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...1 0 √ x2 + y2 + (z − w)2 dw dx dy dz + 1 5 ∫ 1 0 ∫ 1 0 ∫ 1 0 ∫ 1 0 √ 1 + (y − u)2 + (z − w)2 du dw dy dz = 4 75 + 17 75 √ 2− 2 25 √ 3− 7 75 pi + 7 25 log ( 1 + √ 2 ) + 7 25 log ( 7 + 4 √ 3 ) . 13 See =-=[7]-=- for details and some additional examples. It is not known whether similar closed forms exist for higher-dimensional cubes. 8 Ramanujan’s AGM Continued Fraction Given a, b, η > 0, define Rη(a, b) = a ...