#A VERY SHORT PROOF OF A SHORT EMPEROR'S THEOREM
              #By SHALOSH B. EKHAD(ekhad@math.temple.edu)
 
      #Call this File shortie, do maple <shortie and see if it is true
 
                                d:=
                              proc(A,
                            B):(A[1]-B
                          [1])^2+(A[2]-B
                       [2])^2: end:c:=proc(T)
                     :solve({d(x,T[1])-d(x,T[2])
                   ,d(x,T[1])-d(x,T[3])},{x[1],x[2]
                }):[subs(%,x[1]),subs(%,x[2])]:end:e:=
              proc(A,B): {A, B, [(B[1]+A[1])/2-(A[2]-B[2])
          *3^(1/2)/2, B[2]/2+(A[1]-B[1])*3^(1/2)/2+A[2]/2]}:end:
       i:=proc(T):evalb(normal({d(T[1],T[2])-d(T[2],T[3]),d(T[2],T[
 3])-d(T[3],T[1])})={0}):end:N:=proc(): i({c(e(A,B)),c(e(B,C)),c(e(C,A))}): end:
                                  N();