Recursive methods are essentially methods that call themselves. They require powerful logic skills to comprehend and implement. Lets take the implementation for the Math.power function. We could write it like this:

public static int power(int base, int power){ if(power == 0) return 1; else{ int answer = 1; int count = 1; while(count <= power){ answer *= base; count++; } return answer; } }

This accomplishes the task, but uses a loop. The same code implemented recursively is:

public static int power(int base, int power){ if (power == 0) return 1; else return base * power(base, power-1); }

As you can see, the latter solution is shortened and, I think, much more elegant. The concept, though, is hard to understand. First, we need to start with a base case, or case where no recursion takes place. In this example, it is power == 0. If we didn't have a base case, the recursion would go on indefinitely. Second, our recursion loop needs to make progress toward the base case or nothing will happen. In this example it is power(base, power-1). Here is a breakdown of what is happening.

Lets take the case of 2 to power of 4. We know the answer is 16, but how does recursion get this.

1) we call power(2,4)

2) power(2,4) calls power(2,3)

3) power(2,3) calls power(2,2)

4) power(2,2) calls power(2,1)

5) power(2,1) calls power(2,0)

6) power(2,0) returns 1

7) power(2,1) returns (2 * 1) or 2

8) power(2,2) returns (2 * 2) or 4

9) power(2,3) returns (2 * 4) or 8

10) power(2,4) returns (2 * 8) or 16

As you can see, power starts at it's highest value and works toward power==0. When it does reach power==0, the recursion moves backward towards the original method call (power(2,4)) a spits out a value. To simply put it, the method expresses 2^4 as 2*2*2*2. The recursion is basically adding another "*2" to the end. This is, in a nutshell, how recursion works.