The On-Line Encyclopedia of Integer Sequences (OEIS)

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A257236

Decimal expansion of the real root of 4*x^3 + 3*x - 40.
(history; published version)

#25 by Jon E. Schoenfield at Sun Sep 20 08:25:07 EDT 2015

STATUS

editing

approved

#24 by Jon E. Schoenfield at Sun Sep 20 08:24:59 EDT 2015

COMMENTS

See also the Fauvel and Gray reference, p. 254, where the problem is translated as "Find me two numbers in double proportion such that when the square of the larger number is multiplied by the smaller, and this product is added to the two original numbers, the result is forty, that is 40." The explanation given there is equivalent to the equation (2x)^2*x + x + 2x = 40, i.e. , 4x^3 + 3x = 40.

STATUS

approved

editing

#23 by Peter Luschny at Sun Sep 20 06:56:48 EDT 2015

STATUS

reviewed

approved

#22 by Joerg Arndt at Sat Sep 19 03:01:40 EDT 2015

STATUS

proposed

reviewed

#21 by Jon E. Schoenfield at Fri Sep 18 21:41:23 EDT 2015

STATUS

editing

proposed

#20 by Jon E. Schoenfield at Fri Sep 18 21:40:58 EDT 2015

COMMENTS

Discussion

Fri Sep 18

21:41

Jon E. Schoenfield: Are these changes to the Comments okay?

The URL under Links takes me to a page about Tartaglio, but that page doesn't include the quote; it's at 

http://www-history.mcs.st-and.ac.uk/HistTopics/Tartaglia_v_Cardan.html

#19 by Jon E. Schoenfield at Fri Sep 18 21:38:54 EDT 2015

COMMENTS

See also the Fauvel and Gray reference, p. 254, where the problem is translated as "Find me two numbers in double proportion such that when the square of the larger number is multiplied by the smaller, and this product is added to the two original numbers, the result is forty, that is 40." The explanation given there is [Equivalent equivalent to the equation (2x)^2*x + x + 2x = 40., i.e. 4x^3 + 3x = 40].

MATHEMATICA

(* Vincenzo Librandi, May 09 2015 *)

STATUS

proposed

editing

#18 by Robert G. Wilson v at Fri Sep 18 17:35:37 EDT 2015

STATUS

editing

proposed

#17 by Robert G. Wilson v at Fri Sep 18 17:35:33 EDT 2015

MATHEMATICA

RealDigits[N[Solve[4 x^3 + 3 x - 40==0, x][[1]][[, 1, 2]], 120111]][[1]] (* _Vincenzo Librandi_, May 09 2015 *)

(* Vincenzo Librandi, May 09 2015 *)

STATUS

proposed

editing

#16 by Michel Marcus at Fri Sep 18 17:24:15 EDT 2015

STATUS

editing

proposed