Constants – Fixed Values in Algebra
A constant is a value that does not change. In algebra, constants appear alongside variables in expressions and equations. Recognising them helps you understand the structure of any algebraic statement.
Some constants are so important they have been studied and refined for thousands of years — pi appears in Babylonian and Egyptian texts dating back to around 1900 BCE, though it was the Greek mathematician Archimedes (c. 250 BCE) who first calculated rigorous upper and lower bounds for it using inscribed and circumscribed polygons. Constants like pi, e, and the golden ratio are called “mathematical constants” specifically because their value is fixed everywhere in the universe — unlike a coefficient such as the “5” in 5x, which is just fixed for one particular problem.
What Is a Constant?
A constant is a fixed number whose value never changes within a given problem. It may be a plain number like 5, or a named constant like pi (approximately 3.14159).
Constants vs Variables
| Constant | Variable | |
|---|---|---|
| Value | Fixed | Can change or is unknown |
| Example in 3x + 7 | 3 and 7 | x |
| Written as | Plain numbers or named symbols | Letters (x, y, n, etc.) |
Famous Mathematical Constants
| Constant | Symbol | Approximate Value | Where Used |
|---|---|---|---|
| Pi | pi | 3.14159... | Circle circumference and area |
| Euler number | e | 2.71828... | Exponential growth and logarithms |
| Golden ratio | phi | 1.61803... | Art, nature, and geometry |
Constants in Expressions
In the expression 5x + 3, the number 5 is a coefficient (a constant multiplied by a variable) and 3 is a standalone constant called a constant term. Both are fixed numbers — they do not depend on x.
4 is the coefficient of t squared. 7 is the coefficient of t. 12 is the constant term. The variable is t.
pi is a constant (approximately 3.14159). r is a variable (the radius can be any value). A is also a variable (it changes as r changes).
Why Constants Matter
Constants set the scale and shift of algebraic relationships. In y = 2x + 3, the constant 2 controls how steeply y grows with x, and 3 shifts the whole relationship up by three units. Changing a constant changes the entire behaviour of the expression.
Key Takeaways
- A constant is a fixed number that does not change in a given context.
- Coefficients are constants multiplied by variables.
- Constant terms stand alone — they are not multiplied by any variable.
- Famous constants like pi and e appear throughout mathematics and science.