a^2+b^2+c^2-ab-bc-ac =1/2(2a^2+2b^2+2c^2-2ab-2bc-2ac) =1/2(a^2+b^2-2ab+a^2-2ac+c^2+b^2-2bc+c^2) =1/2[(a-b)^2+(b-c)^2+(a-c)^2]
