Mathematics
Solving Recurrence Relations with the Characteristic Equation
Quick fact
The characteristic equation method is essentially solving a linear recurrence by guessing that the solution grows exponentially, which reduces the problem to a familiar algebraic equation.
Why this is interesting
You know the Fibonacci sequence: each number is the sum of the previous two. But what if you wanted the 100th term without calculating all 99 before it? There's a mathematical shortcut hidden in a quadratic equation.