In algebra variables express a relationship within an equation and these are often used to give meaningful expressions to represent practical situations. These relationships often require a constant to be included in order to balance the equation turning the relationship from one of proportionality to one of equality. The variables themselves are only constant for a given set of conditions. i.e The voltage across a resistance of 60 ohms carrying a current of 4 amps will be 240v. (V= current x resistance). A separate constant is not needed in this case as the resistance is defined by the other two properties.
In science one example of a constant that is thought to be variable is the speed of light, which for all practical purposes is considered to be constant but is thought to have changed gradually with time. I don't know what possible ways there are of verifying this.
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The constant is the number; the variable is the letter.
The question is about an oxymoronic expression. A constant cannot be a variable and a variable cannot be a constant!
Constant variable
The opposite of the word "constant" is "variable".
The constant variable.