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A244467 Decimal expansion of 1 + 22/60 + 7/60^2 + 42/60^3 + 33/60^4 + 4/60^5 + 40/60^6, Fibonacci's solution to x^3 + 2x^2 + 10x = 20. 1

%I

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

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

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

%N Decimal expansion of 1 + 22/60 + 7/60^2 + 42/60^3 + 33/60^4 + 4/60^5 + 40/60^6, Fibonacci's solution to x^3 + 2x^2 + 10x = 20.

%C The equation has no rational solutions. Despite Fibonacci's mistake with the sixth coefficient (40 rather than 38), his solution is a remarkable achievement for the time. Plugged into the equation, it gives 20.0000000006719323...

%D Alfred S. Posamentier & Ingmar Lehmann, The (Fabulous) Fibonacci Numbers. New York: Prometheus Books (2007): 21.

%F 1 + 22/60 + 7/60^2 + 42/60^3 + 33/60^4 + 4/60^5 + 40/60^6 = 1596577777/1166400000.

%e = 1.36880810785322...

%t RealDigits[1596577777/1166400000, 10, 100][[1]]

%Y Cf. A243629, A159990.

%K cons,nonn

%O 1,2

%A _Alonso del Arte_, Jun 28 2014

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