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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-228-minkowski-sums.md

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+---
+id: 5900f4511000cf542c50ff63
+title: 'Problem 228: Minkowski Sums'
+challengeType: 5
+forumTopicId: 301871
+dashedName: problem-228-minkowski-sums
+---
+
+# --description--
+
+<!-- TODO Use MathJax and re-write from projecteuler.net -->
+
+Let Sn be the regular n-sided polygon – or shape – whose vertices
+
+vk (k = 1,2,…,n) have coordinates:
+
+xk = cos( 2k-1/n ×180° )
+
+yk = sin( 2k-1/n ×180° )
+
+Each Sn is to be interpreted as a filled shape consisting of all points on the perimeter and in the interior.
+
+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).
+
+For example, the sum of S3 and S4 is the six-sided shape shown in pink below:
+
+How many sides does S1864 + S1865 + … + S1909 have?
+
+# --hints--
+
+`euler228()` should return 86226.
+
+```js
+assert.strictEqual(euler228(), 86226);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function euler228() {
+
+  return true;
+}
+
+euler228();
+```
+
+# --solutions--
+
+```js
+// solution required
+```