That is what dictionary.com says about quaternions. I have read up on them to start with 3D programming, with great thanks to confuted. So where do a, b, c, d, i, j, and k come from? After I study more about these, I will most definetely have more questions, but please stick with me for it!! Thanks all !Any number of the form a + bi + cj + dk where a, b, c, and d are real numbers, ij = k, i2 = j2 = -1, and ij = -ji. Under addition and multiplication, quaternions have all the properties of a field, except multiplication is not commutative.