---
id: 5900f4511000cf542c50ff63
challengeType: 5
title: 'Problem 228: Minkowski Sums'
---
## Description
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?
## Instructions
## Tests
```yml
tests:
- text: euler228() should return 86226.
testString: assert.strictEqual(euler228(), 86226, 'euler228() should return 86226.');
```
## Challenge Seed
```js
function euler228() {
// Good luck!
return true;
}
euler228();
```