Gaussian Brackets
المؤلف:
Herzberger, M
المصدر:
Modern Geometrical Optics. New York: Interscience Publishers
الجزء والصفحة:
...
2-5-2020
1005
Gaussian Brackets
Gaussian brackets are notation published by Gauss in Disquisitiones Arithmeticae and defined by
![[ ]=1](https://mathworld.wolfram.com/images/equations/GaussianBrackets/NumberedEquation1.gif) |
(1)
|
![[a_1]=a_1](https://mathworld.wolfram.com/images/equations/GaussianBrackets/NumberedEquation2.gif) |
(2)
|
![[a_1,a_2]=[a_1]a_2+[ ]](https://mathworld.wolfram.com/images/equations/GaussianBrackets/NumberedEquation3.gif) |
(3)
|
![[a_1,a_2,...,a_n]=[a_1,a_2,...,a_(n-1)]a_n+[a_1,a_2,...,a_(n-2)].](https://mathworld.wolfram.com/images/equations/GaussianBrackets/NumberedEquation4.gif) |
(4)
|
Gaussian brackets are useful for computing simple continued fractions because
Note that the Gaussian bracket notation ![[a_1,a_2,...]](https://mathworld.wolfram.com/images/equations/GaussianBrackets/Inline7.gif)
corresponds to a different quantity than that denoted by the more established simple continued fraction notation
![[b_0;b_1,b_2,...,b_n]=b_0+1/(b_1+1/(b_2+1/(b_3+...+1/(b_n)))).](https://mathworld.wolfram.com/images/equations/GaussianBrackets/NumberedEquation5.gif) |
(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.
الاكثر قراءة في نظرية الاعداد
اخر الاخبار
اخبار العتبة العباسية المقدسة
