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Irreducible Gaussian Fractions


	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 Suggested by: Michael Trott
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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 a+b i, where a and b 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.

Irreducible Fraction (Wolfram MathWorld)

The Mathematica GuideBook for Graphics (Wolfram web resource)

"Irreducible Gaussian Fractions" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/IrreducibleGaussianFractions/

Contributed by: Eric W. Weisstein

Suggested by: Michael Trott

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