babylonian-method

Babylonian Method for Finding Square Roots

Background

Attractive fixed points play a starring role in this famous method for calculating square roots.

The number you want to find the square root of is called the radicand.

It's square root is some number that is equal to the radicand divided by that same number.

squareRootFn(radicand) === someNumber === radicand / someNumber

For example,

squareRootFn(16) === 4 === 16 / 4

Read more about the Babylonian method and other square root algorithms here

Finding the Square Root

Step 1:

• Guess a number less than half of your radicand

Step 2:

• If your guess is smaller than the actual answer, the radicand divided by your guess will be larger than the answer, and vice versa. The true answer will always be somewhere in between the two values: your guess and the result of the radicand divided by your guess.

Step 3:

• After your initial guess, take both values and find their average. Use this value as your new guess and keep going. You will converge towards the true square root at a fairly nice speed.

Fun fact: The number of correct digits in your approximation will roughly double after every iteration.

Getting Started

The file you will be editing is babylonian.js.

The babylonian-test.js file includes a test suite to run your code against.

Run node babylonian-test.js to run the test suite in full. As you write code to pass tests, make sure you unskip succeeding tests by changing test.skip to just test.