Geometry rules

Plato declared that "God forever geometrizes." Consequently geometry offers a window from which to view the Divine Wisdom of Universe. Bucky's system of systems, i.e. Synergetic Geometry, was on ongoing discovery of the eternal principles operating in Nature and Universe. He was convinced that these principles were accessible to all via our everyday experiences.

Bucky further believed that spherical geometry is intuitively much easier to learn than plane geometry and should be taught as a lead-in to plane geometry because it is based on experience of physical space and systems.

"We are all born geniuses," he reminded us. Some of us are just "de-genuised" faster than others by our formal compartmentalized educational systems. (GW)

Learning Geometry Without a Protractor

By Sindyan N. Bhandoo
New York Times
May 23, 2011

Although many school-going youth might disagree, a new study finds that geometry is an intuitive subject that is easy to grasp even in the absence of formal training.

Researchers posed questions in Euclidean planar geometry to adults and children from the Mundurucú community, an isolated indigenous group in the Amazon. Despite having no formal education, the Mundurucú were able to quickly grasp concepts in planar geometry relating to points, lines and triangles.

The study appears in the current issue of Proceedings of the National Academy of Sciences.

The Mundurucú were able to correctly answer questions like, “Can a line be made to cross two other parallel-looking lines?” and “Can a line cross one of two parallel-looking lines but not the other?”

Their aptitude was in fact similar to that of American adults and French children who did have formal training in geometry, said Véronique Izard, a psychologist at the Descartes campus of the University of Paris and the study’s first author. The children were of the same age as the Mundurucú children — from 7 to 13.

“I would say that this means Euclidean geometry is probably universal to all human beings,” she said. “We find people grasping concepts of geometry that go beyond the perceivable.”

It remains to be understood why this is so, she said.

Curiously, when the same tests were performed on young American children, ages 5 and 6, they fared poorly.

This means that if the ability to understand planar geometry is innate, it is something that appears only after time.

“Perhaps it’s something that is learned from the environment, but in this case it must be something generic to all environments,” Dr. Izard said.

She and her colleagues are continuing to study the issue.