This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A294969 #16 May 23 2025 11:35:38 %S A294969 1,8,7,0,8,2,8,6,9,3,3,8,6,9,7,0,6,9,2,7,9,1,8,7,4,3,6,6,1,5,8,2,7,4, %T A294969 6,5,0,8,7,8,0,0,9,9,0,3,8,8,9,3,6,3,4,7,3,1,5,1,8,7,2,7,3,3,6,6,0,0, %U A294969 1,7,5,7,8,1,5,3,4,6,9,5,1,3,9,8,8,4,0,4,9,4,7,5,9,7,1,8,9,7,8 %N A294969 Decimal expansion of sqrt(14)/2 = sqrt(7/2) = A010471/2. %C A294969 The regular continued fraction of sqrt(14)/2 is [1, repeat(1, 6, 1, 2)]. %C A294969 The convergents are given in A295336/A295337. %C A294969 sqrt(14)/2 appears in a regular hexagon inscribed in a circle of radius 1 unit in the following way. Draw a straight line through two opposed midpoints of a side (halving the hexagon). The length between one of the midpoints, say M, and one of the two vertices nearest to the opposed midpoint is sqrt(13)/2 = A295330 units. A circle through M with this length ratio sqrt(13)/2 intersects the line below the hexagon at a point, say P. Then the length ratio between P and one of the two vertices nearest to M is sqrt(14)/2 (from a right triangle (1/2, sqrt(13)/2, sqrt(14)/2)). %e A294969 1.87082869338697069279187436615827465087800990388936347315187273366001757815... %t A294969 First[RealDigits[Sqrt[14]/2, 10, 100]] (* _Paolo Xausa_, May 23 2025 *) %Y A294969 Cf. A010471, A295330, A295336/A295337. %K A294969 nonn,cons,easy %O A294969 1,2 %A A294969 _Wolfdieter Lang_, Nov 27 2017