Cubic equation (English Wikipedia)

Høyrup, Jens (1992), "The Babylonian Cellar Text BM 85200 + VAT 6599 Retranslation and Analysis", Amphora: Festschrift for Hans Wussing on the Occasion of his 65th Birthday, Birkhäuser, pp. 315–358, doi:10.1007/978-3-0348-8599-7_16, ISBN 978-3-0348-8599-7
Guilbeau (1930, p. 8) states that "the Egyptians considered the solution impossible, but the Greeks came nearer to a solution." Guilbeau, Lucye (1930), "The History of the Solution of the Cubic Equation", Mathematics News Letter, 5 (4): 8–12, doi:10.2307/3027812, JSTOR 3027812
Guilbeau (1930, pp. 8–9) Guilbeau, Lucye (1930), "The History of the Solution of the Cubic Equation", Mathematics News Letter, 5 (4): 8–12, doi:10.2307/3027812, JSTOR 3027812
Guilbeau (1930, p. 9) states, "Omar Al Hay of Chorassan, about 1079 AD did most to elevate to a method the solution of the algebraic equations by intersecting conics." Guilbeau, Lucye (1930), "The History of the Solution of the Cubic Equation", Mathematics News Letter, 5 (4): 8–12, doi:10.2307/3027812, JSTOR 3027812
Berggren, J. L. (1990), "Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī's Muʿādalāt", Journal of the American Oriental Society, 110 (2): 304–309, doi:10.2307/604533, JSTOR 604533
La Nave, Federica; Mazur, Barry (2002), "Reading Bombelli", The Mathematical Intelligencer, 24 (1): 12–21, doi:10.1007/BF03025306, S2CID 189888034
Nickalls, R.W.D. (July 2006). "Viète, Descartes, and the cubic equation" (PDF). Mathematical Gazette. 90 (518): 203–208. doi:10.1017/S0025557200179598. S2CID 124980170.
Zucker, I.J. (July 2008). "The cubic equation — a new look at the irreducible case". Mathematical Gazette. 92: 264–268. doi:10.1017/S0025557200183135. S2CID 125986006.
Gleason, Andrew Mattei (March 1988). "Angle trisection, the heptagon, and the triskaidecagon" (PDF). The American Mathematical Monthly. 95 (3): 185–194. doi:10.2307/2323624. JSTOR 2323624. Archived from the original (PDF) on 2015-12-19.
Nickalls, R. W. D. (November 1993), "A new approach to solving the cubic: Cardan's solution revealed" (PDF), The Mathematical Gazette, 77 (480): 354–359, doi:10.2307/3619777, ISSN 0025-5572, JSTOR 3619777, S2CID 172730765 See esp. Fig. 2.
Henriquez, Garcia (June–July 1935), "The graphical interpretation of the complex roots of cubic equations", American Mathematical Monthly, 42 (6): 383–384, doi:10.2307/2301359, JSTOR 2301359
Barr, C. F. (1918), "Discussions: Relating to the Graph of a Cubic Equation Having Complex Roots", American Mathematical Monthly, 25 (6): 268–269, doi:10.2307/2972885, JSTOR 2972885
Irwin, Frank; Wright, H. N. (1917), "Some Properties of Polynomial Curves.", Annals of Mathematics, 19 (2): 152–158, doi:10.2307/1967772, JSTOR 1967772

jstor.org

Guilbeau (1930, p. 8) states that "the Egyptians considered the solution impossible, but the Greeks came nearer to a solution." Guilbeau, Lucye (1930), "The History of the Solution of the Cubic Equation", Mathematics News Letter, 5 (4): 8–12, doi:10.2307/3027812, JSTOR 3027812
Guilbeau (1930, pp. 8–9) Guilbeau, Lucye (1930), "The History of the Solution of the Cubic Equation", Mathematics News Letter, 5 (4): 8–12, doi:10.2307/3027812, JSTOR 3027812
Guilbeau (1930, p. 9) states, "Omar Al Hay of Chorassan, about 1079 AD did most to elevate to a method the solution of the algebraic equations by intersecting conics." Guilbeau, Lucye (1930), "The History of the Solution of the Cubic Equation", Mathematics News Letter, 5 (4): 8–12, doi:10.2307/3027812, JSTOR 3027812
Berggren, J. L. (1990), "Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī's Muʿādalāt", Journal of the American Oriental Society, 110 (2): 304–309, doi:10.2307/604533, JSTOR 604533
Gleason, Andrew Mattei (March 1988). "Angle trisection, the heptagon, and the triskaidecagon" (PDF). The American Mathematical Monthly. 95 (3): 185–194. doi:10.2307/2323624. JSTOR 2323624. Archived from the original (PDF) on 2015-12-19.
Nickalls, R. W. D. (November 1993), "A new approach to solving the cubic: Cardan's solution revealed" (PDF), The Mathematical Gazette, 77 (480): 354–359, doi:10.2307/3619777, ISSN 0025-5572, JSTOR 3619777, S2CID 172730765 See esp. Fig. 2.
Henriquez, Garcia (June–July 1935), "The graphical interpretation of the complex roots of cubic equations", American Mathematical Monthly, 42 (6): 383–384, doi:10.2307/2301359, JSTOR 2301359
Barr, C. F. (1918), "Discussions: Relating to the Graph of a Cubic Equation Having Complex Roots", American Mathematical Monthly, 25 (6): 268–269, doi:10.2307/2972885, JSTOR 2972885
Irwin, Frank; Wright, H. N. (1917), "Some Properties of Polynomial Curves.", Annals of Mathematics, 19 (2): 152–158, doi:10.2307/1967772, JSTOR 1967772

