Mathematical Definitions 1

Just as in other walks of life, when communicating math it is important to be precise about what you are trying to describe. For instance, if I describe something as a rectangle, it suggests that the shape has 4 sides, the opposite sides are equal in length, and all the internal angles are right-angles. If my shape is missing any of these properties then it is not a rectangle, and I could mislead other people.

There are a number of words that we use in everyday life that have a different, or more precise meaning when used mathematically. Think of the word ‘similar’. In day-to-day language we use ‘similar’ to compare two objects that are alike in some ways, but not identical. However, in math shapes can only be described as ‘similar’ if their corresponding sides are proportional to each other, AND corresponding angles are the same size. If we take the smaller shape, then each side is multiplied by the same scale factor to produce the enlargement, and all the angles stay the same.

Then there are those unusual words that only get used in math, but not in the real world. CONGRUENT is one of these, can you think of any more? You still need to know what they mean, so best you start tucking into that math dictionary!