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%I #15 Mar 16 2015 10:10:08
%S 3,3,1,2,3,7,6,4,7,7,8,7,1,3,2,1,8,5,1,1,1,0,4,9,6,4,1,3,5,7,3,7,3,2,
%T 5,1,8,7,3,3,0,8,6,1,8,8,5,1,4,0,0,9,3,4,8,2,5,4,1,6,9,3,6,2,6,6,2,5,
%U 5,2,4,6,5,9,1,0,6,8,7,9,0,0,7,4,6,8,0,4,5,0,4,6,5,5,1,6,6,8,3,0,6,5,9,6,3,7,3,8,0
%N Decimal expansion of A such that y = A*x^2 cuts the triangle with vertices (0,0), (1,0), (0,1) into two equal areas.
%C A is found by solving the equation A*x^2+3*A^2*x^3 = 3 or equivalently 3*A*x^2+(1-3*A)*x+2 = 0 where x = (-1+sqrt(1+4*A))/(2*A) in both equations. Using the quadratic formula, one can reduce this equation to solely sqrt(9*A^2-30*A+1)+3*sqrt(4*A+1) = 3*A+2.
%C Also, decimal expansion of (14+5*sqrt(10))/9.
%F ( 14 + 5*sqrt(10) )/9.
%e 3.31237647787132185111049641357373251873308...
%o (PARI) default(realprecision, 110);x=(14+5*sqrt(10))/9;for(n=1,100,d=floor(x);x=(x-d)*10;print1(d,", "))
%o (PARI) (14+5*sqrt(10))/9
%K nonn,cons,easy
%O 1,1
%A _Derek Orr_, Mar 11 2015
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