Sibling curves and complex roots 1: looking back

References

• O’Connor , JJ and Robertson , EF . 2006 . The fundamental theorem of algebra . The MacTutor History of Mathematics archive , Retrieved March 2007 from www-groups.dcs.st-and.ac.uk/∼history/HistTopics/Fund_theorem_of_algebra.html
   Google Scholar
• O’Connor , JJ and Robertson , EF . 2006 . “ Quadratic, cubic and quartic equations ” . In The MacTutor History of Mathematics archive Retrieved March 2007 from www-groups.dcs.st-and.ac.uk/∼history/HistTopics/Quadratic_etc_equations.html
   Google Scholar
• O’Connor , JJ and Robertson , EF . 2006 . “ Tartaglia versus Cardan ” . In The MacTutor History of Mathematics archive Retrieved March 2007 from www-groups.dcs.st-and.ac.uk/∼history/HistTopics/Tartaglia_v_Cardan.html
   Google Scholar
• Throop , A . 2005 . The Fundamental Theorem of Algebra , Kennesaw, GA : Kennesaw State University . Student project, Retrieved April 2007 from http://ksuweb.kennesaw.edu/∼jderado/Students/ProofFTA.pdf
   Google Scholar
• Guilbeau , L . 1930 . The history of the solution of the cubic equation . Mathematics News Letter , 5 ( 4 ) : 8 – 12 .
   Google Scholar
• Struik , DJ . 1962 . A Concise History of Mathematics , London : G Bell & Sons .
   Google Scholar
• Passagen (Current) . Internet website. Retrieved April 2007 fromhttp://hem.passagen.se/ceem
   Google Scholar
• Wikipedia. (Current) . Various articles on mathematics and the history of mathematics Retrieved February 2007 from http://en.wikipedia.org
   Google Scholar
• Wolfram Mathworld. (Current) . Quadratic equation Retrieved April 2007 from http://mathworld.wolfram.com/QuadraticEquation.html
   Google Scholar
• Gillings , RJ . 1982 . Mathematics in the time of the Pharaohs , 161 New York : Dover .
   Google Scholar
• Smith , D . 1951 . History of Mathematics , Vol. 1 , New York : Dover .
   Google Scholar
• Smith , D . 1953 . History of Mathematics , Vol. 2 , New York : Dover .
   Google Scholar
• Nordgaard , MA . 1938 . Sidelights on the Cardan-Tartaglia controversy . National Mathematics Magazine , 12 ( 7 ) : 327 – 346 .
   Google Scholar
• Feynman , RP . 1988 . What Do You Care What Other People Think? , New York : W. W. Norton .
   Google Scholar
• Griffiths , HB and Hirst , AE . 1994 . Cubic equations, or where did the examination question come from . American Mathematical Monthly , 101 ( 2 ) : 151 – 161 .
   Web of Science ®Google Scholar
• Math , Ask dr . 1994 . Complex roots. Internet discussion on The Math Forum@Drexel Retrieved March 2007 from http://mathforum.org/library/drmath/view/53808.html
   Google Scholar
• Ballantine , JP . 1920 . A graphic solution of the cubic equation . The American Mathematical Monthly , 27 ( 5 ) : 204
   Google Scholar
• Braden , B . 1985 . Picturing functions of a complex variable . The College Mathematics Journal , 16 ( 1 ) : 63 – 72 .
   Google Scholar
• Crawley , ES . 1918 . Relating to the graph of a cubic equation having complex roots . American Mathematical Monthly , 25 ( 6 ) : 268 – 269 .
   Google Scholar
• Curtis , HB . 1938 . A graphical solution of the cubic . National Mathematics Magazine , 12 ( 7 ) : 325 – 326 .
   Google Scholar
• Faucette , WM . 1996 . A geometric interpretation of the solution of the general quartic polynomial . American Mathematical Monthly , 103 ( 1 ) : 51 – 57 .
   Web of Science ®Google Scholar
• Gomez-Calderon , J and Wells , DM . 1996 . Why polynomials have roots . The College Mathematics Journal , 27 ( 2 ) : 90 – 94 .
   Google Scholar
• Rees , EL . 1922 . Graphical discussion of the roots of a quartic equation . American Mathematical Monthly , 29 ( 2 ) : 51 – 55 .
   Google Scholar
• Running , TR . 1921 . Graphical solutions of quadratic, cubic, and biquadratic equations . The American Mathematical Monthly , 28 ( 11/12 ) : 415 – 423 .
   Google Scholar
• Travers , R and Kim , D . 1982 . Those elusive imaginary zeroes . Mathematics Teacher , 75 : 62 – 64 .
   Google Scholar
• Teacher 2 Teacher . 2003 . “ The geometry of the complex roots of graphs ” . In Internet discussion on Mathforum Retrieved April 2007 from http://mathforum.org/t2t/message.taco?thread = 12605&message = 1
   Google Scholar
• Norton , A and Lotto , B . 1984 . Complex roots made visible . The College Mathematics Journal , 15 ( 3 ) : 248 – 249 .
   Google Scholar
• Gleason , RE . 1910 . A simple method for graphically obtaining the complex roots of a cubic equation . The Annals of Mathematics 2nd Series , 11 ( 3 ) : 95 – 96 .
   Google Scholar
• Irwin , F and Wright , HM . 1917 . Some properties of polynomial curves . The Annals of Mathematics , 19 ( 2 ) : 152 – 158 .
   Google Scholar
• Wessels , SFG . 1981 . The complex roots of a quadratic from its graph . Mathematical Gazette , 65 : p 39
   Google Scholar
• Henriquez , G . 1935 . The graphical interpretation of the complex roots of cubic equations . American Mathematical Monthly , 42 ( 6 ) : 383 – 384 .
   Google Scholar
• Yanosik , GA . 1936 . A graphical solution for the complex roots of a cubic . National Mathematics Magazine , 10 ( 4 ) : 139 – 140 .
   Google Scholar
• Gehman , HM . 1941 . Complex roots of a polynomial equation . American Mathematical Monthly , 48 ( 4 ) : 237 – 239 .
   Google Scholar
• Yanosik , GA . 1943 . Graphical solutions for complex roots of quadratics, cubics and quartics . National Mathematics Magazine , 17 ( 4 ) : 147 – 150 .
   Google Scholar
• Ward , JA . 1937 . Graphical representation of complex roots . National Mathematics Magazine , 11 ( 7 ) : 297 – 303 .
   Google Scholar
• Long , CA . 1971 . A note on the geometry of zeros of polynomials . Mathematics Magazine , 44 ( 3 ) : 157 – 159 .
   Google Scholar
• Long , CA . 1972 . The quadratic polynomial and its zeros . The Two-Year College Mathematics Journal , 3 ( 1 ) : 23 – 29 .
   Google Scholar
• Long , C and Hern , T . 1989 . Graphing the complex zeros of polynomials using modulus surfaces . The College Mathematics Journal , 20 ( 2 ) : 98 – 105 .
   Google Scholar
• Velleman , DJ . The Fundamental Theorem of Algebra: A visual approach Unpublished paper. Retrieved March 2007 from http://www.cs.amherst.edu/∼djv/FTAp.pdf
   Google Scholar