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# Template:Sequence of the Day for May 30

Intended for: May 30, 2012

## Timetable

• First draft entered by Alonso del Arte on August 10, 2011
• Draft reviewed by Daniel Forgues on May 29, 2012
• Draft to be approved by April 30, 2012

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A053003: Simple continued fraction for Gauß's constant $\scriptstyle \frac{2}{\pi} \int_{0}^{1} \frac{1}{\sqrt{1 - x^4}} dx \,$

$1 + \frac{1}{5 + \cfrac{1}{21 + \cfrac{1}{3 + \cfrac{1}{\ddots\qquad{}}}}} \,$

This is the reciprocal of the arithmetic-geometric mean of 1 and $\scriptstyle \sqrt{2} \,$. It was on May 30, 1799 that Carl Friedrich Gauß discovered the integral for this number shown above. (For its decimal expansion, see A014549.)