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 (May 16, 2016) ✓
• 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

2 π ∫ 1 0   1 2√  1  −  x 4  d x

.

The [simple] continued fraction is

     

1 +  1 5 +  1 21 +  1 3 +  1 ⋱

This is the reciprocal of the arithmetic-geometric mean of 1 and

2√  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.)