history of mathematics - National STEM Centre

Descartes
Practice exercises for
this chapter are on
no
Descartes's only mathematical work was La Geometric. He did correspond with
other mathematicians, among them Fermat.
What has happened subsequently to analytical geometry since Descartes and
Fermat? Very soon, other mathematicians adopted the Cartesian approach and
systematic research into curves flourished. Algebra, without the law of
homogeneity, became a powerful tool for analysing geometry.
Once differential calculus had been developed, by the end of the 17th century,
virtually all the problems of classical geometry were tackled and solved.
Mathematicians of later date, among them Euler, also contributed to the intellectual
achievements now known as analytical geometry.
Reflecting on Chapter 8
What you should know
• how the work of Descartes compares with that of Pierre Fermat
• evidence of Descartes's approach to negative and imaginary solutions of
equations
• how Descartes constructed a normal to a given curve
• the relationship between algebra and geometry in La Geometric.
Preparing for your next review
• Bring your answer to Activity 8.1 to the review together with half a page in your
own words describing the revolutionary features of La Geometric.
• Answer the following check questions.
1 Prepare a presentation explaining how the work of Descartes was influenced by
van Schooten, Viete and Fermat.
2 Use Descartes's method to find the equation of the normal to y 2 = 4x at (1,2).