

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



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, 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, 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
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OFFSET

1,2


COMMENTS

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...


REFERENCES

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


LINKS



FORMULA

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


EXAMPLE

= 1.36880810785322...


MATHEMATICA

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


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



