Gaussian Brackets

Gaussian brackets are notation published by Gauss in Disquisitiones Arithmeticae and defined by

 [ ]=1
 [a_1,a_2]=[a_1]a_2+[ ]

Gaussian brackets are useful for computing simple continued fractions because


Note that the Gaussian bracket notation [a_1,a_2,...] corresponds to a different quantity than that denoted by the more established simple continued fraction notation


See also

Continued Fraction, Regular Continued Fraction, Simple Continued Fraction

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Fowler, D. H. The Mathematics of Plato's Academy: A New Reconstruction, 2nd ed. Oxford, England: Oxford University Press, 1999.Herzberger, M. Modern Geometrical Optics. New York: Interscience Publishers, pp. 457-462, 1958.

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Gaussian Brackets

Cite this as:

Weisstein, Eric W. "Gaussian Brackets." From MathWorld--A Wolfram Web Resource.

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