In Section 1.1, we talked about constants and variables in an abstract way. When we deal with the applications of mathematics in science, engineering, etc., we can say:
- A quantity is anything that can be measured, as distance, time, weight, and number.
- A quantity whose value remains unchanged throughout a given problem or discussion is called a constant.
For example, if we assume that the temperature does not change during an experiment, then the temperature (often denoted by $T$ in physics) is a constant.
- A quantity which changes its value in the course of a problem or discussion is called a variable.
For example, if we heat up the water in a container, its temperature $T$ changes. Then here, $T$ is a variable. Or consider a particle that moves in a circle (Figure 1). If we connect this particle to the center of the circle, the angle $\theta$ that this ray makes with the horizon is a variable that varies between 0 and $360^{\circ}$, but the distance of this particle from the center of the circle (denoted by $R$) is a constant.
- Parameters or arbitrary constants are constants to which infinitely many numbers may be assigned, and they retain these assigned values through the investigation.
For example, one form of the equation of a straight line is $y=mx+b$, where $m$ and $b$ represent the slope and the $y$-intercept of the line. $m$ and $b$ can assume any values but those values are fixed numbers, so $m$ and $b$ are two parameters of the equation of a straight
line.