Classifying shapes

Technical terms in geometry - part 1

Why are there so many technical terms to learn in geometry? We need the special language of geometry in order to classify shapes into categories. Classification is an important intellectual process that helps us to make sense of our experiences. By coding information into categories we condense it and gain some control over it. Classification is at the heart of mathematics at all levels. The intellectual process involved is another example of the ‘same but different’ principle.

Teaching Point

Pupils will develop geometric concepts by experiences of classifying, using various attributes of shapes, informally in the first instance, looking for exemplars and non-exemplars, and discussing the relationships between shapes in terms of sameness and differences.

We form categories in mathematics by recognising attributes shared by various elements (such as numbers or shapes). These elements are then formed into a set.

Although the elements in the set are different they have something the same about them. When it is a particularly interesting or significant set we give it a name. Because it is important that we should be able to determine definitely whether or not a particular element is in the set, the next stage of the process is often to formulate a precise definition.

For example, in number we recognize that the attribute shared by these numbers, (2, 3, 5, 7, 11, 13, 17 ….), is that they have no factors apart from 1 and themselves. This led to putting them into a set and giving them a name, ‘prime numbers’. Because of some uncertainty about whether or not the number 1 was prime, a definition was then produced, namely, that a prime number is a natural number that has precisely two factors.