The history of geometry

Engineers, architects and people of many other professions use lines and figures in their daily work. The study of lines and closed figures made by lines is called geometry. Geometry is the branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines and angles.

Geometry is the Greek name for the science which the early Egyptians began and developed about 5000 years ago. The word geometry is derived from two Greek words: geo meaning earth and metron meaning measure.

For erecting pyramids the early Egyptians needed professional geometers who were able to locate a line running north and south.

The geometry known to the Egyptians consisted principally of rules and formulas for finding areas and volumes. The Egyptians were principally interested in the practical application of their rules.

After a time Greek philosophers and teachers developed and perfected the proofs of the Egyptians. The most important of the early Greek teachers was Pythagoras¹ who was born about 569 before our era. He founded a school in Italy. The students were divided into two classes ‑ beginners and Pythagorians.

Plato², who lived more than a hundred years later than Pythagoras, was primarily a philosopher. His interest in geometry was not because of its practical use, but because of the logic contained in the proofs.

The best known name in connection with geometry is Euclid³. Euclid was a teacher of geometry in Alexandria. He used to say that geometry trained the habits of expressing thoughts accurately. One of his most important textbooks is called The Elements. The Elements of Euclid has been used as a basis for all textbooks on geometry since his time.

Another famous scientist of ancient times was Archimedes who lived in Sicily⁴. Archimedes discovered many laws of mathematics.

For over twenty centuries Euclidean geometry was the ruling theory. In the I9th century the Russian mathematician Lobatchevsky founded non-Euclidean geometry of two dimensions. Such kind of geometry is called hyperbolic. It is based on the assumption⁵ that the axiom on parallels⁶ is not true, and through a point any number of straight lines can be drawn parallel to a given straight line.

The third system of geometry was developed by Riemann and is called elliptic geometry. Riemann assumes that no straight line can be drawn which will not meet any other straight line.

Thus we have three systems of geometry.

Notes

1. Pythagoras – Пифагор

2. Plato – Платон

3. Euclid – Евклид

4. Silicy – Сицилия

5. assumption – предположение

6. axiom parallels – аксиома параллелей.

Устные темы

Тема № 1

Introducing Myself

Let me introduce myself. I’m Svetlana Alexandrova. I was born on the 29^th of March 1985 in Minsk under the zodiac sign of Aries. I believe that stars influence our fate and character. As you see, I am Aries. They say that Aries is full of energy, a leader, straight talker, ambitious and frank, likes sport, stubborn, hot temper, but quick to apologize. Partially it is true. I can't admit I am stubborn. Actually, I'm persistent. It is different, I think.

As to my appearance, I’m rather tall and slim. I have never thought I am a beauty. I wish I were more beautiful. I think, that I’m even-tempered, rather reserved, calm and modest. But sometimes I can lose my temper and become either angry or sad. I like staying alone and sometimes I retire into my shell. But at the same time I like my friends, I like to laugh and to joke. I have got a sense of humour. It means I understand humour and appreciate it. But unfortunately, I’m not often witty myself. I think, I am able to «keep my head when all about me are losing theirs» and to stand up to difficulties when things are not going my way. Besides, I am sincere and tolerant, friendly and faithful, hard-working and serious.

There are many things in our life which I like and some I dislike. I like when everything is OK. Being happy is one way of being wise. I like to study, because knowledge is useful sometimes. I am fond of reading as it gives not only knowledge but also wonderful moments of joy and pleasure. Sometimes I enjoy watching TV or listening to the radio. Especially when I can hear some wonderful pieces of music. I like music. It makes people better. It awakens the best feelings and high emotions. But there is a thing that makes me crazy. I'm fond of horses and equestrian skill. I dislike overcrowded buses. And I hate getting up early. I'm happy I have got more things I like than I dislike.

Ответьте на вопросы.

1. What is your name and surname?

2. When and where were you born?

3. Do you know your zodiac sing?

4. Can you describe yourself?

5. What are things that you like and dislike?