Meaning of geometry

Geometry is a very old subject. It probably began in Baby­lon and Egypt. Men needed practical ways for measuring their land, for building pyramids, and for defining volumes. The Egyp­tians were mostly concerned with applying geometry to their every­day problems. Yet, as the knowledge of Egyptians spread to Greece the Greeks found the ideas about geometry very intriguing and my­sterious. In 300 В. C. all the known facts about Greek geometry were put into a logical sequence by Euclid. His book, called Elements, is one of the most famous books of mathematics. In recent years men have improved on Euclid's work.

Today geometry includes not only the study of the shape and size of the earth and all things on it, but also the study of relations between geometric objects. The most fundamental idea in the study of geometry is the idea of a point. A point is an exact loca­tion in space. You cannot see a point, feel a point, or move a point, because it has no dimensions. There are points (locations) on the earth, in the earth, in the sky, on the sun, and everywhere in space. In writing we represent the points by dots. Remember the dot is only a picture of a point and not the point itself. Points are commonly referred to by using capital letters.

If you mark two points on your paper and, by using a ruler, draw a straight line between them, you will get a figure. This figure is a line seg­ment. The line segment includes endpoints and all the points between them.

If we extend the segment indefinitely we will get a line. It is impossible to draw the complete picture of such an extension because a line has no endpoints.

The branch of geometry which studies shapes like lines or circles is called plane geometry. Plane geometry studies the objects that can be drawn on a flat surface called a plane.

Solid geometry is the geometry of three-dimensional space, the kind of space we live in. It studies three dimensional objects like cube or prisms.

Task 11

Read the text again and find the English equivalents for the following:

Стародавня наука, можливо, земля, практичні засоби, щоденні проблеми, знання, логічна послідовність, одна з найбільш відомих книжок, протягом останніх років, відношення між предметами, найбільш фундаментальне поняття, простір, вимір, бачити, відчу­вати, рухати, продовження, галузь геометрії, коло, площина, куб.

Task 12

Answer the questions on the text.

1. Is geometry an old subject?

2. Did geometry begin in England?

3. Were Egyptians mostly concerned with the practical use of geometry?

4. Did the knowledge of Egyptians spread to Greece?

5. Is Euclid’s book called Elements famous ?

6. Does geometry include only the study of the shape and size objects?

7. In the idea of a point fundamental in geometry?

8. Can one feel, see, move or hold a point?

9. Has a point any dimensions?

10. Are points represented by dots?

11. Does a line segment include its endpoints?

12. Can you draw a straight line by using a ruler?

13. What main branches of geometry do you know? What do they study?

Task 13

Inform your groupmates about the following:

1. Euclid and his Elements.

2. Geometry in ancient Egypt.

3. The use of geometry by ancient Greeks.

Task 14

Retell the text "Meaning of geometry". Make use of the questions to the text as a plan.

Task 15

Ask questions to which the following sentences could be the answers:

1. We consider your data very helpful. 2. All these combinations have been repeated over and over again. 3. There is a diagram below. 4. The change of the order may affect the result. 6. It has to be pointed out that the procedure developed is very complicated. 6. On the right and on the left of the comma you see three digits. 7. He ob­tained the difference after he had subtracted the numeral. 8. The identity property is being considered by the students. 9. The value of the digit is defined by its position. 10. Yes, the necessary procedure has always been followed. 11. The given definition corresponds to the idea of uniqueness. 12. You may change 3.29 to 3.290 if it helps you to obtain the correct answer. 13. When you deal with decimal numbers you are to align the decimal points. 14. In the operation of multiplication it is the product of the numerator and the denomina­tor that we actually find. 15. We can multiply these numbers as we have so far been doing with integers. 16. Students must study this illustration carefully. 17. In the given example we have been trying to show the validity of these principles. 18. This system of notation has to be observed. 19. These digits are separated from 6 by a point. 20. The scientists have been shown the pattern of the future system. 21. I have no idea of the situation. 22. All the points have been aligned on the vertical line.

Task 16

Read the text and render it in English