Find the words or phrases (1–5) in the text above which are explained / defined (a–e)? The first and the last letter are given to help you.

1 s---d(s) a hard of firm, with a fixed shape, and not a liquid or gas
2 d-------n(s) b measurement of any sort
3 s-----d c to do well in your job, especially because you have worked hard at it for a long time
4 m---------e d a work that is of very high quality or that is the best that particular person has produced
5 i-----------e e something that is essential, so important or useful that it is impossible to manage without them

Test yourself. Cover the dictionary meanings and look at the words. What are the meanings?

HELP box

Grammar focus: Some and Any.

Use in positive sentences in questions in negative sentences
some ● (in questions that are requests or offers)

I’d like to use some diagrams by Euclid in my report.

Are there any diagrams by Lobachevsky in your report?

There are no any diagrams by Lobachevsky in the report.

The rules are the same for the compounds someone, something, somewhere, anybody, anything, anywhere, etc.

some     + thing
+ one/body
any where

Do you know anything about geometry in Egypt?

Is there anybody who knows in your group?

I have read something about it in our book ‘English for Mathematics students’.

A Underline the correct item.

1. Olga can’t work abroad because she doesn’t speak some/any foreign languages.

2. Would you like some/any more space to draw simple closed figures here?

3. Do you have some/any questions you’d like to ask me about ‘non-Euclidean Geometry’?

4. In the 19-th century there were some/any mathematicians who developed non-Euclidean geometry.

5. We need some/any more information about the development of geometry in ancient time.

6. Can you ask someone/anyone in your family to help you with measuring your room?

7. Why didn’t you buy some/any works by Lobachevsky? 


B Complete the dialogues with a word from the box.

something anything somewhere anywhere somebody anybody

A: Do you know 1 _____ about the history of Geometry?

B: Oh, I see… I can tell 2 _____ about non-Euclidean geometry .


A: I’m hungry. I need 3 _____ to eat.

B: Well, there’s food in the fridge.


A: 4 _____ told me that their new album is very good.

B: Really? I don’t know 5 _____ who likes it.

A: Where did you go last night?

B: I didn’t go 6 _____ I was too tired. I stayed in.


A: I’m so bored. There isn’t 7 _____ to do in this town!

B: That’s not true. There are a lot of places to go and to see.



C A   O B                                    D

Read the text and do the tasks below it.

A circle is a plane figure bounded by the curved line all points of which are the same distance away from the fixed point called a center. OD is a radius. It is a line segment joining any point of the circle with the center. A line segment CD is a chord. It is a line segment whose endpoints are points on the circle. BD is a diameter. It is a chord which passes through the center of the circle. Any part of a curved line which makes the circle is an arc. No matter how short an arc is, it is curved at least slightly. The arc AC, for example, is symbolized as AC. The length of the curved line around the circle is its circumference. Fortunately mathematicians have discovered that the ratio of the circumference (C) to a diameter (d) is the same for all circles. This ratio is represented by the formulae    . Since the length of a diameter is equal to twice the length of a radius of the same circle, the following denote the same ratio:

 =  since d = 2r.

The number  =  which is the same for all circles, is designated by π. This allows us to state the following:

 =  = π.

By using the multiplication property of equation, we obtain the following:

C = πd or C = 2πr.

In pairs, look at the highlighted words and phrases. Try to guess what they mean from the context. Then check with your dictionary or teacher. Work out the list of the terms involved, make a kind of glossary.

2. In the text find the definition of:

a. a diameter

b. a chord

c. an arc

d. a circumference of a circle

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