题目228：明可夫斯基和
Minkowski SumsLet 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?
题目：
设 Sn 为正 n 多边形——或者说为顶点 vk (k = 1,2,…,n) 满足以下坐标的图形：
xk = cos（ 2k-1/n ×180°）
yk = sin（2k-1/n ×180°）
每个 Sn 表示一个由边界上和图形内部的点组成的填充图形。
明可夫斯基和 S+T，为 T 中每个点加上 S 中每个点的结果，其中点的加法用坐标表示为：(u, v) + (x, y) = (u+x, v+y)。
例如，S3 与 S4 的和为下面的粉红色六边形：
S1864 + S1865 + … + S1909 有多少条边?
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