64 lines
1.3 KiB
Markdown
64 lines
1.3 KiB
Markdown
---
|
|
id: 5900f3a51000cf542c50feb8
|
|
challengeType: 5
|
|
title: 'Problem 57: Square root convergents'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
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 + ... ))) = 1.414213...
|
|
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 one-thousand expansions, how many fractions contain a numerator with more digits than denominator?
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler57()</code> should return 153.
|
|
testString: 'assert.strictEqual(euler57(), 153, "<code>euler57()</code> should return 153.");'
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler57() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler57();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|