"Descartes' parabola" and the traditional parabola : a reconstruction of a historical method with the help of the "mathematica" program
Master thesis
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http://hdl.handle.net/11250/138045Utgivelsesdato
2007Metadata
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Sammendrag
This study concentrates on Descartes’ geometry, especially 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. His
work had a great influence on both mathematicians and philosophers. In mathematics
Descartes chief contribution was in analytical geometry. Descartes made other known
contributions to mathematics. He was the first to use the first letters of the alphabet to
represent known quantities, and the last letters to represent unknown ones. Descartes also
formulated a rule known as Descartes' rule of signs, for finding the positive and negative roots
of an algebraic equation.
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 and five lines Pappus’ problems.
Secondly, 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.
Beskrivelse
Masteroppgave i matematikkdidaktikk 2007 - Høgskolen i Agder, Kristiansand
Utgiver
Høgskolen i AgderAgder University College