The Historical Development of the Concept of Angle ( 2 ) 1

In the first part of this article published in the Summer 1990 issue of the Mathematics Educator, we discussed the use of directions by paleolithic and neolithic cultures. We saw how angles, as distinct geometric entities, had their origin in Greek culture, and we discussed several problems associated with them. We also saw how other cultures like the Chinese and the Hindus could solve geometric problems without angles. In this second part, we will proceed by discussing the notion of angle during the middle ages, the narrowing of the concept by seventeenth century mathematicians, and the enlargement of the notion of angle by nineteenth century mathematicians. Finally, we will briefly discuss contemporary approaches to angle, namely its disappearance in a branch of contemporary geometry.