22afc2a0ca
Co-authored-by: Oliver Eyton-Williams <ojeytonwilliams@gmail.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Beau Carnes <beaucarnes@gmail.com>
77 lines
1.7 KiB
Markdown
77 lines
1.7 KiB
Markdown
---
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id: 5900f4f71000cf542c51000a
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challengeType: 5
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isHidden: false
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title: 'Problem 395: Pythagorean tree'
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forumTopicId: 302060
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---
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## Description
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<section id='description'>
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The Pythagorean tree is a fractal generated by the following procedure:
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Start with a unit square. Then, calling one of the sides its base (in the animation, the bottom side is the base):
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Attach a right triangle to the side opposite the base, with the hypotenuse coinciding with that side and with the sides in a 3-4-5 ratio. Note that the smaller side of the triangle must be on the 'right' side with respect to the base (see animation).
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Attach a square to each leg of the right triangle, with one of its sides coinciding with that leg.
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Repeat this procedure for both squares, considering as their bases the sides touching the triangle.
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The resulting figure, after an infinite number of iterations, is the Pythagorean tree.
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It can be shown that there exists at least one rectangle, whose sides are parallel to the largest square of the Pythagorean tree, which encloses the Pythagorean tree completely.
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Find the smallest area possible for such a bounding rectangle, and give your answer rounded to 10 decimal places.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler395()</code> should return 28.2453753155.
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testString: assert.strictEqual(euler395(), 28.2453753155);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler395() {
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// Good luck!
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return true;
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}
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euler395();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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