Variable

Some algebraic equations, known as functions, represent relationships between two variables. In these functions, the value of one variable is said to depend on the value of the other. For instance, the sales tax on a pair of gym shoes depends on the price of the shoes. The distance a car travels in a given time depends on its speed. In these examples, the sales tax and the distance travelled are called dependent variables because their value depends on the value of the other variable in the function. This variable, known as the independent variable, is represented by the price of the gym shoes and the speed of the car.

Using variables to represent unknowns was an important part of the development of algebra. Variables have distinct advantages over the rhetorical (written out) algebra of the ancient Greeks. They allow mathematical ideas to be communicated clearly and briefly. The equation 2x² + y = 6 is much clearer than the equivalent phrase "two times some number times itself, plus some other number is equal to six." Variables also make mathematics more generally applicable. For instance, the area of a certain square with sides of 2 cm is 4 cm². The area of another square with 3 cm sides is 9 cm². By representing the side of any square with the variable s, the area of any square can be represented by s².

Although any letter or character can represent any variable, over time, mathematicians and scientists have used certain letters to represent certain values. The letters x, y, and z are the most commonly used variables to represent unknown values in polynomial equations. The letter r is often used to represent the radius of a circle and the character q is used to signify an unknown angle. Other commonly used variables include t to represent time, s to represent speed, and p to represent pressure.