Template:Sequence of the Day for August 17

Intended for: August 17, 2011

Timetable

• First draft entered by Alonso del Arte on May 29, 2011 as a verbatim copy of the write-up from December 17, 2010 ✓
• Draft reviewed by Alonso del Arte on July 16, 2011 ✓
• Draft approved by Daniel Forgues on July 20, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

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A014549: Gauß’s constant

2 π ∫ 1 0   1 2√  1  −  x 4 d x

.

0.834626841674...

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.

Its simple continued fraction is (see A053002)

     

1 M  (1, 2√  2  )  =  1 1 +  1 5 +  1 21 +  1 3 +  1 4 +  1 14 +  1 ⋱  .