1. In the fig.1 R is the center of the circle.

2. RM is called a radius of the circle.

3. RL has the same length as a radius.

4. ML is twice as long as a radius of the circle. It is a diameter of a circle.

5. ∆ MRN is an equilateral triangle.

6. Point R is called the center of the circle and the vertex MRN.

Unit 9

THE LANGUAGE OF MATHEMATICS

Reading and Vocabulary

1. Match the definitions/explanations in A (1–7) with the words in B (a–g):

Read the article below and complete it with a word from the task 1 (column B).

The language of mathematics may be called the language of science. It consists mostly of signs and symbols, and, in a sense, it is an unspokenlanguage. There can be no more 1_____ or simple language. It is the same throughout the civilized world, though the people of each country translate it into their own particular spoken language. For example, the symbol 5 means the same to a person in the UK, Germany, Ukraine or any other country, but in each country it is called by a different spoken word. Some of the best known symbols in maths are the numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 and the signs of addition (+), subtraction (-), multiplication (×), division (:), equality (=) and the letters of the Greek and Latin alphabets.

2_____ language is one of the basic characteristics of modern mathematics. With the help of symbolism mathematicians can make transition in reasoning almost mechanically by the eye and leave their mind free to grasp the fundamental ideas of the subject matter. Unlike the common language which is the product of custom, social and political movements, the language of maths is 3_____, 4_____ and often 5_____ designed.

Maths language is preciseand 6_____, so people unaccustomed to its forms find it confusing. The symbolism used in maths language is essential todistinguish meanings often confused in common speech. Maths style aims at brevityand formal perfection. Let us suppose we wish to express in general terms the Pythagorian theorem known to every pupil at school. We can say, ‘We have a right triangle. If we construct two squares each having a leg (cathetus) of the triangle as a side and if we construct a square having the hypotenuse of the triangle for its side, then the area of the third square is equal to the sum of the areas of the first two’. But no mathematician expresses himself that way. He prefers, ‘The sum of the squares on the legs (catheti) of a right triangle equals the square on the hypotenuse’. In symbols it can be stated as follows: c² = a² + b². This economy of words makes for conciseness of presentation, and maths writing is 7_____ because it encompasses much in a few words. So maths language expresses verbally stated facts in signs and symbols of maths. We use signs and symbols for convenience. In some cases symbols are abbreviations of words, but they often don’t have such relations to the things they stand for. We define their meaning by common agreement.

The student must always remember that understanding any subject in maths presupposes clear knowledge of the previous material. This is the reason why ‘there is no royal road to mathematics’ and why the study of maths is discouraging to weak minds.