Editing Gaussian rational (section)

==Ford spheres==
The concept of [[Ford circle]]s 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 [[Euclidean space]], and for each Gaussian rational point in this plane one constructs a sphere tangent to the plane at that point. For a Gaussian rational represented in lowest terms as <math>p/q</math> (i.e. {{tmath|p}} and {{tmath|q}} are relatively prime), the radius of this sphere should be <math>1/2|q|^2</math> where <math>|q|^2 = q \bar q</math> is the squared modulus, and {{tmath|\bar q}} is the [[complex conjugate]]. The resulting spheres are [[tangent]] for pairs of Gaussian rationals <math>P/Q</math> and <math>p/q</math> with <math>|Pq-pQ|=1</math>, and otherwise they do not intersect each other.<ref>{{citation|title=Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning|first=Clifford A.|last=Pickover|authorlink=Clifford A. Pickover|publisher=Oxford University Press|year=2001|isbn=9780195348002|contribution=Chapter 103. Beauty and Gaussian Rational Numbers|pages=243–246|url=https://books.google.com/books?id=52N0JJBspM0C&pg=PA243}}.</ref><ref>{{citation|year=2015|arxiv=1503.00813|title=Ford Circles and Spheres|first=Sam|last=Northshield|bibcode=2015arXiv150300813N}}.</ref>