Gaussian Brackets

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

(1)

(2)

(3)

(4)

Gaussian brackets are useful for computing simple continued fractions because

			(5)
			(6)

Note that the Gaussian bracket notation  corresponds to a different quantity than that denoted by the more established simple continued fraction notation

(7)

REFERENCES:

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.