ABSTRACT
Long before he can think about ‘similar’ figures a child can directly perceive whether figures having different dimensions possess similar relationships. Hence the origin of the idea of proportions must be sought in the actual perception of figures. But even within the realm of perception there is room for variations in the process of ‘transposition’, as the perceptual recognition of two shapes as similar has been called. Thus transposition from a small square to a large one involves the square considered as a whole (the square as such), the size of the angles (which remain right-angles), and the relative lengths of the sides or diagonals (which remain equal to each other). On the other hand if two rectangles are compared, the overall shape and the angles can remain the same, though one figure may be longer or wider than the other. This transposition entails transposition of angles but not the relative lengths of the sides. Finally, a pair of triangles or rhombuses may be perceived as the same overall shape in that they are always triangles or rhombuses, but this does not entail transposition of the angles or the relative length of the sides. Thus it may be seen that perceptual transposition by no means leads automatically to perception of geometric similarity.
