59 lines
1.1 KiB
Markdown
59 lines
1.1 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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<!-- TODO Use MathJax and re-write from projecteuler.net -->
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Let Sn be the regular n-sided polygon – or shape – whose vertices
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vk (k = 1,2,…,n) have coordinates:
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xk = cos( 2k-1/n ×180° )
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yk = sin( 2k-1/n ×180° )
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Each Sn 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
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adding every point in S to every point in T, where point addition is performed coordinate-wise:
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(u, v) + (x, y) = (u+x, v+y).
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For example, the sum of S3 and S4 is the six-sided shape shown in pink below:
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How many sides does S1864 + S1865 + … + S1909 have?
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# --hints--
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`euler228()` should return 86226.
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```js
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assert.strictEqual(euler228(), 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 euler228() {
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return true;
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}
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euler228();
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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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