants, the scientists asked them to imagine two worlds, one flat (plane) and the second round (sphere), on which were dotted villages (corresponding to the points in Euclidean geometry) and paths (straight lines). They then asked them a series of questions illustrated by geometric figures displayed on a computer screen.
Around thirty adults and children from France and the United States, who, unlike the Mundurucu, had studied geometry at school, were also subjected to the same tests.
The result was that the Mundurucu Indians proved to be fully capable of resolving geometric problems, particularly in terms of planar geometry. For example, to the question Can two paths never cross?, a very large majority answered Yes. Their responses to the second test, that of the triangle, highlight the intuitive character of an essential property in planar geometry, namely the fact that the sum of the angles of the apexes of a triangle is constant (equal to 180°).
Art by Jetter Green