Royaumont's Aftermath in Iceland - Motion Geometry, Transformations and Groups

Abstract

In the Meran Program in 1905 and at the Royaumont Seminar in 1959, among the main themes were transformation geometry, including motion geometry, and group theory. Those themes entered some Danish mathematics textbooks and the English School Mathematics Project's textbook series, both used in Iceland around 1970. One of the arguments for including group theory in school mathematics was that its structure corresponded to structures in the minds of children. Eventually, the emphasis on motion in geometry subordinated the structure of the transformation groups. These ideas proved short-lived in Iceland, they coincided with a great expansion of the school system, students were unaccustomed to studying textbooks in English, available teachers were not receptive, and mathematical analysis was considered neglected. In later applications, geometric transformations have become the basis of a large industry: animations in motion pictures and games.

In the Meran Program in 1905 and at the Royaumont Seminar in 1959, among the main themes were transformation geometry, including motion geometry, and group theory. Those themes entered some Danish mathematics textbooks and the English School Mathematics Project’s textbook series, both used in Iceland around 1970. One of the arguments for including group theory in school mathematics was that its structure corresponded to structures in the minds of children. Eventually, the emphasis on motion in geometry subordinated the structure of the transformation groups. These ideas proved short-lived in Iceland, they coincided with a great expansion of the school system, students were unaccustomed to studying textbooks in English, available teachers were not receptive, and mathematical analysis was considered neglected. In later applications, geometric transformations have become the basis of a large industry: animations in motion pictures and games.