formulaes.txt

Brahmagupta’s formula
s = (a+b+c+d)/2
area = sqrt((s-a)*(s-b)*(s-c)*(s-d))
d = 0 => area = sqrt((s-a)*(s-b)*(s-c)*s)

a and m coprime
a^ϕ(m) = 1 mod m
a^n = a^(n mod ϕ(m))

a and m not coprime, a,m and n >= log2m
a^n = a ^ ( ϕ(m)+[n mod ϕ(m)] ) mod m

Vertex Cover
To construct such a cover, let U be the set of unmatched vertices in L(possibly empty), and let Z be the set of vertices that are either in U or are connected to U U by alternating paths (paths that alternate between edges that are in the matching and edges that are not in the matching). Let K = ( L ∖ Z ) ∪ ( R ∩ Z ).