email inflection extrema nickalls geometry trig substitution Casus http://www.sosmath.com/algebra/factor/fac111/fac111.html hknaust@sosmath.com William Dunham Journey Through Genius point of inflection of ax^3 +bx^2 +cx +d =0 x= -b/3a f(x)= 2b^3/27a^2 - bc/3a +d substitution x= y -b/3a y= 0 f(y=0)= 2b^3/27a^2 - bc/3a +d f(y) relative to inflection point f(y)= ay^3 +(c -b^2/3a)y =0 f'(y) = 3ay^2 +c -b^2/3a f'(delta) = 0 delta = +- (b^2/3a - c)^0.5 / (3a)^0.5 f(delta)= -2*a*delta^3 f(y)= ay^3 -3a*delta^2*y f(delta) =2a*delta^3 quadratic calculator: http://members.aol.com/sregan34/calculat.htm http://forum.swarthmore.edu/library/more_info.html?id=10064 webmaster@mathforum.com complex: http://www.netsrq.com/~hahn/cubic.html hahn@netsrq.com http://www-history.mcs.st-and.ac.uk/history//HistTopics/Quadratic_etc_equations.html joc@st-andrews.ac.uk John O'Connor edmund@dcs.st-and.ac.uk Edmund F Robertson http://www.doctormath.com/faq/faq.cubic.equations.html webmaster@forum.swarthmore.edu depress the square term: http://www.sosmath.com/algebra/factor/fac11/fac11.html http://www.unican.es/sosmath/algebra/factor/fac11/fac11.html http://www.netsrq.com/~hahn/cubic.html http://home.cwru.edu/~adf3/cubic.htm adf3@po.cwru.edu trap? http://www.newton.dep.anl.gov/newton/askasci/1995/math/MATH052.HTM hmyron@dep.anl.gov http://forum.swarthmore.edu/dr.math/faq/faq/faq.cubic.equations.html http://mathforum.com/dr.math/problems/renton5.22.98.html http://forum.swarthmore.edu/dr.math/ http://www-history.mcs.st-and.ac.uk/history/HistTopics/References/Quadratic_etc_equations.html derivation quartic http://pines.hsu.edu/faculty/worthf/cubic.html http://www.hsu.edu/faculty/worthf/cubic.html worthf@hsu.edu pair of factors: http://www.mcn.net/~jimloy/quad.html jimloy@mcn.net general quartic: http://mathforum.com/dr.math/faq/faq.cubic.equations.html fundamental theorem of algebra http://www.und.edu/instruct/lgeller/fundalg.html laurie NorthDakota Cardano Tartaglia http://www.clarku.edu/~djoyce/complex/cubic.html djoyce@clarku.edu Bombell1 1572 http://www.ort.edu.uy/REDOC/fund_the.htm A History of Algebra BLvanderWaerden Berlin 1985 quintic: http://library.wolfram.com/examples/quintic quintic groups Galois 1832 smallest order 60: http://www.ort.edu.uy/REDOC/developm.htm HWussing TheGenesisoftheAbstractGroupConcept(CambridgeMA,1984) LNovy OriginsofModernAlgebra(Prague,1973) BMKiernan TheDevelopmentofGaloisTheoryfromLagrandetoArtin ArchiveforHistoryofExactSciences 8(1971),40-154 IKleiner The Evolution of Group Theory: a brief survey Mathematics magazine 59(1986),195-215 BChandler and WMagnus The history of combinatorial group theory: a case study in the history of ideas(NewYork,1982) JJNicholson OttoHolder and the Development of Group Theory and Galois Theory (DPhilThesisOxford,1993) http://www.math.utah.edu/lab/math/history/galois.html trig solution: http://mathforum.com/dr.math/problems/vonberwick4.30.98.html geometric solutions: dwh2@cornell.edu DavidWHenderson http://www.math.cornell.edu/~dwh/papers/geomsolu/geomsolu.html Amir-Moez, AR(1963) APaperofOmarKhayyam ScriptsMathematica 26 323-337 Davis PJ Hersh R (1981) TheMathematicalExperience Boston Birkhauser Eves H (1963) A Survey of Geometry Vol1 Boston Allyn and Bacon Heath TL (1956) The Thirteen Books of Euclid's Elements NewYork Dover Heath TL (1961) Appolonios of Perga Treatise on conic Sections NewYork Dover Hilbert, David Cohn-Vossen (1952) Geometry and the Imagination NewYork Chelsea KarpinskiLC ed(19150 RobertofChester'sLatinTranslationofhteAlgebraof al-Khowarizmi NewYork Macmillan Kasir DS ed(19310 TheAlgebraofOmarKhayyam NewYork ColumbiaTeachersCollege Prakash (1968) Baudhayana-Sulbasutram Bombay Seidenberg A (1961) TherRitualOriginofGeometry ArchivefortheHistoryoftheExactSciences 1 488-527 Valens EG (1976) TheNumberofThings:Pythagoras, Geometry and Humming Strings NewYork Dutton Witmer TR ed(1968) TheGreatArtortheRulesofAlgebrabyGirolanoCardano Cambridge TheMITPress roots in graphical manner: http://skruse.freepage.de/index_eng.html http://www.math.uga.edu/104/104doc/Sect2-3/Sect2-3.htm three equations three unknowns: http://www.alumni.caltech.edu/~chamness/equation/equation.html famous curves: http://www-history.mcs.st-and.ac.uk/history/Curves/Curves.html factoring: http://www.iaw.on.ca/~rgerryts/cgi-bin/ws.cgi?T=FOIL inverse functions: http://library.thinkquest.org/2647/algebra/functype.htm software for algebra: http://www.doctormath.com/algebra/alg.software.html mathematical topics http://www.newton.dep.anl.gov.askasci/math98.htm