In each case we have a quadratic form
Q
with
Q
(
x
)
=
x
x
―
≥
0
Q
(
x
)
=
0
⟺
x
=
0
and
Q
(
x
y
)
=
Q
(
x
)
Q
(
y
)
So, the real numbers, complex numbers, quaternions and octonions are called
'normed division algebras'.
They're the only ones. Repeating the process does not give another!