nickalls.org

Nickalls, R.W.D. (July 2006). "Viète, Descartes, and the cubic equation" (PDF). Mathematical Gazette. 90 (518): 203–208. doi:10.1017/S0025557200179598. S2CID 124980170.
Nickalls, R. W. D. (November 1993), "A new approach to solving the cubic: Cardan's solution revealed" (PDF), The Mathematical Gazette, 77 (480): 354–359, doi:10.2307/3619777, ISSN 0025-5572, JSTOR 3619777, S2CID 172730765 See esp. Fig. 2.

nthu.edu.tw

apollonius.math.nthu.edu.tw

Gleason, Andrew Mattei (March 1988). "Angle trisection, the heptagon, and the triskaidecagon" (PDF). The American Mathematical Monthly. 95 (3): 185–194. doi:10.2307/2323624. JSTOR 2323624. Archived from the original (PDF) on 2015-12-19.

semanticscholar.org

api.semanticscholar.org

La Nave, Federica; Mazur, Barry (2002), "Reading Bombelli", The Mathematical Intelligencer, 24 (1): 12–21, doi:10.1007/BF03025306, S2CID 189888034
Nickalls, R.W.D. (July 2006). "Viète, Descartes, and the cubic equation" (PDF). Mathematical Gazette. 90 (518): 203–208. doi:10.1017/S0025557200179598. S2CID 124980170.
Zucker, I.J. (July 2008). "The cubic equation — a new look at the irreducible case". Mathematical Gazette. 92: 264–268. doi:10.1017/S0025557200183135. S2CID 125986006.
Nickalls, R. W. D. (November 1993), "A new approach to solving the cubic: Cardan's solution revealed" (PDF), The Mathematical Gazette, 77 (480): 354–359, doi:10.2307/3619777, ISSN 0025-5572, JSTOR 3619777, S2CID 172730765 See esp. Fig. 2.

st-and.ac.uk

www-groups.dcs.st-and.ac.uk

J. J. O'Connor and E. F. Robertson (1999), Omar Khayyam, MacTutor History of Mathematics archive, states, "Khayyam himself seems to have been the first to conceive a general theory of cubic equations."

st-andrews.ac.uk

mathshistory.st-andrews.ac.uk

In O'Connor, John J.; Robertson, Edmund F., "Omar Khayyam", MacTutor History of Mathematics Archive, University of St Andrews one may read This problem in turn led Khayyam to solve the cubic equation $x 3 + 200 x = 20 x 2 + 2000$ and he found a positive root of this cubic by considering the intersection of a rectangular hyperbola and a circle. An approximate numerical solution was then found by interpolation in trigonometric tables. The geometric construction was perfectly suitable for Omar Khayyam, as it occurs for solving a problem of geometric construction. At the end of his article he says only that, for this geometrical problem, if approximations are sufficient, then a simpler solution may be obtained by consulting trigonometric tables. Textually: If the seeker is satisfied with an estimate, it is up to him to look into the table of chords of Almagest, or the table of sines and versed sines of Mothmed Observatory. This is followed by a short description of this alternate method (seven lines).
O'Connor, John J.; Robertson, Edmund F., "Sharaf al-Din al-Muzaffar al-Tusi", MacTutor History of Mathematics Archive, University of St Andrews
O'Connor, John J.; Robertson, Edmund F., "Fibonacci", MacTutor History of Mathematics Archive, University of St Andrews

uniteasy.com

"Solution for a depressed cubic equation". Math solution. Retrieved 2022-11-23.

web.archive.org

Gleason, Andrew Mattei (March 1988). "Angle trisection, the heptagon, and the triskaidecagon" (PDF). The American Mathematical Monthly. 95 (3): 185–194. doi:10.2307/2323624. JSTOR 2323624. Archived from the original (PDF) on 2015-12-19.

wolfram.com

mathworld.wolfram.com

These are Formulas (80) and (83) of Weisstein, Eric W. 'Cubic Formula'. From MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/CubicFormula.html, rewritten for having a coherent notation.

worldcat.org

Nickalls, R. W. D. (November 1993), "A new approach to solving the cubic: Cardan's solution revealed" (PDF), The Mathematical Gazette, 77 (480): 354–359, doi:10.2307/3619777, ISSN 0025-5572, JSTOR 3619777, S2CID 172730765 See esp. Fig. 2.