1.3 KiB
1.3 KiB
| 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:
<img class="img-responsive center-block" alt="image showing S_3, S_4 and S_3 + S_4" src="https://cdn.freecodecamp.org/curriculum/project-euler/minkowski-sums.png" style="background-color: white; padding: 10px;">
How many sides does $S_{1864} + S_{1865} + \ldots + S_{1909}$ have?
# --hints--
`minkowskiSums()` should return `86226`.
```js
assert.strictEqual(minkowskiSums(), 86226);
```
# --seed--
## --seed-contents--
```js
function minkowskiSums() {
return true;
}
minkowskiSums();
```
# --solutions--
```js
// solution required
```