What does the word dimensions mean in math?

Answer 1

The word dimensions has multiple meanings.

It can refer to measurements of an object like length width or depth, or it can refer to the number of directions of movement that are possible in a system. For example a line has one dimension because movement is only possible back and forth, a plane is said to have two dimensions because movement is possible in two directions (back and forth, side to side) while space has three dimensions.

In higher math, the concept of "dimension" has been generalized beyond the three we're familiar with in ordinary geometry. In this sense, the word refers to the count of separate "coordinates" or "parameters" that uniquely identity a particular element. For example, time is often treated as the fourth dimension because it's possible to use four numbers to uniquely describe an object's existence - 3 coordinates describe where it is in space and a fourth describes when it exists.