It is possible to show that the square root of two can be expressed as an infinite continued fraction.
√ 2 = 1 + 1 / (2 + 1 + (2 + 1 / (2 + ...)))
By expanding this for the first four iterations, we get:
1 + 1/2 = 3/2 = 1.5
1 + 1 + (2+1/2) = 7/5 = 1.4
1 + 1 + (2+1/(2+1/2)) = 17/12 = 1.41666...
1 + 1 + (2+1/(2+1/(2+1/2))) = 41/29 = 1.41379...
The next three expansions are 99/70, 239/169, and 577/408, but the eighth expansion, 1393/985, is the first example where the number of digits in the numerator exceeds the number of digits in the denominator.
In the first n expansions, how many fractions contain a numerator with more digits than the denominator?
Information at Project Euler 057
Getting Started
In the input field, enter a whole number between 10 and 1000 (without leading zeros such as 010) and select the Submit Button. You will see the number entered as well as the number of fractions containing a numerator with more digits than the denominator, unless you have made an invalid input. For example, if you entered and submitted 10, you would expect the result to be 1. Select the Reset Button to clear the information or to start again.
User Stories
As a user, I expect to get an error message, if I do any of:
- Not enter anything in the input field
- Entering text other than a number
- Entering a number less than 10 or greater than 1000
- Including leading zeros such as 010
- Entering a number, but it is not an integer
As a user, if I selected the Reset Button, I can clear the information or start again.
As a user, I expect the function squareRootConvergents(10) to return a number.
As a user, I expect the function squareRootConvergents(10) to return 1.
As a user, I expect the function squareRootConvergents(100) to return 15.
As a user, I expect the function squareRootConvergents(1000) to return 153.
User Stories on function squareRootConvergents(n) taken from FreeCodeCamp - Coding Interview Prep - Project Euler 057
Information Architecture
The function squareRootConvergents(n) returns a number, where n is a number between 10 and 1000.
Allows the user to enter the number in order to find the number of fractions containing a numerator with more digits than the denominator. Performs checks on valid user input. If the input is not valid, an error message is displayed.
Uses HTML5, CSS3, JavaScript with BigInt, Bootstrap 5.2.2 and Google Fonts.
Ensure all user stories have been met.
Deployed on GitHub Pages at the main branch.
Square Root Symbol √ taken from w3schools.com - HTML Symbols, accessed on 12 November 2022.