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curriculum/challenges/japanese/10-coding-interview-prep/project-euler/problem-465-polar-polygons.md
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---
id: 5900f53d1000cf542c510050
title: 'Problem 465: Polar polygons'
title: '問題 465: 極の多角形'
challengeType: 5
forumTopicId: 302140
dashedName: problem-465-polar-polygons
@ -8,27 +8,27 @@ dashedName: problem-465-polar-polygons
# --description--
The kernel of a polygon is defined by the set of points from which the entire polygon's boundary is visible. We define a polar polygon as a polygon for which the origin is strictly contained inside its kernel.
多角形の核は、その多角形の全範囲をそこから見渡せるような点の集合として定義されます。 原点が核の中に厳密に含まれている多角形を「極の多角形」と定義します。
For this problem, a polygon can have collinear consecutive vertices. However, a polygon still cannot have self-intersection and cannot have zero area.
この問題では、多角形は同一線上に連続する頂点を持つことができます。 しかし、多角形は自己交差してはならず、面積が 0 であってはいけません。
For example, only the first of the following is a polar polygon (the kernels of the second, third, and fourth do not strictly contain the origin, and the fifth does not have a kernel at all):
例えば、次のうち 1 つ目だけが極の多角形です (2 つ目、3 つ目、4 つ目の多角形の核は厳密には原点を含んでおらず、5 つ目には核が全くありません)。
<img class="img-responsive center-block" alt="five example polygons" src="https://cdn.freecodecamp.org/curriculum/project-euler/polar-polygons.png" style="background-color: white; padding: 10px;" />
<img class="img-responsive center-block" alt="多角形の 5 例" src="https://cdn.freecodecamp.org/curriculum/project-euler/polar-polygons.png" style="background-color: white; padding: 10px;" />
Notice that the first polygon has three consecutive collinear vertices.
1 つ目の多角形で、3 つの頂点が同一線上で連続していることに注目してください。
Let $P(n)$ be the number of polar polygons such that the vertices $(x, y)$ have integer coordinates whose absolute values are not greater than $n$.
絶対値が $n$ を超えない整数座標 $(x, y)$ に頂点があるような極の多角形の個数を、$P(n)$ とします。
Note that polygons should be counted as different if they have different set of edges, even if they enclose the same area. For example, the polygon with vertices [(0,0), (0,3), (1,1), (3,0)] is distinct from the polygon with vertices [(0,0), (0,3), (1,1), (3,0), (1,0)].
注意点として、たとえ同じ領域を囲んでいても、辺の集合が異なる多角形は区別して数えられます。 例えば、[(0,0), (0,3), (1,1), (3,0)] を頂点とする多角形は、[(0,0), (0,3), (1,1), (3,0), (1,0)] を頂点とする多角形と区別されます。
For example, $P(1) = 131$, $P(2) = 1\\,648\\,531$, $P(3) = 1\\,099\\,461\\,296\\,175$ and $P(343)\bmod 1\\,000\\,000\\,007 = 937\\,293\\,740$.
例えば、$P(1) = 131$, $P(2) = 1\\,648\\,531$, $P(3) = 1\\,099\\,461\\,296\\,175$, $P(343)\bmod 1\\,000\\,000\\,007 = 937\\,293\\,740$ です。
Find $P(7^{13})\bmod 1\\,000\\,000\\,007$.
$P(7^{13})\bmod 1\\,000\\,000\\,007$ を求めなさい。
# --hints--
`polarPolygons()` should return `585965659`.
`polarPolygons()` は `585965659` を返す必要があります。
```js
assert.strictEqual(polarPolygons(), 585965659);