
Quaternion is a 4tuple with rules for addition and multiplication . . . . . .
Wikipedia: Quaternion
Mathworld: Quaternion
Fact archive: Quaternion
Euclidean Space: quaternions
Complex, Quaternion, Octonion, and Sedenion numbers are ntuples of real numbers, where n=2,4,8,16, respectively.
Sums of Squares  Every positive integer can be expressed as the sum of four squares; Primes of the form 4k+1 (and their products using the Complex Product Identity) can be expressed as the sum of two squares; Primes of the form 4k+3 (and their products using the Quaternion Identity) can be expressed as the sum of four squares.
The webmaster and author of this Math Help site is Graeme McRae.