Descartes' parabola and the traditional parabola

This study concentrates on Descartes geometry,
especially for the Descartes parabola and traditional
parabola. Who is Descartes? René Descartes
(1596-1650) was a 17th century French philosopher,
mathematician and a man of science whose work, La
géométrie, includes his application of algebra to
geometry from which we now have Cartesian geometry.
First, this study concentrates on the Descartes
studies of Pappus problem. Also I explicitly explain
how Descartes found the traditional parabola and
Descartes parabola, and how he used the four five
lines Pappus problems. Also this study concentrates
on the Descartes construction (that means
geometrical solution) of equations by using
Descartes parabola and the traditional parabola. I
clearly explain Descartes construction of third and
fourth degree equations by circle and traditional
parabola, and the construction for fifth and sixth
degree equations by using circle and Descartes
parabola. Finally, I also explain the construction of
higher degree equations. Furthermore I give three
numerical examples by solving them with the
mathematica program, which was designed by Stephen
wolfram.

Autorentext

B.Sc(Hons): Studied Mathematics at Jaffna University, Sri Lanka.M.Sc: Studied Applied Statistics at Peradeniya University, Sri Lanka.M.Sc: Studied Mathematics Education at Agder University, Norway.

Klappentext

This study concentrates on Descartes geometry,especially for the Descartes parabola and traditionalparabola. Who is Descartes? René Descartes(1596-1650) was a 17th century French philosopher,mathematician and a man of science whose work, Lagéométrie, includes his application of algebra togeometry from which we now have Cartesian geometry.First, this study concentrates on the Descartes'studies of Pappus' problem. Also I explicitly explainhow Descartes' found the traditional parabola andDescartes' parabola, and how he used the four fivelines Pappus' problems. Also this study concentrateson the Descartes' ''construction'' (that meansgeometrical solution) of equations by usingDescartes' parabola and the traditional parabola. Iclearly explain Descartes' construction of third andfourth degree equations by circle and traditionalparabola, and the construction for fifth and sixthdegree equations by using circle and Descartes'parabola. Finally, I also explain the construction ofhigher degree equations. Furthermore I give threenumerical examples by solving them with themathematica program, which was designed by Stephenwolfram.