The Quaternions

O. A. Ivanov
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O. A. Ivanov: St. Petersburg State University, Department of Mathematics and Mechanics

Chapter Chapter 8 in Easy as π?, 1999, pp 118-127 from Springer

Abstract: Abstract This chapter contains no elementary problems; its inclusion was prompted chiefly by internal necessity. The main motive was a desire to elucidate the strange and beautiful identity introduced at the end of the preceding chapter, known as Euler’s identity. Furthermore, the skew-field of quaternions is an archetype of a general (and important) kind of algebraic structure, namely that of an “algebra,” and so serves as a “jumping-off point” for studying such objects. Lastly, we have as a consequence of one of the main theorems of this chapter that the chain of number-fields ℚcℝ⊂ℂ extends no further.

Date: 1999
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DOI: 10.1007/978-1-4612-0553-1_8

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