---
id: 5900f4511000cf542c50ff63
challengeType: 5
title: 'Problem 228: Minkowski Sums'
forumTopicId: 301871
---

## Description
<section id='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?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler228()</code> should return 86226.
    testString: assert.strictEqual(euler228(), 86226);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler228() {

  return true;
}

euler228();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>