П'єр Ферма

(1601-1665)

П'єр Ферма − видатний французький математик, один із основоположників аналітичної геометрії і теорії чисел. Він є автором робіт в області теорії ймовірності, оптики, численних нескінченно-малих величин. У 1637 році П'єр Ферма сформулював так звану "Велику теорему Ферма", яка була доведена американським математиком Ендрю Уайлсом лише у 1995 році. Теорема стверджує, що для будь-якого натурального n>2 i xyz<>0 рівняння хⁿ+уⁿ=zⁿ  не можна розв’язати в цілих (і раціональних) числах.

SPEAKING

35. A Discuss the following questions in small groups.

1. What counting systems do you know?

2. Analyse the advantages of the 12 system (used in UK and US) over the decimal system and vice versa.

3. What problems must the Romans have had with their system?

4. What are the specialized uses of Roman numerals today?

5. Could we manage just cardinal numbers, rather than having both cardinal and ordinal?

B. Prepare a short talk for your classmates. Choose the topic from the given: "Maya numerals", "Babylonian numerals", "Quipus".

36. A. Look at the portraits of famous mathematicians, name them and tell about their contribution to science.

a)		b)		c)
d)		e)		f)

B. You want to create an Internet site about the greatest mathematicians of all times. First, you need to write a list of the greatest mathematicians (not less than 15). Continue the list: Isaac Newton, Archimedes, Carl Gauss, ........, ......., .........,

C. You are Pythagoras of Samos. Prove the Pythagorean theorem.

The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

D. In pairs ask and answer questions based on the text "Who Created the Quadratic Formula?" (Further Reading, UNIT 7).

37. You are a mathematician at Oxford University. It is your first lecture. The theme of your lecture is: "Introduction in Mathematics". Think about the points that you would like to cover at this lecture. You may also use the information from the text "Mathematics − the language of science".

LISTENING

38. You are going to listen to some information about mathematics. Decide whether the facts from the text are true or false.

1	2	3	4	5	6

1. The word “mathematics” comes from the Latin “math”.

2. The term “mathematics” meant “astrology” in English until 1700.

3. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs.

4. The research in Maths required to solve some problems.

5. The earliest uses of Maths where, besides the others, in painting, recording of time, medicine.

6. There is no such a notion as “ pure mathematics”.

39. Complete the sentences.

1. Mathematicians seek out…

2. Arguments sufficient to convince other mathematicians of their…

3. Maths is used all over the world as an essential…

4. Often Maths proves useful in many…

5. … in Maths are valued.

WRITING

40. Complete the phrases.

1. Mathematics is …

2. Arithmetic is …

3. A language is …

4. Geometry is …

5. A symbol is …

6. Geometric Algebra is ......

7. Number Theory is ....

41. Write 5 sentences using abbreviations or shortenings from exercise 6.

42. Write our equivalents to the numbers and measures in the suggested joke.

A Joke

A boy (enters a grocer’s shop) – A pound of sugar at 90 pence, a pound of butter at one pound and 80 pence, a pound of cheese at two pounds and 20 pence, two pounds of tea at five and six a pound. If I give you 20 and 6, how much would you give me a change?

Grocer (writing it all down) − 13 pounds. And why?

Boy – Please, give me that bill. It’s my home-work for tonight. Thank you.

43. Write an essay (150 words) that ends: "As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection." J.-L. Lagrange. Follow this structure:

• Introduction

Paragraph 1 (state the topic)

• Main Body

Paragraphs 2-3 (viewpoints, examples)

• Conclusions

Final paragraph (summarise).

PROBLEM-SOLVING

44. Try to solve curious problems and puzzles (see Problem-Solving, UNIT 7).