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 A181828 #19 Feb 12 2018 16:50:47 %S A181828 1,3,7,8,8,7,4,3,1,4,8,1,2,6,7,5,6,2,0,2,4,3,7,8,4,0,5,4,1,3,2,1,7,1, %T A181828 5,6,1,2,8,2,7,1,7,5,3,3,6,0,1,4,2,0,0,7,7,3,6,3,4,2,2,5,0,2,3,0,8,2, %U A181828 7,6,0,4,0,0,5,1,5,4,4,2,8,0,6,1,0,0,1,4,4,3,1,3,0,8,1,0,9,8,4,7 %N A181828 Decimal expansion of the positive value of r that maximizes the expression (1 + r + r^2)*(1 + r - r^2)*(1 - r + r^2)*(-1 + r + r^2). %C A181828 If the sides of a triangle form a geometric progression in the ratio 1:r:r^2 then when r=1.378874314... it uniquely maximizes the area of the triangle. This triangle has approximate internal angles of 30.534, 44.470 and 104.996 degrees. %F A181828 Sqrt(1/2 + (4-sqrt(921)/9)^(1/3)/2 + (4+sqrt(307/27))^(1/3)/2). - _Charles R Greathouse IV_, Feb 13 2011 %e A181828 1.378874314... %t A181828 N[Maximize[Sqrt[(1 + r + r^2)*(1 + r - r^2)*(1 - r + r^2)*(-1 + r + r^2)]/4, r], 100] %t A181828 Root[ 2#^6-3#^4-#^2-1 &, 1] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Mar 05 2013 *) %o A181828 (PARI) solve(r=1, 2, 2*r^6 - 3*r^4 - r^2 - 1) \\ _Charles R Greathouse IV_, Feb 13 2011 %K A181828 nonn,cons,easy %O A181828 1,2 %A A181828 _Frank M Jackson_, Nov 13 2010 %E A181828 Edited by _Frank M Jackson_, Nov 13 2010