53 lines
1.7 KiB
Markdown
53 lines
1.7 KiB
Markdown
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---
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id: 5900f4f71000cf542c51000a
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title: 'Problem 395: Pythagorean tree'
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challengeType: 5
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forumTopicId: 302060
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dashedName: problem-395-pythagorean-tree
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---
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# --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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1. 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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2. Attach a square to each leg of the right triangle, with one of its sides coinciding with that leg.
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3. 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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<img class="img-responsive center-block" alt="animation showing 8 iterations of the procedure" src="https://cdn.freecodecamp.org/curriculum/project-euler/pythagorean-tree.gif" style="background-color: white; padding: 10px;" />
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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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# --hints--
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`pythagoreanTree()` should return `28.2453753155`.
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```js
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assert.strictEqual(pythagoreanTree(), 28.2453753155);
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```
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# --seed--
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## --seed-contents--
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```js
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function pythagoreanTree() {
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return true;
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}
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pythagoreanTree();
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```
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# --solutions--
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```js
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// solution required
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```
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