variable and constant

variable and constant

The magnitudes studied in mathematics are divided into two classes: constants and variables.

constant

A magnitude is called a constant when it retains the same (invariable) value in a given investigation.

variable

 a magnitude is a variable when, for one reason or another, it can assume different values in a given investigation. 

constant will to be variable!

It is evident from these definitions that the concepts of constant and variable are largely a matter of convention and depend on the circumstances in which the given phenomenon is studied. A magnitude that may be considered as a constant under certain conditions, can become a variable under different conditions, and conversely.

example

For instance, it is important to know, when measuring the weights of bodies, whether the weighing operations are carried out at the same point of the earth's surface, or at different points: if the measurements are made at the same point, the acceleration due to gravity, on which the weight depends, will remain constant, and differences in weight between different bodies will depend only on their masses. On the other hand, if the measurements are made at different points on the

earth's surface, the acceleration due to gravity cannot be looked on as a constant, since the centrifugal force due to the rotation of the earth must be considered. As a result of this factor, the same body will weigh less at the equator than at the poles, as can be observed if a spring-balance is used, instead of a lever-balance. Similarly, the length of the rods used in the construction of some technical device can be looked on as invariable for the purposes of rough calculation. When greater accuracy is needed, so that regard is taken of the effect of temperature on the measurement, the length of a rod becomes variable, with the natural result that all calculations become more complex.

the source:

A COURSE OF Higher Mathematics VOLUME I. SMIRNOV.

By: Fady tarek