Ridders' method
Imagine you're trying to find the answer to a math problem, but you don't know what the answer is, only that it's between two different numbers. Ridders' method is like a guessing game that helps you get closer to the answer by dividing up the space between the two numbers you already know.
First, you pick a spot right in the middle of those two numbers. This is your first guess. Then, you use that guess to make another guess that's even closer to the real answer. But how do you do that?
You draw a straight line between your two starting numbers and see where your first guess lands on that line. Then, you draw another straight line through that first guess, but instead of being straight up and down like the first line, it's angled off to one side. This new line should hit the original line at a different spot.
Now, you look at where that second line hits the original line and use that as your new guess. This should be even closer to the real answer. You keep doing this over and over, making new guesses that get closer and closer to the answer until you've found it.
So when you're trying to find the answer to a math problem and you only know two numbers it could be between, Ridders' method helps you make smart guesses that get closer to the real answer with each one.
First, you pick a spot right in the middle of those two numbers. This is your first guess. Then, you use that guess to make another guess that's even closer to the real answer. But how do you do that?
You draw a straight line between your two starting numbers and see where your first guess lands on that line. Then, you draw another straight line through that first guess, but instead of being straight up and down like the first line, it's angled off to one side. This new line should hit the original line at a different spot.
Now, you look at where that second line hits the original line and use that as your new guess. This should be even closer to the real answer. You keep doing this over and over, making new guesses that get closer and closer to the answer until you've found it.
So when you're trying to find the answer to a math problem and you only know two numbers it could be between, Ridders' method helps you make smart guesses that get closer to the real answer with each one.