Didactical analysis of primary geometric concepts iii

Milosav M. Marjanoviĉ

This paper contains essays on angle, circle and rectangle aimed to illuminate these concepts at all levels of their gradual building. Angles, when conceived of as magnitudes expressing the degree up to which directions of two rays differ, are compared using an instrument called comparator---protractor without graduation on it. Avoiding the formalism of differential calculus, we approach the concept of curvature of lines in an elementary way. Speaking of the average rate of the change of direction of tangent happens to be sufficient to see circles as the lines being equally curved everywhere and the straight lines as being nowhere curved. Rectangular shape (an inherent geometry concept) and rectangle (a visual geometry concept) are treated with due attention to detail. In particular, the role of this shape has been related to everyday comparison in length and width. When comparison is concerned, such an activity is clearly seen as the relationship between magnitudes of the same nature.