54 lines
1.3 KiB
Markdown
54 lines
1.3 KiB
Markdown
---
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id: 5900f4511000cf542c50ff63
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title: 'Problem 228: Minkowski Sums'
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challengeType: 5
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forumTopicId: 301871
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dashedName: problem-228-minkowski-sums
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---
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# --description--
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Let $S_n$ be the regular $n$-sided polygon – or shape – whose vertices $v_k (k = 1, 2, \ldots, n)$ have coordinates:
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$$\begin{align}
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& x_k = cos(\frac{2k - 1}{n} × 180°) \\\\
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& y_k = sin(\frac{2k - 1}{n} × 180°)
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\end{align}$$
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Each $S_n$ is to be interpreted as a filled shape consisting of all points on the perimeter and in the interior.
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The Minkowski sum, $S + T$, of two shapes $S$ and $T$ is the result of adding every point in $S$ to every point in $T$, where point addition is performed coordinate-wise: $(u, v) + (x, y) = (u + x, v + y)$.
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For example, the sum of $S_3$ and $S_4$ is the six-sided shape shown in pink below:
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<img class="img-responsive center-block" alt="image showing S_3, S_4 and S_3 + S_4" src="https://cdn.freecodecamp.org/curriculum/project-euler/minkowski-sums.png" style="background-color: white; padding: 10px;">
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How many sides does $S_{1864} + S_{1865} + \ldots + S_{1909}$ have?
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# --hints--
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`minkowskiSums()` should return `86226`.
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```js
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assert.strictEqual(minkowskiSums(), 86226);
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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 minkowskiSums() {
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return true;
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}
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minkowskiSums();
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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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