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

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4511000cf542c50ff63	Problem 228: Minkowski Sums	5	301871	problem-228-minkowski-sums

--description--

Let S_n be the regular $n$-sided polygon – or shape – whose vertices v_k (k = 1, 2, \ldots, n) have coordinates:

$$\begin{align} & x_k = cos(\frac{2k - 1}{n} × 180°) \\ & y_k = sin(\frac{2k - 1}{n} × 180°) \end{align}$$

Each S_n 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 S_3 and S_4 is the six-sided shape shown in pink below:

How many sides does S_{1864} + S_{1865} + \ldots + S_{1909} have?

--hints--

minkowskiSums() should return 86226.

assert.strictEqual(minkowskiSums(), 86226);

--seed--

--seed-contents--

function minkowskiSums() {

  return true;
}

minkowskiSums();

--solutions--

// solution required