Irreducible Gaussian Fractions

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Move the sliders to see the irreducible fractions for Gaussian integers in the given range and with specified zoom level in the complex plane.

Contributed by: Eric W. Weisstein (March 2011)
Suggested by: Michael Trott
Open content licensed under CC BY-NC-SA


Snapshots


Details

An irreducible fraction is a fraction such that and have no common factor. This definition applies to ratios of ordinary integers as well as to Gaussian integers, which are of the form , where and are integers and . By rationalizing the denominator, such complex fractions can be put in the form , where and are real fractions; are the numbers plotted.

Heavily based on code by Michael Trott in The Mathematica GuideBook for Graphics New York: Springer-Verlag, 2004.



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