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Template:Sequence of the Day for May 30

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Intended for: May 30, 2012


  • 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
Yesterday's SOTD * Tomorrow's SOTD

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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.)

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