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Decimal expansion of A such that y = A*x^2 cuts the first quadrant of the unit circle into two equal areas.
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%I #16 Mar 16 2015 10:07:50

%S 2,3,5,2,2,3,0,1,5,3,9,1,5,8,0,7,6,3,4,8,5,2,7,7,2,5,1,2,1,1,7,5,4,1,

%T 5,8,0,7,3,9,2,1,5,4,2,4,8,8,0,2,4,3,0,8,9,2,3,5,7,8,2,9,7,7,4,2,8,1,

%U 3,7,8,6,8,5,9,3,7,7,0,4,8,9,3,4,0,0,4,6,7,7,6,4,0,0,0,9,4,9,8,3,6,4,7,1,4,2,4,1

%N Decimal expansion of A such that y = A*x^2 cuts the first quadrant of the unit circle into two equal areas.

%C A is found by solving the equation A*x^3/3 = Pi/4 - arcsin(x), where x = sqrt( (sqrt(4*A^2+1)-1)/(2*A^2) ).

%e 2.352230153915807634852772512117541580739215424880243089235782...

%o (PARI) solve(A = 2, 3, A/3*(sqrt((sqrt(4*A^2+1)-1)/(2*A^2)))^3 - Pi/4 + asin(sqrt((sqrt(4*A^2+1)-1)/(2*A^2)))) \\ _Michel Marcus_, Mar 11 2015

%K nonn,cons,easy

%O 1,1

%A _Derek Orr_, Mar 10 2015