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can be generalized from the rational numbers to the
Gaussian rationals, giving Ford spheres. In this construction, the complex numbers are embedded as a plane in a three-dimensional
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Wonders of
Numbers: Adventures in Mathematics, Mind, and Meaning
51:. The set of all Gaussian rationals forms the Gaussian rational
605:(2001), "Chapter 103. Beauty and Gaussian Rational Numbers",
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are relatively prime), the radius of this sphere should be
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The field of
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The field of
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449:for pairs of Gaussian rationals
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408:is the squared modulus, and
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432:{\displaystyle {\bar {q}}}
346:{\displaystyle 1/2|q|^{2}}
70:to the field of rationals
632:Northshield, Sam (2015),
546:{\displaystyle |Pq-pQ|=1}
144:(as a metric space). The
634:Ford Circles and Spheres
578:Algebraic Number Theory
206:{\displaystyle \{1,i\}}
78:Properties of the field
678:-related article is a
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498:{\displaystyle p/q}
470:{\displaystyle P/Q}
250:{\displaystyle p/q}
119:complex conjugation
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729:Cyclotomic fields
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296:{\displaystyle q}
272:{\displaystyle p}
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557:References
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