Pronunciation guide

Abu Sahl al-Quhi

Girard Desargues

Hellenistic

Interior

Janos Bolyai

Postulate

Spatial

B Comprehension

Read the text and choose the correct answer.

1 Geometry was first used to solve

A common problems.

B abstract problems.

2 During the Classical Period of Greek civilisation,

A the way problems were solved changed.

B people were only interested in geometry.

3 The Greeks made important advances in geometry

A only during the Classical Period.

B during both the Classical and Hellenistic Periods.

4 After the decline of Greek civilisation,

A mathematicians used geometry to solve other kinds of problems.

B nothing new was discovered.

5 Between the 17^th and 19^th centuries, European thinkers

A ignored the Greeks' ideas about geometry.

B created new types of geometry.

Before you read

Discuss these questions with your partner.

-» What developments in geometry do you know about that occurred during the Renaissance

(c 15^th -17^th centuries AD)?

-» What differences and what similarities can you think of between maths and philosophy?

D Vocabulary

Find a synonym in the box for the words or phrases in green in the sentences.

Then check your answers in the text.

N knowledgeable n tutor

n prosperity nsynthetic geometry

N goal n advance

N on the continent n analytic geometry

N harsh

1 The country was going through a time of successfulness. .............................................

2 The climate was very cold and unpleasant. .............................................

3 Her aim in life was to become a philosopher.............................................

4 He lived in Europe, not Britain. .............................................

5 She studied a kind of geometry that used theorems and observations to reach conclusions.............................................

6 He taught a kind of geometry involving curves and understanding them. .............................................

7She is very well-educated;she always beats me at Trivial Pursuit. .............................................

8 Computer technology is expected to developimmensely in the next couple of years.

.............................................

9 She wants to find a Maths teacher to teach her children at home. .............................................

Reading

Rene Descartes

Rene Descartes was born in France on 31^st March, 1596, at a time of major change in the world. The great wars which had been going on throughout Europe had finally ended, creating an atmosphere of peace and stability which encouraged creative thinking, experimentation and the questioning of old beliefs and ways. After the fall of Constantinople in 1453, Greek and Islamic texts had been rediscovered and read by learned men around Europe. Ideas of the great Renaissance artists and thinkers had quickly spread across the continent. What is more, with the discovery of the New World by Columbus in 1492, a period of exploration, expansion and prosperity had begun.

After completing his education at the Jesuit College and the University of Poitiers, both in France, Descartes began to work on his goal of presenting a new way of looking at philosophy and mathematics. Although his first essays were probably written earlier than 1628, the year he moved to Holland, he was not well known until 1637, when a collection of his essays appeared and attracted the interest of the scientific world. His great work Discourse on the Method was one of the essays included in this collection.

Descartes was knowledgeable about the work of Plato and Aristotle, as well as that of earlier European philosophers like Augustine and Aquinas. Descartes' goal was to reach true knowledge about things by applying mathematical methodology to find answers to philosophical questions. Starting with the principle that the only thing he could be sure of was that he himself existed (Cogito, ergo sum meaning, I think, there/ore I am), he reached his own conclusions about God and the physical world. Because his ideas were very different from traditional ideas of his time, he was often criticised by religious leaders. His work had a great influence on later philosophers, including Benedict de Spinoza, Blaise Pascal, John Locke and Immanuel Kant.

Another of his goals was to advance the field of mathematics, particularly geometry. Until that time, Euclidean geometry was the type most well known. Also known as synthetic geometry, Euclidean geometry uses theorems and observations to reach conclusions.

Building on the work of the ancient Greek, Apollonius of Perga (262-190 BG), Descartes realised that it would be useful and important to be able to measure curved lines in addition to straight ones. This led to his invention of the Cartesian coordinate system, a way of algebraically measuring curves and understanding things about them. This was the start of analytic geometry (also called coordinate geometry and Cartesian geometry) and eventually led to the invention of calculus. In addition to his work in philosophy and geometry, Descartes contributed to algebra, optics and even physiology and psychology.

Descartes became one of the most important figures of his time. Queen Christina of Sweden invited Descartes to tutor her, which he did. However, he became ill in Sweden, possibly because he was not used to the cold, harsh climate, and died on 11^th February, 1650. To honour him for his many contributions, people call him the 'Founder of Modern Philosophy' and the 'Father of Modern Mathematics'.

Date: 2016-01-14; view: 903