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%I #38 Aug 21 2023 11:45:08
%S 1,2,0,0,2,3,8,3,7,8,5,6,9,1,7,1,8,1,2,3,0,5,7,3,8,1,6,6,9,9,5,0,4,4,
%T 0,4,0,7,5,0,6,8,5,1,2,2,0,5,0,8,9,2,7,5,3,6,0,2,8,8,1,3,0,7,3,3,9,5,
%U 0,2,4,2,1,2,7,6,7,9,4,4,6,5,6,3,4,3,0,2,0,1,0,9,6,8,0,8,2,0,3,2,3,0,8,4,2
%N Decimal expansion of the cube root of 1729.03.
%C The problem of extracting this cube root pitted an abacus salesman against Nobel Prize winning physicist Richard Feynman one afternoon in Rio de Janeiro.
%C An algebraic number of degree 3 and denominator 10; minimal polynomial 100x^3 - 172903. - _Charles R Greathouse IV_, Apr 20 2016
%D Richard Feynman and Ralph Leighton, Surely You're Joking, Mr. Feynman! (Adventures of a Curious Character), chapter "Lucky Numbers," W. W. Norton & Co., NY 1985, pp. 192-198.
%D Dana Mackenzie, The Universe in Zero Words, The Story of Mathematics as Told Through Equations, Princeton University Press, Princeton and Oxford, 2012, Introduction - The Abacist versus the Algorist, page 13.
%H Luis Fernandes, <a href="http://www.ee.ryerson.ca/~elf/abacus/feynman.html">Feynman vs. The Abacus</a>
%H Dana Mackenzie, <a href="http://danamackenzie.com/books/the-universe-in-zero-words/">The Universe in Zero Words</a>
%H Eric W. Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NewtonsMethod.html">Newton's Method</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Newton's_method">Newton's method</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Root-finding_algorithm">Root-finding algorithm</a>
%H <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>
%e 12.002383785691718123057381669950440407506851220508927536028813073395024212767944...
%t RealDigits[ 1729030^(1/3), 10, 105][[1]] (* please notice the lack of a decimal point *)
%o (PARI) sqrtn(1729.03,3) \\ _Charles R Greathouse IV_, Apr 20 2016
%Y Cf. A000578, A001021, A001235, A005898, A018010, A034126.
%K nonn,cons,easy,less
%O 2,2
%A _Dana Mackenzie_ and _Robert G. Wilson v_, Nov 10 2014
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