history of mathematics - National STEM Centre

Descartes
fiene Descartes (1596-
1650) was a Frenchman.
He lived a few kilometres
south of Tours, and also
in Holland and Sweden.
He has been called the
father of modern
philosophy.
Chapter 6
The approach
of Descartes
Chapter 7
Constructing
algebraic solutions
Chapter 8
An overview of
Lei Geometrie
Introduction
You can think of the algebra of the 12th to 16th centuries in Europe as being based
on Latin translations of Arabic work, and being broadly algorithmic in nature. It was
not until the 16th century that the Greek mathematical texts became available in
comprehensible Latin.
It was then that the transformation of algebra under the influence of Greek geometry
begun by the Arabic mathematicians was continued in Europe, first by a French
mathematician, Viete. Another Frenchman Descartes, by discarding some of Viete's
ideas and building on others, was able to make the major breakthrough you will
study in this unit.
In Chapter 6 of this unit you will learn how Descartes used the introduction of
algebra to make Greek construction problems considerably easier to solve.
In Chapter 7 you will meet his methods, which show his full genius. Thanks to his
mathematical ideas, an algebraic approach for all geometric problems became
available, and the basis for modern algebraic geometry was laid.
In Chapter 8 Descartes's work is put into perspective.
This unit is designed to take about 15 hours of your learning time. About half of f*
this time will be outside the classroom.
Work through the chapters in sequence.
Many of the activities are in a different style from usual. They ask you to read a
translation of Descartes's work, and to answer questions to ensure that you have
understood it.
There are summaries and further practice exercises in Chapter 12. |||
Mathematical knowledge assumed
• the contents of Chapter 3 in The Greeks unit is particularly relevant to this unit
• for Activity 6.13, you will need to know some of the angle properties of circles;
in particular you should know the 'angle at the centre is twice the angle at the
circumference' and 'the angles in the same segments are equal' theorems.
7/