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Ordered Pairs

Published online by Cambridge University Press:  28 July 2025

F. Gerrish
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Most of us who teach “complex numbers” (especially to classes where the emphasis is primarily mathematical) take the opportunity at some stage to place the theory firmly on the concept of ordered pair (of real numbers), assuring the students that they have long been familiar with this notion (e.g. plane cartesian coordinates) and its manipulation (e.g. rational numbers as ordered pairs of integers and their arithmetic) without explicitly recognising it. Later we might ask (or even be asked!): How about ordered pairs of complex numbers? This article, consisting of chips from several quite old blocks, offers some forwardlooking ideas for investigation and development. An excellent general reference is [0].

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Articles
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The Mathematical Gazette , Volume 79 , Issue 484 , March 1995, pp. 30 - 46
Copyright
Copyright © The Mathematical Association 1995

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Footnotes

*

A much expanded version of a “short presentation” (at the 1993 MA Conference in Plymouth), itself extracted from a talk I gave in 1965 to a student Mathematical Society.

References

0. Ewing, J.H. (ed.), Numbers, Springer (1991).Google Scholar
1. Altmann, S.L., Hamilton, , Rodrigues, and the quaternion scandal, Mathematics Magazine 62 (1989) pp. 291–308.CrossRefGoogle Scholar
2. Albert, A.A. (ed.), Studies in modern algebra, Mathematical Association of America (1963).Google Scholar
3. Shafer, R.D., On the algebras formed by the Cayley-Dickson process, American Journal of Mathematics 76 (1954) pp. 435–446.CrossRefGoogle Scholar
4. Jacobson, N., Basic algebra I (2nd ed.), Freeman (1985).Google Scholar
5. Massey, W.S., Cross products of vectors in higher-dimensional euclidean spaces, American Mathematical Monthly 90 (1983) pp. 697–700.CrossRefGoogle Scholar
6. Walsh, B., The scarcity of cross products on euclidean spaces, American Mathematical Monthly 74 (1967) pp. 188–194.Google Scholar
7. Sobczyk, A., Equivalence of an identity in vector analysis to quaternion associativity, and ramifications, American Mathematical Monthly 88 (1981) pp. 441–443.CrossRefGoogle Scholar