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From the Daily Mail

Tests taken by an Amazonian tribe indicate that children understand the basic principles of geometry without an education.

Amazonian children in the Mundurucu tribe could solve basic problems with lines and points, suggesting that geometry skills are innate in humans.

According to a paper published in the Proceedings of the National Academy of Sciences, the results show that abstract geometry may be learned naturally through day-to-day interaction with the world.

Researchers found eight children aged between seven and 13, as well as 22 adults from the Mundurucu tribe could identify the number of lines that can be drawn through two points, correctly complete unfinished triangles and estimate angles.

Their results were compared with equivalent tests on French and U.S. schoolchildren.

Basic geometric principles as most people know them were first established by the Greek mathematician Euclid about 2,300 years ago.

'Euclidean geometry' includes familiar tenets such as the fact that the angles of a triangle always add up to the same total, a line can connect two points, and that two parallel lines never cross.

The Amazonian tribe test results 'suggest Euclidean geometry, inasmuch as it concerns basic objects such as points and line on a plane, is a cross-cultural universal that results from the inherent properties of the human mind as it develops in its natural environment' according to the paper's authors.

Researchers said the control groups showed the same performance profile as the Amazonians, except for the American children, who were younger.

The researchers asked the children and adults questions about lines, planes, angles, triangles and spheres.

They were given sketches of lines and asked questions such as 'Can a line be drawn through two points?' and 'Can two such lines be drawn?'

All groups performed better at planar than spherical geometry, the study said.