数学公式备忘

1^2 + 2^2 + 3^2 + ... + n^2 = n*(n+1)*(2n+1)/6
1^3 + 2^3 + 3^3 + ... + n^3 = n^2*(n+1)^2/4
1^4 + 2^4 + 3^4 + ... + n^4 = n*(n+1)*(2n+1)*(3n^2+3n-1)/30

C(n,m) = C(n-1,m) + C(n-1,m-1)

以(x1,y1),(x2,y2)为对角顶点的正方形的另外两个顶点坐标为( (x1+x2+y2-y1)/2,(y1+y2-x2+x1)/2 ),( (x1+x2-y2+y1)/2,(y1+y2+x2-x1)/2 )
以(x1,y1),(x2,y2)为相邻顶点的正方形的另外两个顶点坐标为(x1-y2+y1,y1+x2-x1),(x2-y2+y1,y2+x2-x1)或者(x1+y2-y1,y1-x2+x1),(x2+y2-y1,y2-x2+x1)